text:
Electricity and magnetism/Magnetism

Magnets

Like electric forces, magnetic forces obey the principle of the attraction of opposites. Magnets always have two poles, a North Pole which is naturally attracted to the Earth's magnetic South Pole, and a South Pole, which is naturally attracted to the Earth's magnetic North Pole. In a compass, the North Pole of the magnetic needle indicates the geographic North Pole of the Earth. The geographic North and South are therefore reversed in relation to the magnetic North and South.

When magnets love each other, they do this in a somewhat special way. The North Pole of one sticks to the South Pole of the other, as if magnetism had chosen the eroticism of 69.

Unlike electric forces, isolated magnetic charges have never been found. Apparently Nature did not welcome magnetic monopoles. Magnets are always dipoles. If we cut a magnet in the middle between its two poles, we do not obtain two monopoles, but two new dipoles, two new magnets which each have two poles:

It is explained by assuming that a magnetic material is composed of microscopic magnets all aligned in the same direction:

Magnetostatics is the study of magnetic forces between stationary magnets. The calculation of magnetic forces is similar to that of electric forces, except that we reason on dipoles, and never on monopoles:

Like the electric field $$\mathbf{E}$$ for electric charges, the magnetic field $$\mathbf{B}$$ is like a mathematical intermediary that is used to calculate the forces between magnetized materials. It is also used to calculate the forces exerted by magnets on moving charges, the forces exerted by moving charges on magnets, and the forces exerted between moving charges. But it is also much more than a mathematical intermediary, because it has an autonomous existence.

Magnetic force is produced by electric currents
A magnet naturally orients itself perpendicular to an electric current. Its direction depends on the direction of the current. An electric current is therefore a source of magnetic force. This is a discovery made by Hans Christian Ørsted in 1820:

If we cut the current, this magnetic force disappears:

Ampère concluded that an electric current can behave like a magnet. This conclusion led him to the discovery of Ampère's law (1825):

Two parallel electrical wires carrying a current attract each other if the currents go in the same direction and repel each other if the currents go in the opposite direction.

The force between two electrical wires carrying a current is the magnetic force. It cannot be an electric force since the two wires are electrically neutral.

The unit of measurement of electric current, the ampere, was defined from the magnetic force between two wires carrying a current:

"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length." (International Bureau of Weights and Measures, 1948)

Since 1 A = 1 C/s, the definition of the ampere also defines the Coulomb.

When Ampère discovered his law, electrons were not known, so the ampere could not be defined as a current of electrons. Now that the electrons are known and their charge -q = -1.602 176 487 ×10−19 C has been precisely measured, we can define the ampere by the number of electrons it takes to make 1 C: 1 ampere = 6.241509074×1018 electrons per second, roughly six billion billion electrons every second.

Current loops behave like magnets. Two parallel loops attract each other if their currents go in the same direction and repel each other if they go in the opposite direction. A current loop is therefore a magnetic dipole:

The magnetic field produced by a current loop is similar to the electric field produced by an electric dipole:

Ampère assumed that the magnetic force of magnets is produced by microscopic current loops. We now know that it comes mainly from the spin of electrons. Electrons are magnetic dipoles because they behave like spinning tops. The rotation of electrons is not an electric current, but the effect is similar to that of a microscopic current loop.

As with the electric field, the magnetic field produced by several sources is the sum of the fields produced by each of them separately. For two parallel wires carrying currents in opposite directions, we obtain the total field by making a vector sum:

The Earth's magnetic field is produced at the center of the Earth by its constantly moving liquid iron core:

Coulomb's law in electrodynamics
To calculate the forces between moving charges we need generalized Coulomb's law:

If a charge is eternally stationary in an inertial frame of reference, then the force it exerts on a moving charge is the same as the electrostatic force it would exert on that charge if it were stationary at the same position.

If a charge is eternally immobile in an inertial frame of reference, the electric field of which it is the source has had time to propagate throughout space and establish itself there.

If a charge is accelerated, there is no inertial frame of reference in which it is eternally stationary. The Coulomb field of which it is the source in its rest frame at a given moment takes time to propagate. At a later time, it is the source of another Coulomb field, in another rest frame. This is why accelerated charges are the source of electromagnetic waves that propagate throughout space. Light is produced by accelerated electrical charges:

An immobile electric charge is not a source of light because no waves propagate in the electric field it establishes around it.

Generalized Coulomb's law makes it possible to calculate the electric force field of any system of charges in uniform rectilinear motion relative to each other. To calculate the force exerted by all the charges, we calculate the sum of the forces exerted separately by each charge. To calculate the force exerted by a charge, we consider the frame of reference where it is at rest and calculate the Coulomb force. The Lorentz transformation then makes it possible to calculate this force in any frame of reference.

(Animation: Coulomb field produced by a charge in uniform rectilinear motion)

The magnetic force of the electric current is a consequence of the Fitzgerald contraction and the Coulomb force
Fitzgerald contraction is the contraction of all solid bodies in the direction of their motion. It is appreciable only for bodies whose speed $$v$$ approaches the speed $$c$$ of light. The contraction factor is $$\sqrt{1 - v^2/c^2}$$.

When an electrically charged body is contracted, its charge density increases. This effect is at the origin of the magnetic force of the electric current. The relative movement of positive and negative charges can give rise to differences in charge density and therefore electrostatic forces. These electrostatic forces in one frame of reference are magnetic forces in another frame of reference.

We can make a model of a conducting wire carrying an electric current with two insulating wires which carry opposite charges and which slide over each other. Let $$\lambda$$ be the charge density on the positive wire assumed to be stationary and $$\lambda_-$$ the charge density on the negative wire which goes at speed $$v$$. The current $$I = \lambda_- v$$.

The negative wire represents the conduction electrons, the positive wire represents the rest of the metal wire. In the frame of reference R where the metal wire is at rest, it is electrically neutral. So in this frame $$\lambda_- = -\lambda$$.

Let R' be a frame of reference which goes at speed $$v$$ with respect to R, $$\lambda'_-$$ and $$\lambda'_+$$ the densities of negative and positive charge, measured in R'. The negative wire is therefore at rest in R'.

$$\lambda'_+ = \gamma \lambda_+$$, because from the point of view of R', the positive wire is contracted in the direction of its movement. $$\gamma= 1/\sqrt{1 - v^2/c^2}$$ is the inverse of the length contraction coefficient.

$$\lambda_- = \gamma \lambda'_- $$, because from the point of view of R, the negative wire is contracted in the direction of its movement.

So $$\lambda'_- \neq -\lambda'_+$$.

From the point of view of R', the superposition of the two wires, positive and negative, is not electrically neutral, it is therefore the source of an electrostatic field.

Consider a charge $$q$$ of speed $$v$$ in R at distance $$a$$ from the wire. The force F+ exerted by the positive wire on the charge $$q$$ is perpendicular to the wire:

Measured in R,

$$F_+ =\frac{\lambda_+ q}{2\pi a\epsilon_0}$$

This result is proven from Gauss' theorem in the chapter on Maxwell's equations.

The charge $$q$$ is at rest in R'. The electrostatic force $$F'_-$$ exerted by the negative wire on the charge $$q$$ is perpendicular to the wire.

$$F'_- = \frac{\lambda'_- q}{2\pi a\epsilon_0} = -\frac{\lambda_- q}{2 \pi a\epsilon_0 \gamma}$$

Measured in R the force $$F_-$$ of the negative wire on the charge $$q$$ is equal to $$F'_-/\gamma$$. The charge $$q$$ therefore experiences a force

$$F_+ + F_- = \frac{\lambda_+ q (1 - 1/\gamma^2)}{2 \pi a\epsilon_0} = \frac{\lambda_+ q v^2}{2 \pi a \epsilon_0 c^2 } = - \frac{I q v}{2 \pi a \epsilon_0 c^2}$$

If we set $$B = - \frac{I}{2 \pi a \epsilon_0 c^2}$$ we obtain

$$F_L = F_+ + F_- = qvB$$

$$B$$ is the magnitude of the magnetic field $$\mathbf{B}$$ created by the current $$I$$ in a wire of infinite length. The Lorentz force $$F_L = qvB$$ is the magnetic force exerted on a charge $$q$$ which moves at speed $$v$$ in a magnetic field $$\mathbf{B }$$ if its speed is perpendicular to the field.

We thus find that the magnetic field only acts on moving electric charges.

In the frame of reference R there is no electrostatic force, because the wire carrying a current is electrically neutral. But in the frame of reference R' the negative charge density is lower than the positive charge density, because of the Fitzgerald contraction. The charge density is not zero and is the source of an electrostatic force field. This electrostatic force in R' is the magnetic force in R.

The Fitzgerald contraction and the Coulomb force are therefore sufficient to explain the existence of the magnetic force produced by an electric current.

A wire carrying a current repels negative charges that go in the conventional direction of the current (a current of positive charges) and attracts negative charges that go in the opposite direction. We thus find Ampère's law: two parallel wires carrying a current attract each other if the currents go in the same direction and repel each other if the currents go in the opposite direction.

Reference: Feynman's physics course, Electromagnetism, chapter 13-6.

The vector product
To calculate the magnetic forces produced by moving charges and the magnetic forces exerted on moving charges, one must know the cross product of two vectors in three-dimensional space:

The vector product w = u×v of two vectors u and v is the vector

 * whose length is uv sin$$\theta$$ where $$\theta$$ is the angle between u and v, u and v are the lengths of u and v,

 * whose direction is perpendicular to u and v

 * such that the triplet u, v, w is positively oriented.

The triplet (thumb, index, middle finger) of the right hand is positively oriented. The one of the left hand is negatively oriented. (right, front, above) is positively oriented. In general, the x, y and z axes of a coordinate system are chosen positively oriented.

The cross product of two vectors with the same direction is the zero vector. The length of the cross product of two perpendicular vectors is the product of their lengths.

The Biot-Savart law
If the regime is stationary (the electric currents do not change) the magnetic field $$\mathbf{B}$$ produced at the point $$\mathbf{r}$$ by a current $$I $$ in a segment $$\mathbf{d\ell}$$ of an electric wire is

$$\mathbf{B} (\mathbf{r}) = \frac{\mu_0}{4\pi} \frac{I \mathbf{d\ell} \times \mathbf{\hat r}}{r ^2}$$

where $$\mathbf{r}$$ is the vector which goes from the segment $$\mathbf{d\ell}$$ to the point considered, $$r$$ is its length, $$\mathbf{\hat r} = \mathbf{r}/r$$ is the unit length vector in the direction of $$\mathbf{r}$$ and $$\mu_0 $$ is a constant which depends on the choice of units of measurement.

With the Biot-Savart law, we can calculate the magnetic field produced by an electric current. If the wire is straight and of infinite length, the lines of the magnetic field are circles centered on the wire:

The Biot-Savart law has a mathematical form similar to that of Coulomb's law. Force is inversely proportional to the square of the distance. It is not a coincidence. We can deduce the Biot-Savart law from Coulomb's law, because the magnetic force of electric current has an electrostatic origin.

The Lorentz force
An electric field $$\mathbf{E}$$ and a magnetic field $$\mathbf{B}$$ exert on a particle of charge $$q$$ a force $$\mathbf{F}_L = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}$$).

$$\mathbf{F}_L$$ is the Lorentz force:

With the Lorentz force, we explain the magnetic force on an electric current:

The principle of an electric motor:

If a current loop is parallel to a uniform magnetic field, the Lorentz force on the moving charges produces a torque that turns the loop.

The Lorentz force equation and Maxwell's equations are the fundamental laws of electromagnetism. Maxwell's equations tell how charges produce electric and magnetic fields throughout space and how these fields change over time. The Lorentz equation then tells how these fields act on charges.

The Biot-Savart law allows us to calculate the magnetic field produced by an electric current. The Lorentz force then makes it possible to calculate the force between two wires carrying a current. The magnetic field is like a mathematical intermediary for calculating the forces between moving electric charges. But it is more than a simple mathematical intermediary, because it has an autonomous existence.

We can calculate the magnetic force produced by a current from the Biot-Savart law and from Coulomb's law. The equality of the two results shows that

$$\epsilon_0 \mu_0 = 1/c^2$$

$$\epsilon_0$$ and $$\mu_0$$ are physical constants that have been measured independently of the speed $$c$$ of light. When Maxwell discovered the fundamental laws of the electromagnetic field, he discovered that $$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$$ is the speed of electromagnetic waves. Since $$c$$ is also the speed of light, he concluded that light is an electromagnetic wave.

The electromotive force of magnetism
The magnetic force on a charged particle is always perpendicular to its velocity. The work of force is therefore always zero. The kinetic energy of the particle is not changed, only its direction. So how can magnetic forces produce an electric current? How can they set in motion charges initially at rest?

If a particle moves in the field created by a stationary magnet, it experiences a magnetic force. But in a frame of reference where the particle is at rest, it does not experience any magnetic force, since its speed is zero. It can only be subjected to an electrical force. So a moving magnet is the source of electrical forces and can thus produce an electric current.

If we place a conducting loop in a constant magnetic field and rotate it around a diameter perpendicular to the magnetic field, the Lorentz force sets the electrons in motion in the direction of the conducting wire, as soon as the rotation of the loop imposes on them a movement which is not parallel to the magnetic field. This movement of electrons in the direction of the wire manifests the presence of an electrical voltage. We can therefore make an electric generator by rotating a conductive loop in a constant magnetic field:

The blue area is proportional to the flux of the magnetic field through the loop. Faraday's law, presented in the chapter on Maxwell's equations, says that the voltage across the two terminals of the loop is the opposite of the rate of change of the flux of the magnetic field through the loop.

Like the magnetic force of electric current, the electromotive force of magnetism has an electrostatic origin.

To understand it, we just need to think about a square circuit traversed by a current. Let $$\lambda$$ be the linear density of the conduction electrons. The intensity of the current is $$\lambda v$$ where $$v$$ is the average speed of the electrons in the frame R where the circuit is at rest. Let $$q$$ be an electric charge placed in the center of the circuit with speed $$v$$ relative to R, in the direction of one of the sides of the square traveled by a current. Let R' be a frame of reference such that the charge $$q$$ y at rest. From the point of view of R', the charge $$q$$ cannot experience a magnetic force, because its speed is zero, but it experiences an electrostatic force.

From the point of view of R', the two sides of the square parallel to its movement are contracted in the direction of the movement, but not the two sides perpendicular to the movement. The linear density of the conduction electrons, on the side where their average speed is zero, is equal to $$\lambda / \gamma$$ where $$\gamma= 1/\sqrt{1 - v^2/c ^2}$$ is the inverse of the length contraction coefficient. The linear density of conduction electrons on the other side is $$\lambda \gamma$$. It is different, because the conduction electrons have a non-zero average speed compared to R'.

From the point of view of R', the charge $$q$$ experiences an electrostatic force, perpendicular to the movement of the circuit and proportional to $$\lambda(\gamma - 1/\gamma)$$. From the point of view of R, this force is $$\gamma$$ times smaller, therefore proportional to $$\lambda (1-1/\gamma^2) = \lambda v^2/c^ 2$$. It is the magnetic force experienced by the moving charge in R.

In R', the electric circuit is a variable magnetic field source that exerts an electric force on the charge $$q$$. The variation of the magnetic field therefore has an electromotive force.

title: Electricity and magnetism/Magnetism


text:
User:Edwina24wang/sandbox

Technology
Australia Post is a corporation that offers postal delivery service to Australia operating for over 200 years. It works to deliver goods including letters and parcels across people, businesses and communities in Australia.

The technological characteristics of Australia Post have evolved overtime as Australia Post shifts its strategies and service focuses to match with its loyal clients - Australia. In the modern age with increasing digitisation of information and communication, the key technological characteristic of Australia Post is its physicality - the mail and packages delivered are physical objects to be held and kept. The main advantage and market of this would lie in parcels - physical object deliveries which cannot be made through an email.

During the initialisation of Australian Post however, the essential technological characteristic had been the efficient transmission of information as a means of communication. At its creation the main advantage of Australian Post was through delivery of letters and communications across Australia - in particular between the early settlers, officials and convicts and their hometowns in Britain. Naturally the main market of the postal service was hence the people in Australia wishing to deliver letters across space and oceans. The Australian Post was created as a means of organising the masses of letters being delivered to allow the correct recipient to receive or collect their mail. It has since grown into a network of delivery across modes of pack-horse, carriage, trains, motor vehicles and planes.

Early 1800s Context
Prior to the establishment of the first Australian post office in 1809, connection between Australia and Britain could only be made through letters on ships arriving in Sydney. This system was limited as it meant ships could be mobbed and crimes of fraud and theft ran rampant. Centralised postal service had already been organised in Britain in 1516 but early settlers needed time to organise this system around the development of the Australian colony. Progression was made from mobbed ships with letters into a mail delivery service in 1803 with boatmen delivering letters across Sydney and Parramatta. This is described in the "Sydney Gazette” (first newspaper printed in Australia ) issue of the 10th July 1803 . This system was still to evolve further as this delivery system involved no prepayment. Recipients of letters would be expected to pay which led to an unreliable delivery system . The chaos of these earlier years created a need for a system of organisation for mail among early settlers in Australia. This was reflected in growing complaints to the Lieutenant-Governor until change was made.

1809: First Australian Post Office established
The beginning of the Australian Post office is often attributed to the opening of the first Australian Post office with Post Master Isaac Nichols appointed on 25th April 1809 in Sydney. This appointment was notified through the "Sydney Gazette" by the Lieutenant-Governor to address the concerns of stolen mail enabling fraudulent crimes. The purpose of this post office was for all parcels and letters coming from ships to be deposited and then organised to be distributed to correct recipients. The establishment of the post office in Australia did not implement much technological innovation other than incorporating the early British centralised postal service into Australia as the settler population grew. Isaac Nichols would use his home – which served as the post office – to sort mail. Rules for the method of handling mail and costs for the service were all outlined in this order forming the initial policy to shape the Australian Post in its birthing phase. The role of Postmaster gave Nichols the right to board ships and obtain mail addressed to Australians on their behalf - a list of names of people with mail to be collected would then be printed in the "Sydney Gazette". A fixed collection fee was charged and this business remained private until 1825. At its birth, the post office served the market of early Australians who were struggling to correctly receive their mail. The system required the recipient to travel to the post office and receive their mail as at this stage and the number of letters were still limited enough for this system to be manageable. With the growing population and land occupied by the settler population in Australia however, the natural progression of the technology and system would be for a delivery system to be established to allow service to those who lived further away.

1825-1828: Growth - First Postal Act and Delivery services
In 1825 "An Act to Regulate the Postage of Letters in New South Wales" was passed by the New South Wales Legislative Council. This transferred the Post office from a private business to the public sector. The Governor was authorised to establish more post offices in Sydney and the New South Wales Colony. This allowed the postal office system to grow with the population of settlers across New South Wales. The Governor was also given the authority to fix the postmaster's wage and mail collection fees. As with the establishment of the first post office, this legislation seemed to lag behind the growing population of New South Wales that already passed 30,000 by 1821 - it was put in place after growing market demand.

In 1828, postal delivery services were established in Sydney. A postman would be responsible for delivering and collecting letters using a pack-horse. This technological development allowed postal offices to better organise mail so as to not be over-flooded by those who were collecting mail. Mail routes were established and Postmasters were appointed in other parts of Australia. Coach services were established between Melbourne and Sydney in 1838 to allow overland delivery. During this period roads and horses were the primary technological characteristic of postal delivery. It was the more efficient alternative to walking - delivering 50,000 letters and newspapers with a staff of three people: Postmaster, clerk and postman, but would lack the later reliability of steam trains.

1828-1901: Emerging technologies
Emerging technologies appeared for delivering mail in the 1800s including the Cobb and Co. Coaches that were brought to Australia with the gold rush. These coaches replaced the pack-horse as the official transport mode of mail from 1862. This was an upgrade from the pack-horse to allow larger volumes of mail to be held during a delivery run. As railways developed throughout New South Wales they were also increasingly adopted for larger distance mail delivery - particularly between Sydney and Parramatta from 1855 onwards.

During the 1800s other technologies also developed that challenged the function of letters in communication across distances. Telegraph services were opened in Australia in 1854 and allowed communication across distances that was far more rapid than mail delivery. This new technology, initially private, was incorporated by the government into the postal office however and spread with the postal offices across the nation. Likewise in 1878, the first telephone call was made in Australia. These technologies allowed for rapid communication across distances greatly lowering the market need for letters and mail. The adoption of telegraph systems within post offices however kept post offices serving the existing market of those looking to communicate across time and space.

Timelines of key developments and growth
Key technological developments and their effects within the post office are listed in the table below:

Maturity and decline
With peak Australian letter volumes being achieved in 2008, this has been prescribed as the mature phase of the mode. From the rise of technological advancements such as the e-mail and internet replacing postal letters the mode has become less economic and rapidly declined. Australian Post has attempted to shift focus towards parcels but faces competition with other delivery services that have risen with the rise of online shopping. This attempt to shift is reflected in the 2021 opening of a new $33 million processing station in Adelaide - capable of processing 130,000 parcels in a day. The future prospects of Australian Post after consultation with the Australian Public is a business model which aims to decrease normal delivery speed in an attempt to minimise expenses while maintaining revenue through express delivery.

Model
The life cycle of Australian Post has be modelled using the S-curve with periods of birthing, growth and maturity. Data analysing the productive output of Australian Post was fitted to the logistic function $$S(t) = \frac{S_{max}}{[1+e^{(-b(t-t_0)}]}$$.

where: The observed data used was of Australia Post's Total Output Value which aggregates revenue from reserved letters, other addressed and unaddressed mail and money orders. This data was approximated using the above logistic function and modelled by the following equation:

$$S(t) = \frac{5400}{[1+e^{(-0.127(t-1994)}]}$$

The method of calculating this model was found using Ordinary Least Squares Regression. The Logistic equation was rearranged to obtain a linear equation of the form $$Y = bX + c$$ where the following values were taken.

$$Y = \ln\left(\cfrac{S(t)}{(S_{max}-S(t))}\right)= bt-bt_0$$

Method and Evaluation
Although there is a slight decline in Value output for 2001-2002, with hindsight knowledge that peak achieved in 2008 it is assumed that these were years of fluctuation and $$S_{max}$$ had not yet been fully achieved, hence they were also included in the S-curve approximation. The unknown in this case was $$S_{max}$$, hence different regressions were found for variable values of $$S_{max}$$. The R-squared value was used to evaluate which regression was the best fit for the data. The R-squared value for the final regression chosen was $$0.9829$$.

Given the R-squared value being very close to 1, it is presumed that the model is a good fit. Issues with the model are the larger variations occurring during the earlier and later years. It may be possible that given more data from earlier and later years, a better fitting equation for modelling the life-cycle of the Australian Post office would have greater growth during the 2000s and a later earlier inflection point.

Life-cycle years
From the observed data the periods of birthing, growth and maturity are identified as the following:

Birthing: Pre 1976-1980

Growth: 1980-1999

Maturity: 1999-2002

Narratives
Throughout the life-time of the project different proposals and methods of completing the objective of increasing rail access across the Brisbane River were made. Each proposal promised varying benefits and costs that were balanced in decisions to proceed or abandon projects. Politics particularly had a significant impact on the decision with the BaT project being introduced when the LNP was voted into office and then abandoned by the Labor party when the LNP party was voted out.

2010 Cross River Rail
At this stage the proposed project included:
 * an 18km rail line including 9.8km tunnelled under Brisbane's CBD and river.
 * proposed underground system of two single-track tunnels.
 * 3 new underground inner-city train stations
 * major and minor upgrades to 4 existing stations.
 * Cost estimated at $7 Billion

BaT Project
The proposal included: The incorporation of buses into the project was in attempt to address bus crowing problem on Victoria Bridge.
 * 5.7km bus and train tunnel connecting under the Brisbane CBD.
 * The two tunnels were replaced by plans for a single tunnel which accommodated 2 rail tracks and 2 bus lanes (see adjacent figure).
 * 2 new underground stations
 * The project was estimated to cost less at $5 billion

2017 Business Case
At this stage the proposal included :
 * 10.2 km rail line including 5.9km tunnelled under Brisbane's CBD and river.
 * proposed underground system of two single-track tunnels.
 * 4 new underground inner-city train stations
 * Cost estimated at $5.4 Billion This built upon the 2016 detailed Business case to address policy changes that occurred since 2016. Main differences were the incorporation of the European Train Control System (ETCS) and concerns of the Department of Transport and Main Roads (TMR). Benefits were also recalculated to consider the Fairer Fares Package

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Edwina24wang/sandbox


text:
Transportation Deployment Casebook/2024/Australian Post

Technology
Australia Post is a corporation that offers postal delivery service to Australia operating for over 200 years. It works to deliver goods including letters and parcels across people, businesses and communities in Australia.

The technological characteristics of Australia Post have evolved overtime as Australia Post shifts its strategies and service focuses to match with its loyal clients - Australia. In the modern age with increasing digitisation of information and communication, the key technological characteristic of Australia Post is its physicality - the mail and packages delivered are physical objects to be held and kept. The main advantage and market of this would lie in parcels - physical object deliveries which cannot be made through an email.

During the initialisation of Australian Post however, the essential technological characteristic had been the efficient transmission of information as a means of communication. At its creation the main advantage of Australian Post was through delivery of letters and communications across Australia - in particular between the early settlers, officials and convicts and their hometowns in Britain. Naturally the main market of the postal service was hence the people in Australia wishing to deliver letters across space and oceans. The Australian Post was created as a means of organising the masses of letters being delivered to allow the correct recipient to receive or collect their mail. It has since grown into a network of delivery across modes of pack-horse, carriage, trains, motor vehicles and planes.

Early 1800s Context
Prior to the establishment of the first Australian post office in 1809, connection between Australia and Britain could only be made through letters on ships arriving in Sydney. This system was limited as it meant ships could be mobbed and crimes of fraud and theft ran rampant. Centralised postal service had already been organised in Britain in 1516 but early settlers needed time to organise this system around the development of the Australian colony. Progression was made from mobbed ships with letters into a mail delivery service in 1803 with boatmen delivering letters across Sydney and Parramatta. This is described in the "Sydney Gazette” (first newspaper printed in Australia ) issue of the 10th July 1803 . This system was still to evolve further as this delivery system involved no prepayment. Recipients of letters would be expected to pay which led to an unreliable delivery system . The chaos of these earlier years created a need for a system of organisation for mail among early settlers in Australia. This was reflected in growing complaints to the Lieutenant-Governor until change was made.

1809: First Australian Post Office established
The beginning of the Australian Post office is often attributed to the opening of the first Australian Post office with Post Master Isaac Nichols appointed on 25th April 1809 in Sydney. This appointment was notified through the "Sydney Gazette" by the Lieutenant-Governor to address the concerns of stolen mail enabling fraudulent crimes. The purpose of this post office was for all parcels and letters coming from ships to be deposited and then organised to be distributed to correct recipients. The establishment of the post office in Australia did not implement much technological innovation other than incorporating the early British centralised postal service into Australia as the settler population grew. Isaac Nichols would use his home – which served as the post office – to sort mail. Rules for the method of handling mail and costs for the service were all outlined in this order forming the initial policy to shape the Australian Post in its birthing phase. The role of Postmaster gave Nichols the right to board ships and obtain mail addressed to Australians on their behalf - a list of names of people with mail to be collected would then be printed in the "Sydney Gazette". A fixed collection fee was charged and this business remained private until 1825. At its birth, the post office served the market of early Australians who were struggling to correctly receive their mail. The system required the recipient to travel to the post office and receive their mail as at this stage and the number of letters were still limited enough for this system to be manageable. With the growing population and land occupied by the settler population in Australia however, the natural progression of the technology and system would be for a delivery system to be established to allow service to those who lived further away.

1825-1828: Growth - First Postal Act and Delivery services
In 1825 "An Act to Regulate the Postage of Letters in New South Wales" was passed by the New South Wales Legislative Council. This transferred the Post office from a private business to the public sector. The Governor was authorised to establish more post offices in Sydney and the New South Wales Colony. This allowed the postal office system to grow with the population of settlers across New South Wales. The Governor was also given the authority to fix the postmaster's wage and mail collection fees. As with the establishment of the first post office, this legislation seemed to lag behind the growing population of New South Wales that already passed 30,000 by 1821 - it was put in place after growing market demand.

In 1828, postal delivery services were established in Sydney. A postman would be responsible for delivering and collecting letters using a pack-horse. This technological development allowed postal offices to better organise mail so as to not be over-flooded by those who were collecting mail. Mail routes were established and Postmasters were appointed in other parts of Australia. Coach services were established between Melbourne and Sydney in 1838 to allow overland delivery. During this period roads and horses were the primary technological characteristic of postal delivery. It was the more efficient alternative to walking - delivering 50,000 letters and newspapers with a staff of three people: Postmaster, clerk and postman, but would lack the later reliability of steam trains.

1828-1901: Emerging technologies
Emerging technologies appeared for delivering mail in the 1800s including the Cobb and Co. Coaches that were brought to Australia with the gold rush. These coaches replaced the pack-horse as the official transport mode of mail from 1862. This was an upgrade from the pack-horse to allow larger volumes of mail to be held during a delivery run. As railways developed throughout New South Wales they were also increasingly adopted for larger distance mail delivery - particularly between Sydney and Parramatta from 1855 onwards.

During the 1800s other technologies also developed that challenged the function of letters in communication across distances. Telegraph services were opened in Australia in 1854 and allowed communication across distances that was far more rapid than mail delivery. This new technology, initially private, was incorporated by the government into the postal office however and spread with the postal offices across the nation. Likewise in 1878, the first telephone call was made in Australia. These technologies allowed for rapid communication across distances greatly lowering the market need for letters and mail. The adoption of telegraph systems within post offices however kept post offices serving the existing market of those looking to communicate across time and space.

Timelines of key developments and growth
Key technological developments and their effects within the post office are listed in the table below:

Maturity and decline
With peak Australian letter volumes being achieved in 2008, this has been prescribed as the mature phase of the mode. From the rise of technological advancements such as the e-mail and internet replacing postal letters the mode has become less economic and rapidly declined. Australian Post has attempted to shift focus towards parcels but faces competition with other delivery services that have risen with the rise of online shopping. This attempt to shift is reflected in the 2021 opening of a new $33 million processing station in Adelaide - capable of processing 130,000 parcels in a day. The future prospects of Australian Post after consultation with the Australian Public is a business model which aims to decrease normal delivery speed in an attempt to minimise expenses while maintaining revenue through express delivery.

Model
The life cycle of Australian Post has be modelled using the S-curve with periods of birthing, growth and maturity. Data analysing the productive output of Australian Post was fitted to the logistic function $$S(t) = \frac{S_{max}}{[1+e^{(-b(t-t_0)}]}$$.

where: The observed data used was of Australia Post's Total Output Value which aggregates revenue from reserved letters, other addressed and unaddressed mail and money orders. This data was approximated using the above logistic function and modelled by the following equation:

$$S(t) = \frac{5400}{[1+e^{(-0.127(t-1994)}]}$$

The method of calculating this model was found using Ordinary Least Squares Regression. The Logistic equation was rearranged to obtain a linear equation of the form $$Y = bX + c$$ where the following values were taken.

$$Y = \ln\left(\cfrac{S(t)}{(S_{max}-S(t))}\right)= bt-bt_0$$

Method and Evaluation
Although there is a slight decline in Value output for 2001-2002, with hindsight knowledge that peak achieved in 2008 it is assumed that these were years of fluctuation and $$S_{max}$$ had not yet been fully achieved, hence they were also included in the S-curve approximation. The unknown in this case was $$S_{max}$$, hence different regressions were found for variable values of $$S_{max}$$. The R-squared value was used to evaluate which regression was the best fit for the data. The R-squared value for the final regression chosen was $$0.9829$$.

Given the R-squared value being very close to 1, it is presumed that the model is a good fit. Issues with the model are the larger variations occurring during the earlier and later years. It may be possible that given more data from earlier and later years, a better fitting equation for modelling the life-cycle of the Australian Post office would have greater growth during the 2000s and a later earlier inflection point.

Life-cycle years
From the observed data the periods of birthing, growth and maturity are identified as the following:

Birthing: Pre 1976-1980

Growth: 1980-1999

Maturity: 1999-2002


text:
User talk:Edwina24wang

Welcome!
Welcome, Edwina24wang!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. MathXplore (discuss • contribs) 06:02, 4 March 2024 (UTC)

title: User talk:Edwina24wang


text:
Electricity and magnetism/Maxwell's equations

The divergence of a vector field
To understand the fundamental equations of electromagnetism given by Maxwell, we must understand the divergence and curl of a vector field.

To understand its divergence, one must understand the flux of a vector field across a surface.

If we think of a vector field as the velocity field of a fluid, its flux through a surface is the flow rate of the fluid through that surface. The flux obviously depends on the orientation of the surface:

Let $$dS$$ be a sufficiently small surface element so that we can assume that the vector field $$\mathbf{v}$$ is almost constant. Let $$\mathbf{\hat n}$$ be a vector of unit length perpendicular to $$dS$$. The flux $$d\phi$$ from $$\mathbf{v}$$ through $$dS$$ in the direction of $$\mathbf{\hat n}$$ is then $$d\phi = \mathbf{\hat n}.\mathbf{v}$$ $$dS$$

To find the flux through a surface, we divide the surface into small surface elements and sum all the fluxes. When the magnitude of the surface elements tends to zero, the limit of this sum is an integral. It is the flux $$\phi$$ through the surface.

$$\phi = \int_S d\phi = \int_S \mathbf{\hat n} \cdot \mathbf{v}$$ $$dS$$

To calculate the flux $$\phi$$ we must have chosen a direction of crossing the surface. The flux is positive if the vector field goes in the same direction, negative otherwise.

The divergence $$\operatorname{div} \mathbf{v}$$ of a vector field $$\mathbf{v}$$ is obtained at each point by considering closed surfaces smaller and smaller that surround this point, small spheres centered on the point for example, or small cubes. It is the limit of the flux of the vector field through these small closed surfaces, divided by the volume which they delimit, when this volume tends towards zero. The crossing direction is always chosen from the inside to the outside.

If its divergence at a point is positive, the vector field is divergent at this point, it is like a source of fluid. If its divergence is negative, it is convergent at this point, it is like a sink for a fluid.

As the volume of an incompressible fluid is constant, the divergence of its velocity field is always zero, because there is neither source nor sink.

To calculate the divergence, we use the following formula:

$$\operatorname{div} \mathbf{v} = \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z}$$

for a field $$\mathbf{v}$$ whose three components are $$v_x$$, $$v_y$$ and $$v_z$$.

Proof: we reason about a small cube of side $$a$$ and whose faces are parallel to the xy, xz and yz planes. On faces parallel to yz, therefore perpendicular to the x axis, the flux is $$a^2 v_x$$ and $$a^2 (v_x + a \frac{\partial v_x}{\partial x})$$. The difference of the two is $$a^3 \frac{\partial v_x}{\partial x}$$. The same goes for faces parallel to xz and xy. So the total flux leaving the cube is $$a^3(\frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{ \partial z})$$. This flux is also equal to $$a^3 \operatorname{div} \mathbf{v}$$.

The divergence of a vector field is a real number, positive or negative, defined at each point in space. It is therefore a scalar field derived from a vector field.

Gauss's theorem
The flux of a vector field through a closed surface, from the inside to the outside, is always the integral of its divergence over the entire volume inside the surface.

Proof: if two cubes have a face in common, the flow through the rectangular tile they form together is the sum of the two fluxes through the two cubes, because the two fluxes through the interior face of the tile exactly compensate each other. Everything that comes out of a cube through this face goes into the other.

A volume delimited by a closed surface can always be divided into small adjacent volumes, so

$$\phi = \int_V \operatorname{div} \mathbf{v}$$ $$dV$$

where $$V$$ is the volume delimited by $$S$$.

With Gauss' theorem and Coulomb's law, we find the first of Maxwell's equations:

$$\operatorname{div} \mathbf{E} = \rho/\epsilon_0$$

where $$\rho$$ is the electric charge density. For a uniformly charged volume $$V$$ of charge $$q$$, $$\rho = q/V$$ is the charge density inside $$V$$.

Proof of Maxwell's first equation: we reason about the flux of the electric field produced by a spherical charge through a sphere centered on this charge:

The flux of the electric field created by a charge $$q$$ which passes through a sphere of radius $$r$$ centered on this charge, is $$\phi = 4 \pi r^ 2 E$$ where $$E = \frac{q}{4 \pi \epsilon_0 r^2}$$. So $$\phi = q/\epsilon_0$$. Or $$q = \int_V \rho $$ $$dV$$ where $$\rho$$ is the charge density and $$V$$ is the volume of the sphere centered on $$q$$. So $$\phi = \int_V \operatorname{div} \mathbf{E} $$ $$dV = \int_V \frac{\rho}{\epsilon_0} dV$$. Since this equation is true for any volume that surrounds a charge density $$\rho$$: $$\operatorname{div}\mathbf{E} = \rho/\epsilon_0$$

Maxwell's second equation is:

$$\operatorname{div} \mathbf{B} = 0$$

It says that the magnetic charge density is always zero, so magnetic monopoles do not exist.

The flux of the magnetic field through a surface bounded by a loop depends only on the loop.

Proof: let $$S_1$$ and $$S_2$$ be two surfaces delimited by the same loop. These two surfaces delimit a volume. The flux of the magnetic field leaving this volume is the difference of the fluxes through $$S_1$$ and $$S_2$$. But since the divergence of the magnetic field is always zero, this difference is zero, according to Gauss's theorem. So the two fluxes are equal.

The magnetic field can always be identified with the velocity field of an incompressible fluid. The flux entering a volume is always equal to the flux leaving it. The same is true for the flux of an electric field in a volume that contains no charges.

Gauss' theorem allows us to calculate the electric field created by an infinite electrically charged plane or by an infinite electrically charged line.

The infinite charged plane

Let $$\sigma$$ be the surface charge density of a plane. If the plane has a finite surface, the electric field of which it is the source depends on the distance from its edges. But for a very large surface, this edge effect is negligible, provided that we are far from the edges. The electric field created on an axis perpendicular to the middle of a large electrically charged disk is therefore equal to the field created by an infinite plane which has the same charge per unit area. The charged disk is rotationally symmetrical. Curie's law, which says that effects have the same symmetry as their causes, therefore requires that the electric field it produces is also symmetrical by rotation. On the axis of the disk, it is therefore necessarily in the direction of this axis. The electric field produced by an infinite charged plane is therefore everywhere perpendicular to this plane.

Consider a cylinder whose surface faces $$S$$ are parallel to the charged plane, such that this plane passes through the midpoint between the two faces. The flux of the electric field through the side wall of the cylinder is zero, since it is always parallel to the wall. The flux is therefore the sum of the fluxes on the two sides:

$$\phi = 2 S E$$

where $$E$$ is the magnitude of the electric field on each face.

The electric charge $$q$$ contained in the cylinder is

$$q = \sigma S$$

Gauss' theorem allows us to conclude:

$$E = \frac{\sigma}{2\epsilon_0}$$

$$E$$ does not depend on the distance to the charged plane.

The magnitude $$E$$ of the electric field produced by an infinite electrically charged plane is the same everywhere in space. The electric field is perpendicular to the plane and directed towards it, if its charge is negative, and in the opposite direction, if its charge is positive.

The surface charge of a conductive surface

On one side of the surface the electric field is zero. On the other side it is perpendicular to the surface. Gauss' theorem applied to a small cylinder which crosses the surface and whose faces parallel to it have a surface $$dS$$ gives $$EdS = \frac{\sigma dS}{\epsilon_0}$$ so

$$E = \frac{\sigma}{\epsilon_0}$$

The infinite charged line

If a charged wire is of finite length, the electric field it is the source of depends on the distance from its ends. But for a very long wire, this edge effect is negligible, provided that we are far from the ends. The electric field created in a plane perpendicular to the middle of a long electrically charged finite wire is therefore equal to the field created by a wire of infinite length which has the same charge per unit length. The electric field created in a plane perpendicular to the middle of a long electrically charged finite wire is therefore equal to the field created by a wire of infinite length which has the same charge per unit length.

The electric field created in a plane perpendicular to a uniformly electrically charged wire of finite length, which passes through its middle, is necessarily perpendicular to the wire, by symmetry. If this electric field deviated from this median plane, Curie's law would be violated. This law also shows that the electric field created by a uniformly charged wire is necessarily in a plane parallel to its axis. So it is necessarily directed towards the wire, or in the opposite direction. As the wire is symmetrical by rotation around its axis, Curie's law also shows that the magnitude of the field can only depend on the distance from the wire.

Consider a cylinder of radius $$r$$ and length $$L$$, centered on a uniformly charged infinite wire. The internal charge on the cylinder is equal to $$q = \lambda L$$ where $$\lambda$$ is the linear charge density of the wire. Across both ends of the cylinder, the electric field flux is zero, since the electric field is parallel to them. The flux $$\phi$$ of the electric field $$\mathbf{E}$$ is therefore equal to the surface of the cylinder, apart from its ends, multiplied by the field $$E$$, which is always perpendicular to this surface:

$$\phi = 2 \pi r L E$$

where $$r$$ is the radius of the cylinder, $$L$$ its length and $$E$$ the magnitude of the electric field $$\mathbf{E} created by the uniformly charged wire at distance r from the wire.

So

The curl of a vector field
To understand its curl, we must understand the circulation of a vector field along a loop.

For a uniform vector field \mathbf{v}, the circulation of the field along a straight line \mathbf{dx} is equal to.

If the vector field is not uniform or if the path C is not straight, we consider a broken line which follows the same path and whose segments can be as small as we want. We calculate the circulation of the field by assuming that it is uniform on each segment, and we take the limit of the sum of the circulations of the field on each segment when the length of the segments tends to zero. This limit is an integral and it is the circulation c of the field \mathbf{v} on the path C considered:

.

The work of the electric force on a unit charge along a path is the flow of the electric field along that path.

If a force field derives from a potential, its circulation on a loop is always zero, because the potential at the starting point is equal to the potential at the ending point, which is the same as the starting point.

To measure circulation on a loop, one must choose a direction of circulation on the loop. Circulation in one direction is the opposite of circulation in the opposite direction.

The curl of a vector field is obtained from its circulation in the same way that its divergence is obtained from its flux, but the curl of a vector field in three-dimensional space is a vector field, whereas its divergence is a scalar field.

To understand the curl of a vector field, it is better to start by understanding it in a two-dimensional space, a surface, because then it is a scalar field, and a scalar field is simpler than a vector field.

The curl of a two-dimensional vector field \mathbf{v} at the point \mathbf{r} is the limit of when dS tends to zero, where c is the circulation of \mathbf{v} on a loop whose surface is dS and which surrounds the point \mathbf{r}.

To calculate the curl we use the formula:

for a field \mathbf{v} whose two components are v_x and v_y.

Proof: We reason about a small square with side a and whose sides are parallel to the x and y axes. On the sides parallel to the y axis, therefore perpendicular to the x axis, the circulation is - a v_y and. The sum of the two is. On the sides perpendicular to the y-axis, the circulation is a v_x and. The sum of the two is. So the circulation over the entire square is. This circulation is also equal to.

When the vector field is three-dimensional, we consider its projections on three perpendicular planes. These are three two-dimensional vector fields, each of which has a curl. We can therefore associate three numbers with each point. These are the components of a vector field:

The curl of a three-dimensional vector field is also a three-dimensional vector field.

The divergence of the curl of a three-dimensional vector field is always zero.

Proof:

The curl of a vector field can therefore always be identified with the velocity field of an incompressible fluid.

The flux of the curl of a vector field through a surface bounded by a loop depends only on the loop.

Proof: let S_1 and S_2 be two surfaces delimited by the same loop. These two surfaces delimit a volume. The flux out of this volume is the difference of the fluxes through S_1 and S_2. But since the divergence of a curl is always zero, this difference is zero, according to Gauss's theorem. So the two fluxes are equal.

The curl of the gradient of a potential is always zero.

Proof: let A and B be two points on a loop. The flux of the gradient of a potential V on any path from A to B is equal to V_B - V_A. The circulation of the gradient on the loop is the circulation on a path from A to B plus the circulation on a path from B to A. It is therefore always equal to zero. As the rotational is defined from the circulation on a small loop, it is also always zero for the gradient of a potential.

Stokes' theorem
The circulation of a vector field on a closed loop is the flux of its curl through a surface delimited by this loop.

Proof :

 * Let C be a closed loop, D, E, F and G four points on C, in that order. We can divide the loop C into two loops by adding a link between E and G: DEG and EFG. The circulation of a vector field along the loop C is equal to the sum of the circulations on DE, EF, FG and GD. The circulation on the DEG loop is the sum of the circulations on DE, EG and GD. The circulation on EFG is the sum of the circulations on EF, FG and GE. Now the circulation on EG is the opposite of the circulation on GE, so the circulation on C is the sum of the circulations on the DEG and EFG loops.

 * We can always divide a loop into many small adjacent loops. The circulation on the complete loop is the sum of the circulations on all the small loops that divide it, provided that the same direction of circulation is always chosen.

 * Let dS be a surface delimited by a small loop C parallel to the xy plane. The flux of the curl of a vector field \mathbf{v} through dS is equal to . This flux is therefore equal to the circulation of \mathbf{v} on the loop. The same would happen if dS were parallel to the yz plane or the xz plane.

 * A triangular loop can always be divided into three loops parallel to the xy, yz and xz planes. So the flux of the curl of \mathbf{v} through a triangular loop is always the circulation of \mathbf{v} on the loop.

 * A loop can always be divided into small, almost triangular loops. If they are small enough, their difference from triangular loops is negligible. So the flux of the curl of \mathbf{v} through any loop is equal to the circulation of \mathbf{v} on the loop.

Stokes' theorem is to curl what Gauss' theorem is to divergence. They are both special cases of a very general theorem, also called Stokes' theorem, which can be proved for any finite-dimensional space with the means of differential geometry.

Faraday's law
The work of the electric force on a unit charge along a closed loop is equal to the opposite of the rate of change of the flux of the magnetic field through an area bounded by the loop.

The work of electric force on a unit charge along a closed loop is an electromotive force.

A closed loop can always be thought of as a circuit that connects a generator to a resistor. The resistance is that of the loop. The generator is assumed to have zero resistance and to provide an electromotive force equal to the rate of change of the magnetic field flux. This is why we can always define a potential in an electric circuit, even though it contains loops which can be traversed by variable magnetic fields. Each time an electromotive force appears, we reason as if a generator instantly imposed a potential difference equal to this electromotive force. We can thus define a fictitious potential on the entire electrical circuit.

Faraday's law leads to Maxwell's third equation:

Proof: let a loop be placed in the electromagnetic field. By Stokes' theorem, the circulation of \mathbf{E} over this loop is the flux of through it. According to Faraday's law, it is also the opposite of the rate of change of the flux of \mathbf{B}. The rate of change of the flux of \mathbf{B} is the flux of. The equality of the fluxes of and of  for any small loop proves that  and  are necessarily equal.

Maxwell's fourth equation
Maxwell's fourth equation determines as the sum of two terms. One can be obtained with the Biot-Savart law.

The magnetic field lines around a wire of infinite length carrying a current I are circular and centered on the wire in a plane perpendicular to the wire. With the Biot-Savart law, we can calculate the magnitude B of the field \mathbf{B}

where r is the distance to the wire.

The circulation of \mathbf{B} along a field line is therefore

By Stokes' theorem, the flux of through a loop is always the circulation of \mathbf{B} over this loop. If \mathbf{J} is the current density, I is the flux of \mathbf{J} through a surface crossed by the current. By setting, we therefore find the Biot-Savart law for a wire of infinite length.

cannot be true everywhere.

Proof: let a circuit be made up of a capacitor which discharges into a resistor. Consider a loop that surrounds the circuit wire. The flux of \mathbf{J} through a surface passing through the wire is equal to the current I. But the flux of \mathbf{J} through a surface that passes between the two plates of the capacitor is zero, since there is no current between the two plates. Now the flux of through a surface delimited by the loop only depends on the loop. So cannot always be true.

On the other hand, if we put

we correct this error.

Proof: between the capacitor plates, and is directed perpendicular to the plates. The flow of \mathbf{E} through a surface between the plates is therefore. So the flux of between the capacitor plates is equal to dQ/dt = I, the intensity of the current.

Maxwell's equations
With the Lorentz equation,

)

Maxwell's equations are the fundamental laws of the classical theory of electromagnetism. Classical means here that it is not a quantum theory.

Maxwell's equations explain how moving charges are the sources of the electromagnetic field and how it changes over time. The Lorentz equation explains how this electromagnetic field exerts forces on moving charges.

Light is an electromagnetic wave. We can prove the existence of light from Maxwell's equations.

Aside from gravitation and nuclear forces, electromagnetic forces explain all natural phenomena. Light, atoms, molecules, ions, solids, liquids, gases, plasmas, liquid crystals, electric motors, radio waves, x-rays... are all explained from electromagnetic forces. For physicists, the Maxwell and Lorentz equations are therefore like the tables of the law.

Maxwell's and Lorentz's equations can be deduced from generalized Coulomb's law and the relativistic geometry of space-time. Generalized Coulomb's law is therefore the most fundamental law of classical electromagnetism.

Spacetime geometry assumes the existence of the speed c of light, but it does not impose the existence of light. It is enough to assume the existence of particles that travel at the speed of light. So Coulomb's generalized law and the geometry of space-time prove the existence of light, without presupposing it.

Maxwell's equations in matter
We generally think about point charges. The charge density \rho is infinite at the point where the charge is. We assume that the charge density \rho is a Dirac delta such that \int_V \rho dV = q for a point charge q$$, where $$V$$ is a volume that contains only the charge.

If the charges are ponctual, space is empty almost everywhere, and the Maxwell equations in matter are the same as the equations above, where the charge and current densities are calculated with Dirac deltas.


text:
Magar/Colours

"" Colours Name ""

 * Black - Chicha/Chicklingcha⚫
 * White - Bocha⚪
 * Red - Gyācha🔴
 * Green- Ficha🍏
 * Yellow- Wórcha💛

title: Magar/Colours


text:
Magar/Animals

 * Ant- Mhār🐜
 * Cat- Suthū🐈
 * Cow- Hyant🐄
 * Dog- Chiū🐕
 * Fish- Disyā🐟
 * Goat- Rhā🐐
 * HouseFly- Jhinghā
 * Pig- Wāk 🐖
 * Rat - Byū🐀
 * Ox - Bārdā/Thor🐂
 * Pig- Wāk 🐖
 * Rat - Byū🐀
 * Ox - Bārdā/Thor🐂

title: Magar/Animals


text:
Melbourne Suburban Railway

Technology
Modern day suburban (or metropolitan) railway networks are economic arteries, connecting the central business districts of many cities around the world to their workers in the suburbs. The deployment of suburban railways around the world coincided with the development of cities and has contributed significantly to urban sprawl. Suburban railway networks are advantageous for metropolitan regions as they can operate over long distances and at a higher capacity than other forms of transport such as trams and buses.

The Melbourne Suburban Railway network, officially known as Metro Trains Melbourne, is just one example of many suburban railway networks around the world that are designed to connect the Central Business District of its city to the surrounding suburbs. Today, the network operates 226 electric trains on 15 lines along 998 kilometres of railway track (Metro Trains Melbourne, 2024).

Origins of the passenger railway
The development of the suburban railway network as a mode of transport in Melbourne can be attributed to several prior events. Whilst the following events did not occur in Melbourne, instead in the modern-day United Kingdom, each introduced a component of the technologies which formed both the early and modern-day Melbourne suburban railway network. These are as follows:

1. Deployment of Passenger Railway Systems - Oystermouth Railway
The Oystermouth Railway was the first passenger railway service to commence operation and did so in 1807 (Shaw-Taylor & You, 2018). This service-connected Swansea and Oystermouth with rail wagons being pulled by horses.

2. Deployment of the Locomotive - Stockton & Darlington Railway
The Stockton and Darlington Railway opened in 1825 and whilst built to transport freight and not passengers, it was the first railway to use a steam locomotive (Shaw-Taylor & You, 2018). The opening of this railway line was a catalyst for the development of further locomotive hauled railways in the immediate future (Darroch, 2014).

3. Deployment of Locomotive Hauled Passenger Railway System - Liverpool to Manchester Railway
The Liverpool to Manchester Railway opened in 1930 and is widely attributed as being the first locomotive hauled passenger railway service to enter operation (Shaw-Taylor & You, 2018). George Stephenson’s Rocket locomotive was the first to be used on the railway, capable of reaching almost 50kmh (30mph) (Shaw-Taylor & You, 2018).

4. Deployment of Underground Metropolitan Railway – London Underground
London’s Metropolitan Railway saw the world’s first underground railway open in 1863 connecting the busy London stations of Paddington & Farringdon (Darroch, 2014). The opening of the Underground quickly saw other cities construct and operate their own underground railways. Melbourne, like many other cities globally, would incorporate underground railways service into its network.

As seen above, the deployment of passenger transport on rails, the introduction of the locomotive to railways, the combination of both and the introduction of sub-surface railways all contributed to the suburban railway system adopted in Melbourne.

Before the Railway
The city of Melbourne was established in 1835 on Port Phillip, just 19 years before its first steam railway opened for operation. Melbourne was established by farmers and pastoral workers from Tasmania who sought after more land for agriculture (Records and Archives Branch of the City of Melbourne, 1997). In the short period of time between the establishment of the city and the opening of its first railway, transportation around the newly established city and surrounds was primarily undertaken by foot, horse drawn wagons or other animal hauled methods and by ship through Port Phillip. As the port established at Sandridge (modern day Port Melbourne) experienced increases in import and exports through the 1840s, transporting both people and goods from the port to the city and surrounds became of increasing importance (Harrigan, 1954).

Limitations of foot traffic and animal drawn vehicles
Although the distance between Melbourne and Sandridge was walkable, it was a very unpopular method of transportation, especially in adverse weather conditions and for people carrying luggage and goods. Furthermore, Animal drawn wagons and carts where ultimately limited in their capacity for carrying passengers or goods between the port at Sandridge and the city. Horse drawn vehicles were often unpleasant, slow, unreliable, and caused significant road damage over time. It is these limitations and the increase in demand for transport which made a faster and higher capacity locomotive-hauled railway a popular alternative.

Invention
The invention of the steam locomotive and its deployment on the Stockton and Darlington and Liverpool to Manchester Railways in England allowed for the development of the suburban railway network in Melbourne (as mentioned in section 1). Steam locomotives use coal as a source of thermal energy to heat water in and convert it to steam, this steam is held in the boiler and causes an increase in pressure. The pressurised steam drives the wheels of locomotive by pushing pistons which are connected to a crank mechanism, creating the rotating motion required (Bathurst Rail Museum, n.d).

The deployment of the suburban railway in Melbourne would see improvements made to the transport mode in its early development. The permanent adoption of steel wheels and steel rails in 1868, moving away from the use of iron rails commonly seen in England saw a significant improvement in the durability of both locomotives and track infrastructure (Harrigan, 1954).

Early Market Development
The decision to build Australia’s first steam locomotive railway between the city of Melbourne and Sandridge (modern day Port Melbourne) was in response to the growing industrial activity in the Sandridge area and the increase in ship movements in and out of the port. The success of railways in the United Kingdom prompted many entrepreneurs in Melbourne to investigate building their own railway services in the city. This resulted in the first public meeting for railway entrepreneurs being held on the 7th of December 1851 (Harrigan, 1954). Whilst this meeting attracted interest from potential stakeholders in a railway service, the impact of the gold rush on the city’s population and economy was significant and no definitive action was taken on a railway service until August 1952, when the Melbourne & Hobson’s Bay railway company was formed. W.S Chauncey was subsequently appointed Chief Engineer on the 17th of August 1952 and the official approval to construct the railway line passed on the 20th of January 1953, with the Act of Incorporation (Lee, 2007). The official opening of the Melbourne to Sandridge railway occurred on the 12th of September 1854.

The first year of operation for the Melbourne & Hobson’s Bay Railway Company’s first line was a success, with shareholders receiving an 8% dividend and the capacity for transport between Melbourne & Sandridge increasing significantly (Harrigan, 1954). This success prompted the investigation for the construction of more railway lines and creation of more railway companies. The market appetite for railways following the opening of the Melbourne to Sandridge line is reflected in the opening of the branch line to St. Kilda in May 1857, its subsequent extension to Brighton by the St. Kilda & Brighton Railway Company and the Melbourne & Suburban Railway Company’s lines from Princes Bridge to Hawthorn and Windsor (Dee, 2006; Lee, 2007).

The Role of Policy
During the birthing phase of the Victorian suburban railway network, several key policies shaped its design and patronage.

Gauge Policy
Following the appointment of W.S Chauncey as Chief Engineer in 1852, prior to the opening of the Melbourne-Sandridge Railway, a decision was to be made on the gauge width for the railway line. Chauncey advised the company to adopt the broad-gauge system using a rail spacing of 1600mm (5 feet 3 inches), the same rail gauge which was to be adopted by the Sydney Railway Company (Lee, 2007). Chauncey believed that a standardised rail gauge should be adopted across Australia for the future development of the continent’s railways, and thus wanted to align with the gauge already decided upon in NSW. It should be noted that Sydney would change its decision and adopt the standard gauge of 1435mm with its first railway in 1855 (Wardrop, 2022). The effect of this policy can still be seen today with Melbourne still operating a broad-gauge system and Sydney operating a standard-gauge system.

Building Tickets
To boost ridership on its services, the United Company began to distribute ‘building tickets’ to those who built houses along the railway corridors to Brighton and Elsternwick in October 1865 (Harrigan, 1954). This policy created an incentive for people to build their houses and live along these railway corridors, resulting in increased ridership from these areas to the city.

Government Purchases United Company
Following the opening of the Melbourne to Sandridge Line, the extension to St. Kilda and Brighton, and the lines to Hawthorn and Windsor, the Melbourne & Hobson’s Bay United Railway Company purchased their competitors services and by 1865 operated all 26km of track. By 1870, the United Company would operate over 240 daily services. In 1872 the Victorian Government purchased the United Company’s shares for  £1,320,820 pounds (Harrigan, 1954). The newly amalgamated network of railway lines developed significantly in the 1880s into a radial system connecting the city to the surrounding suburbs in all directions.

Introduction of Rail Motor Cars
The growth period of the Melbourne Suburban Railway saw the development of rail technology and subsequent improvement of passenger service. The first railway motor car was introduced in May 1883, combining an engine cabin containing a vertical boiler and motor into a carriage capable of carrying 40 passengers. These motor cars operated on the Fairfield to Oakleigh and Essendon to Broadmeadow lines until their withdrawal from service in the late 1890s (Harrigan, 1954).

Construction of the new Flinders Street Station
The rapid expansion of the railway network in the late 19th Century resulted in a significant increase in daily train services reaching the city of Melbourne. By 1900 it was evident that the existing station at Flinders Street, originally built for the Melbourne-Sandridge Railway was unable to provide the required capacity needed as expansion continued. In May 1900, the “Green Light” syndicate by James Fawcett and H.P.C Ashworth, two Victorian rail officials, was chosen to provide their design for a new station on Flinders Street (Lee, 2007). The large, French renaissance style station was completed in 1909 and officially opened in 1910, serving as the main station for the city of Melbourne (Victorian Railways, 1965).

The Electrification of the Suburban Railway
The electrification of the railway was initially considered in 1896 by A.W Jones from the General Electric Company. C.H. Merz was appointed in 1907 to further investigate electrifying Melbourne’s Suburban lines and proposed the electrification of 200km (124 miles) of track by 1912 at a cost of £2,227,000 (Harrigan, 1954). Little action was taken on Merz’s initial plan and in 1911 the Victorian Government requested an updated plan in which the cost rose to £3,991,000 (Harrigan, 1954).

The first railway power station was constructed at Newport in 1913 with a production capability of 60,000 kW. The First World War saw significant delays to the electrification programme, with the first generator becoming operational in 1918. It would not be until 1919 that the first electric line commenced operation. By April 1923, the suburban railway network was electrified with the opening of the final stage between Heidelberg and Eltham (Victorian Railways, 1965). The cost of the project had risen to 6,270,000 pounds by its completion (Harrigan, 1954). At this time Melbourne boasted one of the most expansive electrified railway networks in the world.

The electrification of the suburban railway proved to be a great success. Passengers were offered a faster, quieter, and smoother railway service at a lower cost, which significantly boosted ridership in the 1920s and 1930s (Harrigan, 1954). The Electrification of the network brought the suburban railway into the modern era and can be considered the end of the growth phase of the system.

Maturity
By 1949, the Melbourne suburban network had grown in ridership to 182 million in that year compared to 123 million in 1919 when electric operations began (Wardrop, 2022). However, two major factors would cause rapid decline in the usage of the network in the 1940s and 1950s.

Decrease in Patronage - The Deployment of the Motor Car
The private motor vehicle significantly changed the way Melbournians travelled in the years following the 1940s (Lee, 2007). Using a car to travel from home to work became commonplace and there was a significant increase in trips between homes and workplaces that were not in the city of Melbourne. The suburban railway had and still has the disadvantage of being a radial network, where its design is primarily to transport passengers from the suburbs to the city. Thus, the increase in trips to other suburban areas for work and the convenience of the motor vehicle played a major factor in the decline in patronage in the mid to late 20th century (Wardrop, 2022).

Decrease in Patronage - Industrial Action
The Mid 20th century saw a significant increase in the influence of union movements in Victoria. Industrial action taken by the union movements on the Melbourne Suburban Railway did much to destroy confidence in the transport system (Lee, 2007). Concurrent to this, the state of the railway network had severely declined, with overcrowded trains and poor infrastructure causing frequent disruption to service and passenger discomfort. Several instances of industrial action taken by the union movement over conditions such as pay and working conditions caused frequent disruption to the system. Some of the major disruptions are listed below:

The above are three examples of many industrial strikes which took place on the railway network in the 1940s and 1950s and are attributed to the 20% decrease in annual ridership between 1949 and 1951 (Lee, 2007). Industrial disputes continued well into the 1970s. Consistent disruptions to service caused a lack of faith amongst Melbournians in the network and further encouraged the use of motor cars.
 * 1) April 1947: Industrial action at Newport power station caused a 23-day disruption to service.
 * 2) June-August 1949: Coal strikes halved train services during the week and completely halted weekend trains for 6 weeks.
 * 3) October-December 1950: Industrial strike saw the halting of train services for 55 days.
 * 1) October-December 1950: Industrial strike saw the halting of train services for 55 days.
 * 1) October-December 1950: Industrial strike saw the halting of train services for 55 days.

Saving the Network - New Trains & The City Loop.
By 1978, 88% percent of trips in Melbourne were made by car and annual train patronage had dropped to 94.3 million in the same year. By 1983, the network was operating at a loss of $286 million per year. With the intention of stopping the decline in rail patronage, the Victorian Government ordered the production of 300 Comeng (Commonwealth Engineering) railcars which were to be locally manufactured at Dandenong (Lee, 2007). These trains would have automatic doors, be airconditioned and use improved materials with the aim of reducing operating and maintenance costs over their lifecycle. These cars arrived on the network in 1981 and proved a success, providing a more comfortable and reliable journey for customers. As a result, 270 more railcars were ordered in 1985 (Lee, 2007).

Another initiative undertaken by the Victorian Government was the construction of the city loop tunnels. Until the 1980s, the city of Melbourne was served only by 2 major stations at Flinders St. and Spencer St. (now Southern Cross). From these two stations, it was common for passengers to switch to a tram, bus or walk to their place of work. The Melbourne Underground Rail Loop Act was passed in January 1971 and saw the creation of the Melbourne Underground Rail Loop Authority (Lee, 2007; Mees, 2008). The authority oversaw the construction of quadruple tunnels travelling around the city with new sub-surface stations at Flagstaff, Melbourne Central and Parliament. The loop system opened in January 1981, providing increased capacity across all suburban lines, providing new station locations in the city, and reducing pressure on Flinders and Spencer St. stations (Mees, 2008). The new trains and stations played a significant role in the recovery of patronage leading into the 21st century.

Saving the Network - Additional Policies
Several policies were created in between the 1970s and 1990s to attempt to recover patronage levels on the network. Smoking was banned on all services in November 1976 and intermodal ticketing was trialled at the same time to make services more comfortable and ticketing simpler. The Transport Act in July 1983 brought the railway network, tram network and bus network under a new organisation nicknamed “The Met” in an additional effort to improve the reliability of all transport modes and simplify ticketing (Lee, 2007). Between 1983 and 1989, the suburban railway network and trams and buses shared the same tickets and liveries on their vehicles. Electronic ticketing machines were introduced in 1996 to further simplify the ticketing process and make transactions faster with the intent of attracting more patronage.

Saving the Network – Privatisation of Melbourne’s Suburban Railway
Under Jeffery Kennett’s Liberal Government, the Public Transport Reform Program began to privatise much of the railway’s operations. A significant change made by the Kennett government was the removal of guards from trains, which reduced the required staff for network operations to increase reliability and cut costs. Following a major industrial strike in 1997, the government privatised the suburban railway, splitting the operations across two companies, Hillside and Bayside Trains (Lee, 2007). The privatisation of the suburban railway was aimed at improving reliability and reducing the impacts of industrial action on the network. Various iterations of private operation of Melbourne’s railway network have existed since 1997. The network is still privatised as of 2024, being run under “Metro Trains Melbourne”, a joint venture between MTR, John Holland and UGL Rail (Metro Trains Melbourne, 2024; Victorian Auditor-General's Office , 2023).

Quantitative Analysis
Quantitative analysis of annual patronage on the Melbourne Metro Trains network using a three-parameter logistic function has been undertaken using information from several sources including data from Alex Wardrop’s “A Tale of Two Systems”, and several reports released by Victorian Government Agencies (Wardrop, 2022; Public Transport Victoria, 2013; Public Transport Victoria , 2014; Public Transport Victoria , 2012; Public Transport Patronage Trends in Australasian Cities , 2015). Using the three-parameter logistic function allows for the identification of growth peak and decline periods and passenger projections.

The equation for the Three Parameter Logistic Function is shown below:

S(t)=S_max/(1+e^((-b(t-t_i )) ) )

Where: S(t) is the predicted annual patronage for year t	S_max is the saturation level for patronage (in thousands) t is the chosen year t_i is the inflection time b is an estimated coefficient

An appreciation for the fluctuating nature of passenger patronage on Melbourne’s suburban railway network since 1900 prompted the creation of two models, one during the phase of the network’s electrification (1900-1930) and a second model with annual patronage from 1900 to 2022. As will be seen, using data over a 30-year period from 1900 during the electrification phase of the railway produces a logistic curve with a strong fit. However, using data over a 120 year period produces a very weak fitting curve due to several events that have occurred over the life of the network.

Model 1 (1900-1930)
The model using data from 1900-1930 produces an r-squared value of 0.945, just under the acceptable threshold of 0.95 for the three-parameter logistic function. This means that 94.5% of values fit within the regression and for this time, the logistic curve is a strong fit.

Model 2 (1900-2022)
Creating a model using a the three-parameter logistic function yields an r-squared value of 0.222, well below the generally accepted threshold of 0.95. this means that only 22.2% of values fit the regression. As can be seen in the model, there is a fluctuation in annual ridership growth and decline over the 122-year period, with noticeable local peaks in, 1949 and 2019. As explained previously, the electrification of the network resulted in substantial patronage growth in the 1920s, and upgrades to the network in the 1970s and 1980s also resulted in substantial patronage growth up until the global peak in 1919 prior to the COVID-19 pandemic. These fluctuations make it extremely difficult to fit a three-parameter logistic function as reflected in the r-squared value meaning that the curve is not a strong fit.

Furthermore, this model is constrained by the following limitations & assumptions: Data is only available from 1900 onwards (railway service begun in 1854). Data collection methods have changed between 1900 and 2022. Data is collected from ticketing & station entries and thus does not count fare evaders.

Using model two to estimate the birthing, growth, maturity and decline periods of the Victorian suburban railway thus proves difficult. Using the data, the growth period can be estimated to be between 1900 and 1940 with the maturity period being between 1940 and 1970 with decline occurring post 1970. The period between 1996 and 2010 can be potentially classified as a second growth period.

title: Melbourne Suburban Railway


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User:Samekhan221

Furniture Manufacturer: Crafting Comfort and Style

Introduction:

Furniture manufacturers play a crucial role in the global economy and in shaping the aesthetic landscape of our homes, offices, and public spaces. These entities are responsible for designing, producing, and distributing a wide range of furniture pieces that cater to diverse tastes and needs. From traditional wooden chairs to modern, minimalist sofas, furniture manufacturers contribute to enhancing both the functionality and beauty of interior spaces.

History:

The history of furniture manufacturing dates back centuries, with artisans crafting furniture by hand using traditional woodworking techniques. Over time, advancements in technology and manufacturing processes revolutionized the industry, leading to the establishment of large-scale furniture factories and mass production methods. The Industrial Revolution in the 18th and 19th centuries marked a significant turning point, ushering in an era of mechanization and standardization in furniture manufacturing.

Process:

Modern furniture manufacturing involves a multi-step process that begins with design conceptualization and material selection. Skilled designers create prototypes and blueprints, which are then translated into production-ready models. Manufacturing facilities utilize a combination of automated machinery and handcrafting techniques to fabricate furniture pieces, including cutting, shaping, joining, and finishing. Quality control measures are implemented throughout the production process to ensure that each piece meets industry standards and customer expectations.

Materials:

Furniture manufacturers utilize a diverse range of materials to create their products, including wood, metal, plastic, glass, and upholstery fabrics. The choice of materials often depends on factors such as durability, aesthetics, cost, and environmental sustainability. Sustainable sourcing practices and the use of eco-friendly materials have become increasingly important considerations for furniture manufacturers, reflecting growing consumer demand for environmentally responsible products.

Trends and Innovation:

Furniture manufacturing is a dynamic and evolving industry, influenced by changing consumer preferences, design trends, and technological advancements. Manufacturers continuously innovate to stay ahead of the curve, incorporating new materials, production techniques, and design concepts into their products. Trends such as modular furniture, smart technology integration, and sustainable design have gained traction in recent years, shaping the direction of the industry.

Global Impact:

The furniture manufacturing industry has a significant global footprint, with production facilities located in countries around the world. Leading furniture-producing nations include China, the United States, Germany, Italy, and Poland. Global trade networks facilitate the exchange of furniture products across borders, contributing to economic growth and cultural exchange. However, challenges such as supply chain disruptions, fluctuating raw material prices, and regulatory compliance issues can impact the global furniture market.

Conclusion:

Furniture manufacturers play a vital role in enhancing the functionality, comfort, and aesthetic appeal of interior spaces. Through innovation, craftsmanship, and a commitment to quality, these entities contribute to creating environments that inspire and enrich our daily lives. As consumer preferences and design trends continue to evolve, furniture manufacturers will remain at the forefront of innovation, driving the industry forward and shaping the future of interior design.

title: User:Samekhan221


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User talk:TomKeane03

Welcome!
Welcome, TomKeane03!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. MathXplore (discuss • contribs) 10:51, 4 March 2024 (UTC)

title: User talk:TomKeane03


text:
User:DisturbedToFu

.

title: User:DisturbedToFu


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Celestia/Tutorials/Globulars

This tutorial will describe how to add Globular into Celestia. Globular are a bit hard objects to add to Celestia, because most of them can be simulated as bits of STC code.

To add a Globular to Celestia, you need a .stc file. This can be created by taking any plain text file and renaming the file extension to. This file can be named anything as long as it has the  suffix. Then, it should be placed into the "extras" directory (i.e. a folder), or any folder within the "extras" directory.

Now, after you open the .stc file, you need to define a Globular by writing some code in it with your favorite text editor. Information for many Globular can be found in various places, outside of the milky way core

Basic definition
The basic definition looks like this:

Galaxy Name Globular "Globular Name"       { RA 	                Dec Distance Radius With additional (optional) parameters, it looks like this: SMC                     Globular "Globular Name"        {                               RA                    Dec               Distance           Radius         CoreRadius KingConcentration AppMag              Axis  [   ]                   Angle                  } We'll go through the parameters one by one. Let's use the Globular NGC 1466 as an example.

Also, at any point you can add a comment to your .stc code. A comment is started by a  sign and lasts until the next line break. It's a good idea to add comments explaining if you calculated parameters yourself, or if they are guesses.

Name
Galaxy Name "Name"

Here,  is just the name (or names) of the Globular. If a Globular has multiple names, separate them with colons. like this:

SMC "NGC 1466:PGC 2802621"

And it other names. so it would look like this:

SMC "NGC 1466:PGC 2802621:ESO 54SC16"

RA and Dec
RA Dec

These are the right ascension and declination of the Globular, i.e. the coordinates of the Globular on the sky. Note that in an STC file,  is in degrees, unlike a DSC file where it's in hours. Usually the RA will be in hours/minutes/seconds format, and the Dec will be in degrees/arcminutes/arcseconds format. To convert to Celestia's decimal format, use a tool like the RA DEC flexible converter. You can also tell SIMBAD to output decimal coordinates by going to the Output options page and selecting "decimal" from the drop-down menu next to "Coordinates".

Distance
Distance

The distance to the Globular in light-years.

CoreRadius
CoreRadius "Number"

the size of the Core of the Globular the core can be 0.2 (NGC 1466 Size)

AppMag or AbsMag
AppMag or AbsMag

This is the apparent magnitude of the Globular (how bright it appears from Earth), or the absolute magnitude (how bright it would appear from a distance of 10 parsecs), without extinction (dimming, caused by dust that is blocking light). The  in Celestia corresponds to the V-band magnitude in sources such as SIMBAD.

The above parameters are all that's required to define a Globular. Here's the basic definition for NGC 1466:

SMC "NGC 1466:PGC 2802621" { 	RA 0.4478528 Dec -71.5225806 Distance 2.12e+05 Radius 175 CoreRadius 0.2 KingConcentration 1.25 Axis [-0.7429 -0.2364  -0.6263] AppMag 11.705 }

Now for the optional parameters...

Axis
Axis [

axis where the Globular rotation

KingConcentration
KingConcentration

Where it rotation

Radius
Radius

Most globular clusters have a half-light radius of less than ten parsecs (pc), although some globular clusters have very large radii, like NGC 2419

Angle
Angle

It Angle where it on our view

Example code
For the sake of reference, here is what the final .stc code might look like for NGC 1466:

SMC "NGC 1466:PGC 2802621" { 	RA 0.4478528 Dec -71.5225806 Distance 2.12e+05 Radius 175 CoreRadius 0.2 KingConcentration 1.25 Axis [-0.7429 -0.2364  -0.6263] AppMag 11.705 }

title: Celestia/Tutorials/Globulars


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User talk:2600:6C60:5DF0:DF0:3830:9A23:8F14:165E

Your edits have been reverted again. There is no need to remove links just because they are red.--Xania   talk 05:21, 5 March 2024 (UTC)