The properties of elliptical orbits discovered by Kepler can be derived from Newton’s laws of motion and his law of gravity. In other words, once Newton figured out his laws of gravity and motion, he could have predicted Kepler’s laws of planetary orbits. An important exercise in more advanced astronomy courses is to derive all three of Kepler’s laws from Newton's laws. If Newton’s laws are true, the Copernican theory and Kepler’s laws also have to be true. Newton therefore tidied up the miscellaneous observations of preceding centuries and completed the Copernican revolution.
The law of gravity proposed by Newton represents an impressive example of the power of the scientific method. It was developed to explain the motions of only eight astronomical bodies - the Sun, Earth, Moon, and the five visible planets. Yet by calling it a universal law of gravity we are making the presumption that it applies everywhere in the universe. This is an audacious use of induction! Soon afterwards, it was used to explain the orbits of the moons of Jupiter and to predict the return of Halley’s Comet. Later astronomical observations have shown that Newton’s laws apply to the entire universe we have studied. They correctly predict cosmic movements ranging from the motions of binary stars that orbit each other in remote regions of our galaxy, to the motions of galaxies in remote parts of the universe.
Orbital diagram of our solar system. Click here for original source URL.
Memorization is not an important part of learning science, but some facts are so basic you should commit them to memory. It’s important to know the names of the planets in order outward from the Sun. Generations of students have made up mnemonic devices, such as sentences whose words begin with the letters of the planets. An old (but somewhat sexist) mnemonic sentence for the planets was "Men Very Early Made Jars Stand Upright Nicely." When Pluto was discovered, it was necessary to add the word "Period" to the end of the sentence, but more recently Pluto was demoted to the status of a dwarf planet so the mnemonic is slightly shorter again. One mnemonic (from a student at the University of Hawaii) is "My Very Erotic Mate Joyfully Satisfies Unusual Needs Passionately." You will remember a mnemonic sentence like this best if you make one up yourself. Many students lose track of the sequence around Saturn, Uranus, or Neptune, and so it might be helpful to remember that the S.U.N. (Saturn, Uranus, & Neptune, in that order) is also part of the solar system.
Once you’ve learned all the planets, it’s very easy to remember their rough distances from the Sun in terms of the astronomical unit. In 1772, the German astronomer Johann Titius discovered a curious relationship governing the planetary distances. His colleague Johann Bode popularized it, so it’s usually known as Bode’s rule. Bode and Titius noticed that each planet is about 1.5 to 2 times as far from the Sun as the previous planet. This is called a geometric progression, where each number is a fixed factor larger than the previous number (as opposed to an arithmetic progression, where each number increases by the same additive constant).
The discovery of Uranus in 1781 fit the pattern because it’s about twice as far from the Sun as Saturn. Astronomers noticed that Bode’s rule also predicted a planet between Mars and Jupiter, where there is none. German and Italian observers, nicknamed the "celestial police," set out to find the missing planet, but instead discovered Ceres and several other large asteroids at just the right distance! Today we know there are thousands of asteroids between the orbits of Mars and Jupiter, in the place where a planet would have formed if Jupiter’s large gravity hadn’t disrupted it.
Why should we be surprised that the planets have an apparent pattern in their spacing from the Sun? Newton’s law of gravity and Kepler’s laws of orbital motion describe how planets move around the Sun, but they allow for planets at any distance from the Sun. In other words, the spacing of the planets is not built into Newton's or Kepler’s laws. So there must be a different physical explanation for this roughly geometric progression. We now believe that the process of accretion and planet formation controls this spacing.