It’s been over a decade since I read Kim Stanley Robinson’s quite epic novel Red Mars, but I remember one particular paragraph quite well. One character had just set foot on Mars for the first time and noted how the horizon seemed closed, and so it was obvious they were standing on a smaller planet. Which made me wonder… would you actually be able to notice that?
I’ve always loved looking out towards the horizon. Especially by the shore on those beautifully clear days when you can see right to the edge of the sky. But just how far away is the horizon anyway? Actually, it’s pretty easy to calculate.
A fairly simply bit of trigonometry, and it works out that this equation is all you need. Here, d is the distance to the horizon, h is your height off the ground, and R is the radius of whatever planet you happen to be standing on. Of course, this assumes that there are no hills or other objects between you and the horizon, so it only works properly over vast flat expanses. So assuming your eyes are about 5’7 above the ground (average for a human being), and taking Earth’s radius to be 6378.1 km, that means the horizon you see is 4.66 km away. Perhaps a little closer than you might expect.
Mars, on the other hand, is indeed a much smaller planet. The radius of Mars is only 3397 km, which means that from the same height, the martian horizon would appear 3.40 km away.
The Moon is even smaller with a radius of only 1737.4 km, meaning on the moon, the horizon is only 2.43 km away. Take a closer look at those Apollo photographs from the surface of the Moon. You can actually see that. If you were standing on the Moon, you really would notice that it’s much smaller than Earth!