| MadSci Network: Physics |
Reply:
>What would the horizon look like on a very large planet?
I have used POV-Ray, a freeware ray tracing package, to help answer this question. In these pictures, the camera is placed one unit above the surface of the sphere (or plane) standing in for the planet.
From left to right, the planet grows from a radius of 20 units to 100 to 1000 to an infinite plane.
As you can see, the horizon lifts up as the planet gets bigger, just as you guessed. However, the horizon never lifts above the halfway mark, so there is no "bowl" effect. In the case of the earth, the horizon is already just about as flat as it can be. If you've ever been high in an airplane over the ocean, you may have noticed the earth's curvature, but perhaps not, otherwise. The earth's radius is over 6000 km, so at an elevation of 6 km (a high-flying airplane) the ratio would be 1 to 1000, like the third picture above. At typical heights from which we view the earth's surface, the ratio is more like 1 to 1, 000, 000, meaning that it already looks pretty much like an infinite plane. So your second guess is correct--for larger planets, the angular increase in the apparent height of the horizon is so small as not to be noticable.
-Greg Billock