# The furthest horizon in the Solar system

Where can I observe the furthest horizon in the Solar system ? And what the length of it ? The furthest horizon on Earth can be observed from mount Everest ~ 336 km, On Mars - from mount Olympus ~ 386 km.

Edit: If the walls of the Rheasilvia crater can be seen from the opposite sides (it appears so) you can see the surface as far as 505 km.

The distance depends on the diameter of the planet and of your height above the surface (such as on a mountain). The greater the diameter, the farther away the horizon will be.

You can see this in the figure below. $d_3 > d_1 > d_2$. On a large planet your horizon (at distance $d_1$) will be farther away than on a smaller planet with horizon distance $d_2$. But if you stand on a mountain on the same planet then the distance will be even larger ($d_3$).

You can calculate the height from Pythagoras' rule because we have a triangle with one unknown edge. The distance from the planet's centre to the point where you see the horizon is the radius of the planet and the distance of the eye of the observer is the radius of the planet plus the height of the observer above the surface. $$(r+h)^2 = r^2+d^2$$ where $r$ is the radius of the planet, $h$ the height above the surface, and $d$ is the horizon distance. If we rewrite this equation we get: $$d^2 = (r+h)^2 - r^2$$ $$d^2 = r^2+h^2+2rh-r^2$$ $$d^2 = h^2 + 2rh$$

For Venus we have $r=6052\textrm{km}$ and $h=11\textrm{km}$ (Maxwell Montes), we therefore get a horizon distance of 365km. This is still smaller than the horizon distance from Olympus Mons. Olympus Mons is the highest mountain and all other rocky planets are smaller, the horizon distance from Olympus Mons is, therefore, the greatest horizon distance.

Whether the horizon distance in the Rheasilvia crater is greater depends on whether you would be able to see the crater edge from the middle of the crater. Vesta's radius is 262km. If you stand on the crater edge, which is 13km above the crater surface, you would only have a horizon distance of 83km. This means that from the centre of the crater you would not be able to see the crater's edge.

EDIT Above I assume that the 13km is the height of the crater edge above the centre of the crater as measured from the geodesic. If the height is the height above a flat (not spherical flat) surface than the horizon is indeed 505km (see comments below).

• I think you can not apply the formula to calculate the length of the horizon for Vesta, because it is irregular-shape body. Especially in the impact crater area, where the surface is 'flattened' quite a lot. – user3715778 Oct 9 '14 at 16:27
• @user3715778 You are right of course. But the flattening would need to be quite extreme, especially when you consider that the radius of Vesta is 1.5 times smaller then the horizon distance of Olympus Mons! – Dieudonné Oct 9 '14 at 17:00
• The flattening is quite extreme :) dawn.jpl.nasa.gov/multimedia/video/… – user3715778 Oct 9 '14 at 17:16
• Yes that is quite extreme ;-). The formula above assumes $h$ to be the height above the geodesic. There is no way that $h$ is only 13km if you look at the video. The 13km is probable the height of the crater edge assuming that the crater surface is completely flat. – Dieudonné Oct 9 '14 at 17:29
• I've edited the answer accordingly. – Dieudonné Oct 9 '14 at 17:34