Large planets have more distant horizons than small ones, but lower mountains due to higher gravity. On which would you see farther?
Chris Daniel
Glan Conwy, Conwy, UK
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The maximum height of a mountain doesn’t appear to be closely related to the size of the planet, but views from the highest point are generally greater the larger the planet.
The four rocky planets of the solar system are Mercury, Venus, Earth and Mars. Of these, Mars is the third largest after Earth and Venus, but it has by far the highest mountain, Olympus Mons, at over 24,000 metres tall. From its peak, the distance to the horizon, if not obscured by Mars’s red dust, would be 404 kilometres, the most extensive view in the solar system.
Skadi Mons on Venus is less than half the height of Olympus Mons, at 11,520 m, but because Venus is 80 per cent bigger than Mars, the distance potentially visible from that peak is only a little less at 374 km. By comparison, on Earth, about 5 per cent bigger than Venus, climbers on Everest’s 8800-metre summit can see as far as 335 km. Mercury, the smallest of the planets, is just over a quarter of Earth’s size, and its highest peak, Caloris Montes, is only 3000 m, so if you could stand on top of it, the horizon would be 121 km away.
Jupiter’s moon Io has the fourth most distant vistas in the solar system at 258 km, seen from its highest mountain at 18,000 m.
On the asteroid Vesta, orbiting between Mars and Jupiter, there is a large impact crater whose rim is up to 25 km tall, making it possibly higher than Olympus Mons. Vesta has a diameter of just 529 km, however, so the distance visible from its peak is only 118 km.
The gas giants of the outer solar system can’t be said to have mountains, but if one were possible on the largest, Jupiter, which has a diameter of nearly 140,000 km, it would only need a peak of 1167 m for you to be able to see the same distance as from the top of Olympus Mons on Mars.
Martin Gellender
Brisbane, Australia
The distance that you can see to the horizon on a smooth, featureless plain varies with the square root of the radius of the planet and the height of the observer above “ground level”. So, on a featureless spherical rocky planet, the distance to the horizon would double if the radius were four times as much (although the planet would have 64 times the mass and four times the gravity at its surface).
The rocky planets in our solar system do have some flat, featureless areas (lava flows and oceans), but much of their surface is covered with mountains, hills and impact craters. The height of these features varies widely and doesn’t simply correlate with the gravity of the planet. So, the distance you could see to the horizon would depend largely on the local topography and the elevation of the observer.
Mike Follows
Sutton Coldfield, West Midlands, UK
According to a model I have come up with, we would see farthest on planets whose average density is smallest while still being rocky. This is because the maximum distance to the horizon that could be seen from a planet’s highest mountain is inversely proportional to the planet’s average density.
The distance in kilometres is about 1.6 million divided by the density of the planet (expressed in kilograms per cubic metre). This certainly works for Venus, Earth and Mars, giving maximum distances to the horizon of about 290, 295 and 410 km that can be seen from the tallest mountains that could exist in theory, given the following assumptions.
My model assumes that all the mountains are made of granite with a density of 2700 kg/m3. It also assumes that each planet has a uniform density, and it takes no account of mountain-building mechanisms or erosion or even the refraction of light by any atmosphere that might be present.
As a mountain gets taller, the weight acting down on its base increases until the rock there starts to deform or melt. The weight of an object on the surface of a planet increases with gravitational field strength.
This means that planets with bigger gravitational field strengths have shorter mountains because the weight required to deform the rock at their base is achieved with less mass.
Everest is two and a half times shorter than Olympus Mons on Mars because the gravitational field strength on the surface of Earth is just over two and a half times what it is on the surface of Mars.
All else being equal, we should see farther from a taller mountain. However, a smaller value for the gravitational field strength at its surface implies a smaller planet, where the ground falls away over a shorter distance, reducing how far we might otherwise have seen.
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