Ratio between planet-size and terrain elevation?

Let's imagine we have an algorithm that produce an elevation-map for a sphere. I wonder if the ratio between the planet radius and the delta between the highest and lowest altitude is a constant or can be guessed depending a few factors (main chemical components of the planet, atmosphere thickness, ...). Of course, I speak about telluric planets.

For example, Earth has a delta of, approximately, 20 km (Mount Everest in Nepal is 8,848 m hight and Mariana trench is 10,911 m deep in Pacific Ocean). See Wikipedia for more details. And, radius is about 6300 km. So, the final ratio is 0,003 (radius/delta).

On Mars (see here), the highest point is the peak of Olympus Mons at 21,229 m, and the deepest is in the Hellas Impact Crater which is 8,200 m deep. So, the total delta is about 29 km. Then, Mars radius is about 3400 km, which makes a ratio of 0.008.

As you can see, the variation of this ratio between these two planets are quite different.

So, I would like to have some way of "guessing" this ratio (maybe I am missing a few factors that I did not take into account, the radius is probably not enough). My point is to be able to make a map-making algorithm that will stay within realistic elevations when computing the points.

It can also be that I am totally wrong and such ratio do not exist (or has absolutely no sense at all), but, then, I would like to have a few arguments about it.

EDIT

Just to make it clear, what I am looking for is an equation providing the delta of the elevation map (highest and deepest points) according to several parameters such as planet density and planet size (radius) and others...

Something like:

$$\Delta \text{(meter)} = \text{constant(m}^3\text{/kg)} \times \text{planet radius(meters)} \times \text{planet density(kg/m}^3\text{)}$$

EDIT 2

I have collected a few samples to illustrate the formula that I am looking for. I recall that I am looking for the elevation delta based on various physical parameters which are only linked to the physics and NOT evolution of the landscape (no tectonic activity, no erosion, ...).

         delta     radius    density        surface gravity
Earth    20 km     6300 km   5.51 g/cm^3    1g
Mars     29 km     3400 km   3.93 g/cm^3    .376 g
Mercury  30 km     2439 km   5.43 g/cm^3    .38 g
Moon     18 km     1700 km   3.34 g/cm^3    .16 g

Somehow, I suspect that the planet radius and the surface gravity are involved in the formula but I don't see quite well how they interact right now. And, I suspect that I am still missing one parameter.

posted about 10 years ago

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