u/Financial_Bake9889

The void is roughly ≤ 9.8 km deep.

A mountain cannot grow infinitely tall because the pressure at its base increases with its height. Once this pressure exceeds the elastic limit of the rock, the base fails and begins to undergo plastic deformation .

Calculations derived from player movement, fall speeds, and vehicle mechanics indicate a acceleration due gravity on 4546B of roughly 7.3 to 8 m/s².

we can assume the elastic limit of the rock to be roughly 3 × 10⁸ N/m² ,which is an average value of the materials mountains are generally made up of on Earth, since 4546B is quite similar to Earth, but since we are on a geologically active volcano the elastic limit would be much lower due to the heat.

in the Lava Zones, temperatures range from 70° C to 1200°C near the core. If we assume the base of the Crater is heated to roughly 500°c ,the elastic limit drop from 3 ×10⁸ N/m² to roughly 1.5 N/m²

The pressure (p) which the mountain puts on its base is the force exerted by the mountain (f) divided by its area (a)

p = f/a

p = mg/a

[ * f = mg

* Where m is the mass of the mountain and

g is the acceleration due to gravity on

4546b. ]

p = ρgha/a

p = ρgh

[* m = ρha

* Where ρ is the density of the rock

* h is the height of the mountain ]

The pressure exerted by the mountain on its base has to be less than or equal to the the rocks elastic limit

ρgh ≤ 1.5 × 10⁸

h ≤ 1.5 × 10⁸/ρg

The density of the rock is roughly 3000 kg/m³

h ≤ (1.5 × 10⁸)/(3000 × 7.65)

h ≈ 6535 m

However the crater is underwater, which means it can be taller

To find the height of the mountain which is underwater we just account for the net density of the rock underwater, which is the density of water subtracted from the density of the rock, which gives us a value of 2000 kg/m³

h ≤ (1.5 × 10⁸)/(2000 × 7.65)

h ≈ 9803m

This is based on the assumption that the volcano we are on, is the tallest underwater mountain on 4536B which seems likely as we get a good view of it while leaving the planet.

This is just a rough estimate of the tallest underwater mountain physically possible on 4546B it doesn't mean that the volcano we are on hits the maximum possible height as that depends on several factors. However this tells us that the void cannot be deeper than 9.8 km.

This means that the void is almost as deep as the Mariana trench for as far as it stretches.

P.S. if 4536B wasn't volcanically active the abyss would be twice as much deeper doubling to 19.6 km. The heat of 4546B is actually the only thing keeping void so 'low'.

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u/Financial_Bake9889 — 8 days ago