8x mass probably means THOUSANDS of g’s higher gravitational acceleration, if it keeps the same relative density as earth, or thereabouts.
Actually, the gravity does not rise as fast as the mass.
For this example, the mass ratio is 8.47.
Assuming identical density then the planet would have a radius which exceeds that of earth by the cube root of the mass ratio, or 8.47-1/3 = 2.04
Gravitational force is calculated as F = G*m1*m2/r2
IF m1 (the mass of a planet) increases by a factor of 8.47 and the radius increases by 2.04, then the resulting gravitational force increases by 8.47/(2.04)2 = 2.04
Hey, look at that! We now have a rule of thumb for gravitation. Assuming identical densities, the gravity of a planet changes proportional to the radius change.
Let's try this out on Mars. From Wikipedia, the radius of Mars is smaller than that of Earth by a factor of 2106/3959, or 0.53
We should expect the gravity at the surface of Mars to be, then, 0.53 times Earth's gravity. But (also from Wikipedia) we find that Mars has a surface gravity of just 0.376 times that of Earth. What went wrong?
The answer is given by looking at the densities of the two planets. Earth has a density of 5.51 and Mars has a density of 3.93 or only 71% And sure enough, if we multiply the gravity we calculated times the density percentage, we get 0.53 * 0.71 = 0.376
The initial density assumption was wrong but when taken into account we get the right answer.
Let's try Jupiter. The radius ratio is 11.209 times that of Earth. Is the gravity 11.2 times that of Earth? No! It is only 2.528 times that of Earth.
Let's calculate the ratio of densities. The density of Jupiter is 1326 kg/m3 or 1.326 gm/cm3
Earth's density was 5.51, so the ratio of densities is 1.326/5.51 or 0.241
So, if we multiply our initial "rule of thumb" value of 11.209 by 0.241 we get gravity at the surface of Jupiter of 2.70 times that of Earth, close to the Wikipedia value of 2.528
We're still off by a factor of 2.70/2.528 or about 7% hign. Let's all see if we can find the missing mass (or is it mysteriously excess radius?)