Jan
29
Planet X has five times the diameter and three times?
Planet X has five times the diameter and three times the mass of the earth. What is the ration gx: ge of gravitational accleration at the surface of planet X to the gravitational accleration at the surface of the Earth?
Answer by green_meklar
The surface gravity would be about 5.9 m/s^2, or 0.6 times that of Earth.
Know better? Leave your own answer in the comments!
g=GM/R^2, M=mass of the planet,R=radius of the planet
g(X)/g(E)
=M(X)R^2(E)/M(E)R^2(X)
=[M(X)/M(E)][R^2(X)/R^2(E)]
[3][25]
=75
Newton said that the gravitation acceleration at distance r from the center of a sphere of mass M is proportional to the mass of the sphere and inversely proportional to r-squared. That means that it is proportional to M/(r-sq)
So the mass is three times that of Earth. That’s in the numerator. And if the diameter is five times that of Earth, then the radius also is five times that of Earth. Square that to get 25. That is in the denominator (“inversely proportional”).
So the ratio is 3/25, or 12/100 = 12% — much weaker than Earth.