Nov
17
Planet X has two times the diameter and eight times the mass of the earth.?
Planet X has two times the diameter and eight times the mass of the earth.
What is the ratio gx : ge of gravitational acceleration at the surface of planet X to the gravitational acceleration at the surface of the Earth?
Answer by mathematician
Force goes up directly with the mass of the planet and down with the inverse square of the radius. So, the mass would multiply by 8 and the radius would divide by 2^2.
What do you think? Answer below!
The acceleration due to gravity at a planet’s surface is given by:
a = GM/(r^2)
where G is the universal gravitational constant, M is the mass of the planet (in kg) and r is the radius of the planet (in meters). If you multiply the mass by 8 while changing nothing else, you multiply the surface gravity by 8 also. However, doubling the radius (which is in the denominator) does more than cutting the surface gravity in half; because r is squared in this equation, halving the radius will quarter the surface gravity. When you take these two changes into account (mass x 8 and radius x 2), you find that Planet X’s surface gravity would be twice that of Earth.
2
8 times mass over 2 squared = 2