Planet Z-34 has a mass equal to 1/3 that of Earth, a radius equal to 1/3 that of
ID: 1515133 • Letter: P
Question
Planet Z-34 has a mass equal to 1/3 that of Earth, a radius equal to 1/3 that of Earth, and an axial spin rate 1/2 that of Earth. With g representing, as usual, the acceration due to gravity on the surface of earth, find the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-34.
** I substitued in the 1/3M and 1/3R into the accleration equation and got down to a= 3mg/r^2, however i don't understand how the axial spin rate affects the accleration due to gravity. Please explain this.
Explanation / Answer
assume that axial spin rate has significant effect on g
so on equator
g = GM/R^2 - w^2R
for planet
g' = 3GM/R^2 - w^2*R/12 = 3(g - w^2R) - w^2R/12 = 3g - 37w^2R/12
Now, if w does not have significant effect
g' = 3g