The ratio between gravitational force of planet x and y

[gomess]

Homework Statement

Planet X has a radius double of Planet Y. Planet X also has a mass that is double planet Y. How do the surface gravitational fields of X and Y compare?

Homework Equations

g=GM/R

The Attempt at a Solution

So because were looking for the ratio of gx to gy, we can use the equation gx = n(gy) and say that n = gx/gy. So since Planet X has a radius double of Planet Y, we can say that Rx = 2Ry. Also we can say that Mx = 2My. So this turns out to be (2MyG/2Ry) / (MyG/Ry) = n. So this becomes 2MyGRy/2RyMyG = n. Cancelling out Ry, My, and G leaving 2/2 = n. This would say that gx = gy ? Does this make sense to say that at different masses and radii the planets have equal gravitational force?

 

[lep11]

Shouldn't R be squared?

 

[gomess]

No, that would be the force of gravity between two objects, g = GMm/r^2. This is just the force of gravity the object exerts, or gravitational field i guess

 

[lep11]

G= γMm/r^2, on the other hand G=mg
so mg= γMm/r^2
g=γM/r^2

 

[gomess]

oh i see, you were right, the R is squared. LOL thank you very much, i appreciate it