Universal law of gravitation(variables)

[captainsmith1]

Homework Statement

A planet has twice the mass of earth, but both planets share the same acceleration of gravity. The radius of the new planet in terms of the radius R of Earth is...?

Homework Equations

F=G(m₁m₂/r²), G being the universal gravitation constant

The Attempt at a Solution

i think you have to manipulate the equation in some way but i can't figure out what to do first.

 

[ApexOfDE]

From N's law, you have:

$$G\frac{Mm}{r^2} = ma_g$$

Because Earth and planet have same acceleration of gravity => a_g(E) = a_g(P) => relationship between masses and radii => radius of planet.

 

[captainsmith1]

thanks, i understand now