Physics Gravitation

Question

If two planets have the same surface gravity, but planet B has twice the mass of planet A, which has a radius of r, what is the radius of planet B?

Answer 1

If F = Gm•m_PA/r_A² where m_PA is the mass of the planet A, r_A is the radius of planet A, and F = ma (or "mg" in this case), then we can calculate g by equating the two equations:

Gm•m_PA/r_A² = mg then, dividing both sides by "m", we get:

g = Gm_PA/r_A² then if "g" is the same on both planets, then:

Gm_PA/r_A² = Gm_PB/r_B² then dividing both sides by "G" we get:

m_PA/r_A² = m_PB/r_B² but if m_PB = 2m_PA then:

m_PA/r_A² = 2m_PA/r_B² then dividing both sides by m_PA we get:

1/r_A² = 2/r_B² and then cross multiplying we get:

r_B² = 2r_A² or

r_B = √(2r_A²) or, replacing r_A with "r" we get:

r_B = √(2r²) = (√2)r

Answer 2

the force of gravity goes as the mass divided by the square of the distance.

Set up the equations:

F(A) = G*m(A)/(r(A))^2

F(B) = G*m(B)/(r(B))^2

Solve each one for r, then replace m(B) with 2*m(A