Two planets of mass 3 x 1025kg are release from rest 1.5 x 1012 m apart. What is the speed of the planets when they are half this distance apart?

Help! I've been stuck on this for a good bit! I cant seem to find a formula that can help me solve this! I can find the force but i don't know what to do with it!

I think this will help:

https://www.physicsforums.com/threads/two-bodies-attracting-via-gravitation.413391/

To find the speed of the planets when they are half the distance apart, you can use the concept of conservation of energy.

First, calculate the initial gravitational potential energy (U1) of the two planets when they are 1.5 x 10^12 m apart. The formula for gravitational potential energy is:

U = -(G * m1 * m2) / r

where G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two planets, and r is the distance between them.

Substituting the given values, we get:

U1 = -(6.67 x 10^-11 N m^2/kg^2) * (3 x 10^25 kg)^2 / (1.5 x 10^12 m)

Next, calculate the final gravitational potential energy (U2) when the distance between the planets is halved. The formula remains the same, but you will use half of the initial distance:

U2 = -(6.67 x 10^-11 N m^2/kg^2) * (3 x 10^25 kg)^2 / (0.75 x 10^12 m)

Since energy is conserved, the initial potential energy (U1) will be equal to the final potential energy (U2):

U1 = U2

-(6.67 x 10^-11 N m^2/kg^2) * (3 x 10^25 kg)^2 / (1.5 x 10^12 m) = -(6.67 x 10^-11 N m^2/kg^2) * (3 x 10^25 kg)^2 / (0.75 x 10^12 m)

Now, solve for the speed of the planets (v):

v = sqrt((2 * (U1 - U2)) / (m1 + m2))

Plugging in the values and solving the equation will give you the required speed of the planets when they are half the distance apart.