Question

Two hypothetical planets of masses m1 and m2 and radii r1 and r2, respectively, are nearly at rest when they are an infinite distance apart. Because of their gravitational attraction, they head toward each other on a collision course. Note: Both the energy and momentum of the isolated two planet system are constant.

(b) Find the kinetic energy of each planet just before they collide, taking m1 = 1.80* 10^24 kg, m2 = 9.00* 10^24 kg, r1 = 3.40* 10^6 m, and r2 = 5.20* 10^6 m.

please could you help me get kinetic energy
k1 = ?
k2 = ?

please thank you

Answer 1

Since the masses are in a 1:5 ratio, and the total momentum remains zero, the large mass will have 1/5 the velocity of the smaller mass at all times.

They collide when the separation distance is d = r1 + r2 = 5.6*10^6 m

At that time, the total kinetic energy equals the potential energy loss, which is
KE = G*M1*M2/d

With 1/5 of the mass of M2, M1 will have 5 times the velocity and 5 times its kinetic energy, giving it 5/6 of the total KE. M2 will have the other 1/6.