Two hypothetical planets of masses m1 and m2 and radii r1 and r2, respectively,

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.
(a) When their center-to-center separation is d, find expressions for the speed of each planet and for their relative speed. (Use any variable or symbol stated above along with the following as necessary: G, the gravitational constant.)
v1 =
v2 =
vr =

(b) Find the kinetic energy of each planet just before they collide, taking m1 = 2.60 1024 kg, m2 = 7.00 1024 kg, r1 = 2.80 106 m, and r2 = 5.80 106 m.
K1 = J
K2 = J

Explanation / Answer

a)G*m1*m2/d=0.5*m1*vi^2+0.5*m2*v2^2 m1v1=m2v2 vr=|v1-v2| From the 1st 2 equations, solve for v1 and v2. and then find vr from the 3rd equation.

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