What Is the Relative Velocity of Two Colliding Planets?

[lzh]

Homework Statement

Given: G = 6.67259 × 10^−11 Nm2/kg2
Two hypothetical planets of masses 2.5 × 10^23 kg and 7.8×10^23 kg and radii 3.2×10^6 m
and 7.1×10^6 m, respectively, are at rest when
they are an infinite distance apart. Because
of their gravitational attraction, they head
toward each other on a collision course.

When their center-to-center separation is
4.5 × 10^8 m, find their relative velocity. An-
swer in units of m/s.

Homework Equations

The Attempt at a Solution

F=GMm/r^2
M=7.8e23 kg
m=2.5e23 kg
Ki+Ui=Kf+Uf
r=4.5e8+3.2e6 +7.1e6=460300000m
0+0=.5mv^2+(-GMm/r)
.5v^2=GM/r
v=475.54 m/sIs this answer correct?

 

[lzh]

I just tried to take the velocity from above and added the following:
v=at
475.54=at
F=ma
F=GMm/r^2
a=F/m
475.54/a=t

then I took the t value and tried to solve the velocity for the M mass. Then I found the difference between the two velocities. However, this is not right...any help is greatly appreciated!

 

[Dick]

In the frame where the origin is the center of mass of the two planets (which is where you should be working), the two planets don't move with equal velocity. They have to have 0 net momentum as well. m*v=M*V.