- #1

ArticMage

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## Homework Statement

Deep in space, two neutron stars are separated (center-to-center) by a distance of 18 X 106 km apart. Neutron star A has a mass of 153 X 1028 kg and radius 52000 m while the neutron star B has a mass of 159 X 1028 kg and radius 72000 m. They are initially at rest with respect to each other.

a) With respect to that rest frame, how fast are the stars moving when their separation has decreased to one-half its initial value

b) How fast are each moving the instant before they collide?

## The Attempt at a Solution

a) I set this up as follows.

Uia + Uib = Kfa + kfb +Ufa + Ufb

where U is potential energy and K is kinetic.

So i get -2*Ma*Mb*G/R = .5Ma*Va^2 + .5Mb*Vb^2 - 2Ma*Mb*G/R/2

Using conservation of momentum i get Ma*Va=Mb*Vb So Va=Mb*Vb/Ma

sub that in the above equation and solve for Vb I end up with somthing like sqrt( 2*(-2Ma*Mb*G/R +2Ma*Mb*G/R/2) / (Mb^2/Ma + Mb) ) = Vb

i get 105455 m/s and its wrong.

btw i am using 18^9 m for radius

for part b i would do a similar thing except set the radius for each equation equal to the radius for the planets for the final potential energy. I haven't tried this yet because if the first doesn't work I assume I am doign it wrong.