Two neutron stars are separated by a distance of 4.0 Times 10^10 m. They each ha

Question

Two neutron stars are separated by a distance of 4.0 Times 10^10 m. They each have a mass of 1.0 Times 10^10 kg and a radius of 1.0 Times 10^3 m. They are initially at rest with respect to each other. As measured from that rest frame, how fast are they moving at the following positions? Their separation has decreased to one-half its initial value. They are about to collide. Did you conserve the mechanical energy (the sum of the kinetieand potential energies)? Did you use GMm/r for the potential energy?

Explanation / Answer

a)

Conserving mechanical energy:

GMm/(R/2) - GMm/R = 2*(0.5*m*v^2)

So, GM/R = v^2

So, 6.67*10^-11*1*10^30/(4*10^10) = v^2

So, v = 40835 m/s <-------answer

b)

When they are about to collide, conserving mechanical energy:

GMm/((2*10^5)) - GMm/R = 2*(0.5*m*v^2)

So, GM/(2*10^5) - GM/R = v^2

So, 6.67*10^-11*1*10^30(1/(2*10^5) - 1/(4*10^10)) = v^2

So, v = 1.83*10^7 m/s <--------answer

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