Question

Two neutron stars are separated by a distance of 1.0 x 1012 m. They each have a mass of 1.0 x 1030 kg and a radius of 1.0 x 105 m. They are initially at rest with respect to each other. As measured from that rest frame, how fast are they moving when (a) their separation has decreased to one-half its initial value and (b) they are about to collide

Answer 1

of Maso a heation mi a rx10 30 kg radius (8) a excosm Separated by distance (al Ixiohm Petalic Groutadiad Enels] (Q) ? -Gom ४ 6.67X10"x (1030)? U, 2 I X2012 6, 2-6.62x10 x1037 J (@l Gravitatiana potential Eredyny when separated by half the dishane -6.62x16" +(1029) ? Uza Ź (1xcole) Tv Ų 2-1.334 X 1038 J By wing Conservation law' law of Enals otke z U₂ + x Ez The Meatrons are .. KEco initially of rest . K & - 2

1 2 mu? t / mut . O,.Uz mu² z 2 U-U₂ 30 JoxV (6.67710²7) - (-1,8342.10 (a) Velocity when Ve 8167 ml separation has deckosed to holfo 67 Gravitatiana Energy when they ore about to Potential Collide GX/1030) ? helg 3 =-3.335x10 2 %105 20 .: By By using law of Conservation of Energy 0,4 KE, a ₂ tk Ez (ir KE,=c) KE? 0,-03 & mu ²d žmu 2 6606741037) (- 3.335 yordy mu²2 24 3.335 xlo labo xv². 3.335 xolohy velocity when about to callao 12 1.826x107 mly