A satellite of mass `m` is launched vertically ` upwards with an initial speed is from the ` surface of the earth.After it reaches height R ` (R=` radius of the earth) it ejects a rocket of ` mass `(m)/(10)` so that subsequently the satellite ` moves is a circular orbit.The kinetic energy ` of the rocket is `(G` is the gravitational ` constant; M is the mass of the earth).` `
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at height R, using a free body diagram, we get to see that the critical velocity is equal to the K.E smaller satellite. the gravitational force acting on the satellite will be perpendicular to these forces. resolve them and youll get the answer. it comes out to be somewhat around 5m[u^2- 119GM/200R]
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consider conservation of energy
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