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Statement of a problem № 3337

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A satellite of mass m is orbiting in a circular orbit of radius r and velocity v around the earth of mass M . Due to an internal explosion, the satellite breaks into two fragments each of mass m/2. In the frame of reference of the satellite, the two fragments appears to move radially along the line joining the original satellite and the centre of the earth, each with the velocity v0 /2. Show that immediately after the explosion each fragment has total energy -3GM/16r and angular momentum m/2sqrt(GMr), with reference to the centre of the earth.

Solution:
A satellite of mass m is orbiting in a circular orbit of radius r and velocity v

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