Exercise 2: Angular Momentum

If a small mass star orbiting a larger mass star is twice as close at periastron than it is at apastron, how does its velocity change through its orbit?

If our Sun will shrink by a factor of 100 when it becomes a white dwarf, then how fast will it rotate on its axis? The Sun's current rotation period is appoximately 25 days and its current radius is 7 x 105 km (ignore the mass loss processes and assume the white dwarf is one solar mass).

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