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The masses and radii of the earth an moo...

The masses and radii of the earth an moon are `M_(1) and R_(1) and M_(2), R_(2)` respectively. Their centres are at a distacne d apart. Find the minimum speed with which the particle of mass m should be projected from a point mid-way between the two centres so as to escape to infinity.

Text Solution

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The `P.E.` of the mass at `d//2` due to the earth and the moon is
`U=(-GM_(1)m)/(d)xx2-(GM_(2)m)/(d)xx2`
or `U=(2GM)/(d)(M_(1)+M_(2))` (numerically) `=(1)/(2)mV_(e)^(2)=U`
`V_(e )=2sqrt([(G)/(d)(M_(1)+M_(2))])`
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