Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass m is projected from the surface of the planet

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Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre

Acceleration due to gravity will be zero at $P$ therefore,
$\dfrac{GM}{{x}^{2}} = \dfrac{G9M}{( 8R - x{)}^{2}}$
$8R - x = 3x$
$x = 2R$

Apply conservation of energy and consider velocity at $P$ is zero.

$\dfrac{1}{2}m{v}^{2} - \dfrac{GMm}{R} - \dfrac{G9Mm}{7R} = 0 - \dfrac{GMm}{2R} - \dfrac{G9Mm}{6R}$
$∴ V = \sqrt{\dfrac{4}{7}\dfrac{GM}{R}}$

Suppose two planets (spherical in shape) of radii R and 2R, but...

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