Ask Me Help Desk - Speed of a satellite

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Speed of a satellite

what is the speed of a satellite in orbit 270km above Mercuryls surface if the mass of Mercury is 3.30x10^23kg and the radius is 2.44x10^6m?

If the satellite is in circular orbit, then the gravitation acceleration must equal the centripetal acceleration.

Let be $M,R$ the mass and radius of Mercury, $r$ the distance from Mercury (here 270km), and $v$ the speed of the satellite.

Gravitation: $G\frac{M}{(R+r)^2}$
Centripetal: $v^2/(R+r)$

Then solve
$G\frac{M}{(R+r)^2}=v^2/(R+r)$
in v using problem's data.

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