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# The S.Shuttle releases a satellite into a circular orbit 545km above the Earth. How fast must the shuttle be moving when the release occurs?

The space shuttle releases a satellite into a circular orbit 545km above the Earth.

How fast must the shuttle be moving (relative to Earth) when the release occurs?

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- NCSLv 74 months agoFavourite answer
centripetal acceleration = gravitational acceleration

v²/R = GM/R²

v² = GM/R

v² = 6.674e−11N·m²/kg² * 5.98e24kg / (6.371e6+545e3)m

v² = 5.77e7 m²/s²

v = 7600 m/s

- Andrew SmithLv 74 months ago
The centripetal acceleration must equal the gravitational acceleration at this height. The gravitational acceleration reduces according to 1/r^2

v^2 / r = g *(re/r)^2 ->v = re * sqrt( g/r) = 6.37*10^6 * sqrt( 9.8/ ( 6.37*10^6+5.45*10^3) ) = 7.9 * 10^3 m/s

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