Anonymous
Anonymous asked in Science & MathematicsPhysics · 4 months ago

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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  • NCS
    Lv 7
    4 months ago
    Favourite 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

  • 4 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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