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13 April, 22:42

An earth satellite remains in orbit at a distance of 13594 km from the center of the earth. what is its period? the universal gravitational constant is 6.67 * 10-11 n · m2 / kg2 and the mass of the earth is 5.98 * 1024 kg.

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  1. 13 April, 23:59
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    Given: Mass of earth Me = 5.98 x 10²⁴ Kg

    Radius of satellite - radius of the earth

    r = 13,594 Km - 6,380 Km = 7,214 Km convert to meter "m"

    r = 7,214,000 m

    G = 6.67 x 10⁻¹¹ N. m²/Kg²

    Required: What is the period T = ?

    Formula: F = ma; F = GMeMsat/r² Centripetal acceleration ac = V²/r

    but V = 2πr/T

    equate T from all equation.

    F = ma

    GMeMsat/r² = Msat4π²/rT²

    GMe = 4π²r³/T²

    T² = 4π²r³/GMe

    T² = 39.48 (7,214,000 m) ³ / (6.67 x 10⁻¹¹ N. m²/Kg²) (5.98 x 10²⁴ Kg)

    T² = 1.48 x 10²² m³/3.99 x 10¹⁴ m³/s²

    T² = 37,092,731.83 s²

    T = 6,090.38 seconds or 1.7 Hr
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