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14 September, 21:00

Astronomers have discovered a new planet called "Xandar" beyond the orbit of Pluto (No, not really but I need a fake planet for this problem!). It has a satellite called "Jim" that orbits with a period of 12.9 days at a distance of 72,600 km. What is the mass of "Xandar"?

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  1. 14 September, 21:23
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    m = 1.82E+23 kg

    Explanation:

    G = universal gravitational constant = 6.67E-11 N·m²/kg²

    r = radius of orbit = 72,600 km = 7.26E+07 m

    C = circumference of orbit = 2πr = 4.56E+08 m

    P = period of orbit = 12.9 d = 1,114,560 s

    v = orbital velocity of satellite Jim = C/P = 409 m/s

    m = mass of Xandar = to be determined

    v = √ (Gm/r)

    v² = [√ (Gm/r) ]²

    v² = Gm/r

    rv² = Gm

    rv²/G = m

    m = rv²/G

    mG = universal gravitational constant = 6.67E-11 N·m²/kg²

    r = radius of orbit = 72,600 km = 7.26E+07 m

    C = circumference of orbit = 2πr = 4.56E+08 m

    P = period of orbit = 12.9 d = 1,114,560 s

    v = orbital velocity of satellite Jim = C/P = 409 m/s

    m = mass of Xandar = to be determined

    v = √ (Gm/r)

    v² = [√ (Gm/r) ]²

    v² = Gm/r

    rv² = Gm

    rv²/G = m

    m = rv²/G

    m = 1.82E+23 kg
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