Physics

Planet Jupiter revolves around the Sunin 12 years (3.79 X 10^8 sec. What is its mean distance from center of Sun? mass of sun is 1.99 x 10^30 kg.

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  1. F = m A
    A = Ac = v^2/R
    so m A = Mjupiter v^2/R (toward sun)
    F = G Msun MJupiter /R^2 (toward sun)
    so
    G Msun/R^2 = v^2/R
    G Msun = v^2 R
    Time around = circumference /v
    T = 2 pi R/v
    so
    v = 2 pi R/T
    v^2 = (2pi)^2 R^2/T^2
    so
    G Msun = (2 pi)^2 R^3/T^2
    (which by the way is Kepler's Third Law)
    so
    R^3 = G Msun T^2/(2 pi)^2
    G is 6.67*10^-11
    so
    R^3 = 6.67*10^-11*1.99*10^30*14.36*10^16 /39.48

    R^3 = 4.828*10^35
    = .4828 * 10^36
    so
    R = .784 * 10^12 = 7.84 * 10^11 meters

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