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23 April, 01:33

The planet jupiter revolves around the sun in a period of about 12 years (3.79 * 108 seconds). what is its mean distance from the center of the sun? the mass of the sun is 1.99 * 1030 kilograms.

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  1. 23 April, 01:35
    0
    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
  2. 23 April, 01:41
    0
    7.8 * 1011 meters ...
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