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I Moon revolution period 27.32, but got 27.53 from equation?

  1. Aug 28, 2016 #1
    Hello,

    I'm trying to calculate Moon revolution period but always got 27.53 instead of 27.32.
    G = 6.674e-11 (m^3 kg^-1 s^-2)
    M = 5.9724e24 (kg) from http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
    R = 384400000 (m) Earth Moon distance

    From 4π^2 * R^3 = GM*T^2,
    got moon revolution period T = sqrt(4π^2 * R^3/(GM))

    Earth day in seconds = 23*60*60 + 56*60 + 4
    so moon revolution period in Earth day = 27.53

    Why it is not 27.32? Is it because the orbit is not circular? But period should be same if R is the semi major axis or the orbit.

    If I revise the formula and consider Moon gravitational force to the Earth,
    let m be the mass of Moon
    T = sqrt(4π^2 * R^3/(G(M+m)))
    the moon revolution period in Earth day = 27.36, a bit closer but still some error (rounding error?)
     
  2. jcsd
  3. Aug 29, 2016 #2

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    Consider how far the earth revolves in the lunar month?
     
  4. Aug 29, 2016 #3
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