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Stargazing A rough calculation on the duration of lunar eclipse

  1. Mar 4, 2007 #1
    I guess many have watched the lunar eclipse last night
    I was just thinking about the duration of a lunar eclipse on my way home

    sun-to-earth = 1.5x10^8 km, moon-to-earth = 384400 km
    R(Earth) = 6378 km, R(Sun) = 6.96x10^5 km, R(Moon) = 1378 km
    Moon's period around earth = 27.3 days

    x / (x +1.5x10^8) = 6378 / 6.96x10^5
    x = 1.39x10^6 km

    y = x - 384400 = 1.00x10^6 km

    z / 6378 = y / x
    z = 4610 km
    (I guess this is a good approximation for the figure is not to scale)

    For partial eclipse:

    384400 θ = 2z + 1378x2
    θ = 0.0312 rad

    t(partial) = θ /2π x 27.3 x 24 = 3.25 hours

    For total eclipse:
    384400 φ = 2z - 1378x2
    φ = 0.0168 rad

    t(total) = φ /2π x 27.3 x 24 = 1.76 hours

    Please comment and make amendments if you find any mistakes in my calculations
     

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  2. jcsd
  3. Mar 4, 2007 #2

    russ_watters

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    Staff: Mentor

    The calculations are fine, but you missed one thing: The moon need not (and typically does not) pass directly through the thickest part of the earth's shadow.
     
  4. Mar 6, 2007 #3
    right, so this should be the longest duration of lunar eclipse
     
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