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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
suntoearth = 1.5x10^8 km, moontoearth = 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
I was just thinking about the duration of a lunar eclipse on my way home
suntoearth = 1.5x10^8 km, moontoearth = 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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