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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

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

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