A rough calculation on the duration of lunar eclipse

[Valium]

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

 

[russ_watters]

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.

 

[Valium]

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.

right, so this should be the longest duration of lunar eclipse