A rough calculation on the duration of lunar eclipse

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SUMMARY

The discussion focuses on calculating the duration of lunar eclipses using specific astronomical measurements. The calculations indicate that a partial lunar eclipse lasts approximately 3.25 hours, while a total lunar eclipse lasts about 1.76 hours. Key parameters include the distances from the Earth to the Sun and Moon, as well as the Earth's radius. The calculations are accurate, but it is noted that the Moon does not always pass through the densest part of the Earth's shadow, which can affect actual eclipse durations.

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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
 

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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.
 
russ_watters said:
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
 

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