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For one of my project in school, i need to calculate the travel time to the moon. To do that, I thought to use Kepler's third law which is :

(2(pi) / P )^{2}* a^{3}= GM

where :

P : period of travel

a : major semiaxes (not sure in english, but it is the half the longest radius of the ellipse) : in this case half of the earth-moon distance : 380 400km/2= 190 200km

G : gravitational constant : 6.67E-11

M : Earth's mass : 5,972E24 kg

Whit these values, my period is equal to 9 days and 13 hours, so the travel time to the moon is the half of that and is 4 days and 18 hours.

But in the apollo program, it takes about 3 days to go to the moon. Can someone help me to figure out why does I have almost 2 days of difference.

Is it because I didn't took notice of the moon gravity, because the spacecraft wasn't doing an ellipse like this or for another reason?

Thank you for your help

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# Travel time for apollo to the moon with Kepler's thirs law

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