The moon travels an elliptical path with Earth as one focus. The maximum distance from the moon to the earth is 405, 500 km and the minimum distance is 363,300 km. What is the eccentricity of the orbit?

Answer

`0.05489`

Explanation

As shown in the figure, the earth is at focus. A and the moon is travelling in an ellipitical orbit.
The maximum distance from the moon to the earth is AC=405500 km.
The miniumum distance from the moon to the earth is AB=363300km.

Consideering the equation of the orbit as
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
we have a-ae =363300km
and a+ae=405500
`:. (a+ae)/(a-ae)=(405500)/(363300)`
`or (1+e)/(1-e)=(4055)/(3633)`
or `e=(4055-3633)/(4055+3633)=(422)/(7688)~~0.05489`