Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon
The gravitational force of attraction due to earth on the moon follow the inverse square law due to which the as seen from the earth, the moon revolves around it in circular orbit.
When observed from the sun, moon experiences the gravitational pull due to both, the sun and the moon which results in a net force thus changing the trajectory of moon, and hence it does not revolve in strictly elliptical due to influence of both sun and earth.
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