- #1

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Let’s calculate the gravitational field due to the Earth at a distance equal to the moon’s distance from the Earth, the radius of the moon’s orbit.

g = GM/r^2

Substituting r = 60 RE

g = GM/(60 RE)^ 2

Then squaring everything in the denominator

g = GM/(3600 RE^2)

Regrouping to get the term “(GM/RE^2)” alone

g = (GME/RE^2) (1/3600)

Then, using g = 9.8 m/s2 = GM/RE^ 2

g = (9.8 m/s^2) / 3600

g = 0.0027 m/s^2

g = 2.7 x 10^-3m/s^2 towards the center of the Earth

But orbital period of the moon is 27.3 days. So how do I proceed from here to get the answer as 27.3?