The percentage change in the acceleration of the earth towards the Sun from a total eclipse of the Sun to the point where the Moon is on a side of earth directly opposite to the Sun is
(Take r₁ as the distance between the sun and the earth, r₂ as the distance between the earth and the moon, M_s, M_e and M_m are the masses of the sun, the earth and the moon respectively)

Question

The percentage change in the acceleration of the earth towards the Sun from a total eclipse of the Sun to the point where the Moon is on a side of earth directly opposite to the Sun is

(Take r₁ as the distance between the sun and the earth, r₂ as the distance between the earth and the moon, M_s, M_e and M_m are the masses of the sun, the earth and the moon respectively)

Infinity Learn · Accepted Answer

During total eclipse, total attraction on the Earth due to the Sun and the Moon,   $$F1=GMsMer12+GMmMer22When$$ the Moon goes on the opposite side of the earth, the effective force of attraction $$isF2=GMsMer12$$−$$GMmMer22Change$$ in force, Δ$$F=F1$$−$$F2=2GMmMer22Change$$ in acceleration of the earth,Δ$$a=$$Δ$$FMe=2GMmr22Average$$ force on the earth,$$Fav=F1+F22=GMsMer12Average$$ acceleration of the earth,$$aav=FavMe=GMsr12Percentage$$ change in acceleration isΔaaav×$$100=2GMmr22$$×$$r12GMs$$×$$100=2r1r22MmMs$$×$$100$$

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