1/5/2014 11:00 PM 61.5/100 11Bl201402 PM Grad estion 2 ol 11 During a solar ecli

Question

1/5/2014 11:00 PM 61.5/100 11Bl201402 PM Grad estion 2 ol 11 During a solar eclipse the Moon is positioned directly between Earth and the Sun. Find the magnitude of the net gravitational force acting on the Moon then, due to both Earth and the Sun. The masses of Earth, and the Moon are 199 x10 kg, 5.98 x10 kg, and 7.36 x10 kg, respectively. The Moon's mean distance from Earth is 384 *10 m. and Earths mean distance from the Sun is 1.50 x10 m. The gravitational constant is G. 667 10 Nm kg What is the direction of this force? O Toward the Sun O Elsewhere O Toward Earth O Toward Venus O Previous Give up s View Soluuan check Answer O Next SExk

Explanation / Answer

First calculate the force between each i.e Sun on moon; Sun on Earth; moon on Earth. Then we will add them appropriately.

Now F(S-E) = GMm/r^2 = 6.67x10^-11*1.99x10^30kg*5.98x10^24/(1.5... = 3.53x10^22N

F(S-moon) = 6.67x10^-11*1.99x10^30*7.36x10^22/(1.50x... = 4.34x10^20N

F(E-moon) = 6.67x10^-11*5.98x10^24*7.36x10^22/(3.84x... = 1.99x10^20N

a) Both the sun & moon pull to the left on Earth so the two forces add

So F= 3.53x10^22N + 1.99x10^20N = 3.55x10^22N to the left

b) Now the sun pulls to the left and earth pulls to the right so they will subtract
so 4.34x10^20 - 1.99x10^20 = 2.35x10^20N toward the sun.

c) Now both pulled toward the rt so F = 3.53x10^22+ 4.34x10^20 = 3.57x10^22N to the rt

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