During a solar eclipse the Moon is positioned directly between Earth and the Sun

Question

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 the Sun, Earth, and the Moon are 1.99 x 100 kg, 5.98 × 1024 kg, and 7.36 x 10%2 kg, respectively. The Moon's mean distance from Earth is 3.84 × 108 m, and Earth's mean distance from the sun is 1.50 x 1011 m. The gravitational constant is G = 6.67 × 10-11 NmTkg2 Number What is the direction of this force? O Toward the Sun O Toward Earth O Elsewhere O Toward Venus

Explanation / Answer

F(e-m) = GMm/r^2

F(e-m) = 6.67*10^-11*5.98*10^24*7.36*10^22/(3.84*10^8)^2 = 1.99*10^20 N

F(s-m) = 6.67*10^-11*7.36*10^22*1.99*10^30/(1.496*10^11)^2 = 4.36*10^20 N

Fnet = F(m-e) - F(s-m) = - 2.37*10^20 N

Fnet = 2.374*10^20 N

in direction toward the sun

F = GMm/r^2

space station distance from earth center = 545000+6370000 = 6915000 m

F = 6.67*10^-11*5.98*10^24*2050/(6195000)^2 = 21305.82 N

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