My N ·0/9 points | Previous Answers Walker5 12.P008 When the Earth, Moon, and Su

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My N ·0/9 points | Previous Answers Walker5 12.P008 When the Earth, Moon, and Sun form a right triangle with the Moon located at the right angle, as shown in the figure below, the Moon is approaching its third quarter. (The Earth is viewed here from above its north pole.) Find the magnitude and direction of the net force exerted on the Moon. Give the direction relative to the line connecting the Moon and the Sun. 4.30e31 X N counterclockwise from the Moon-to-Sun ray Sun Moon Earth Submit Answer Save Progress -10 points Walker5 12.P010. My N

Explanation / Answer

Both the sun and the Earth exert attractive gravitational force on the Moon.

From the equation of gravitational force F_sun = G M_moon M_sun / ( r_ms)^2

                             = 6.67 *10^-11 * 7.35*10^22kg *2.00*10^30 kg / ( 1.50*10^11m)^2

                             = 4.357*10^20 N

F_Earth = GM_m M_E / ( r_me)^2

= 6.67*10^-11 * 7.35*10^22 kg * 5.97*10^24 kg / ( 3.84*10^11m)^2

= 1.985*10^20 N

F_net   = F_s^2 + F_E^2

            = ( 4.357*10^20 N )^2 + (1.985*10^20 N)^2

           = 4.79*10^20 N

direction = tan^-1 (1.985*10^20 N / 4.357*10^20 N )

= 24.4 degrees towards the earth from sun to moon.

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