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Question: At a certain instant, the earth, the moon, and a stationary 1070 kg spacecraft lie at the vertice...

At a certain instant, the earth, the moon, and a stationary 1070 kg spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84×105km in length.

Find the direction of the net gravitational force exerted on the spacecraft by the earth and moon. State the direction as an angle measured from a line connecting the earth and the spacecraft.

Explanation / Answer

Mass of Earth = 6*1024 kg

mass of Moon = 7.35*1022 kg

mass of satellite = 1070 kg

length of side of equiliateral triangle = 3.84*108 m

Force exerted by Earth on satellite = (6.674*10-11 * 6*1024*1070)/(3.84*108)2 = 2.9 N (towards Earth)

Force exerted by Moon on satellite = (6.674*10-11 * 7.35*1022*1070)/(3.84*108)2 = 0.036 N (towards Moon)

Angle between the forces = 60o

Total force on satellite along line joining satellite and Earth = 2.9+0.036*cos60=2.918 N

Total force on satellite acting along line perpendicular to line joining satellite and earth = 0.036*sin60=0.031 N

The direction of resultant force measured as angle from line joining Earth and satellite = tan-1(0.031/2.918) = 0.61o

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