Summer 2016 Item 4 tem 4 Part A At a certain instant, the 1120 kg triangle whose

Question

Summer 2016 Item 4 tem 4 Part A At a certain instant, the 1120 kg triangle whose sides are 3.84 x 10% km in length. Find the magnitude of the net gravitational force exerted on the spacecraft by the earth and moon ? F. Part B Find the direction of the net gravitational force exerted on the spacecraft by the earth and moon, State the direction as an from a line connecting the earth and the spacecraft Express your answer to three significant figures. My Answers Give Up Part C What is the minimum amount of work that you would have to do to move the spacecraft to a point far from the earth and mo ignore any effects due to the other planets or the sun

Explanation / Answer

a) Given m=1120kg, d=384000km, M1=7.35e+22 kg, M2=5.97e+24 kg, G=6.67e-11 Nm²/kg²

The force due to the moon is: Fm = GM1m/d² = 0.0372N
The force due to the earth is: Fe = GM2m/d² = 3.025N

The net force magnitude can be found by decomposing each force into orthogonal parts, summing parallel vectors, then combining by Pythagorean theorem. I used earth-to-spacecraft line as x-axis to simplify calculations.
F = ((Fe+Fmcos60°)² + (Fmsin60°)²) = 3.04N

b) And the direction of net force is: = atan((Fmsin60°) / (Fe+Fmcos60°)) = 0.6°

c) W = [6.673(5.97*10^2 + 7.35)*10^3]/3.84 = 1.12*10^9 J

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