A) Find the magnitude of the net gravitational force exerted in the spacecraft b

Question

A) Find the magnitude of the net gravitational force exerted in the spacecraft by the earth and moon (units in N)
B) Find the direction of the net gravitational force exerted on the spacecraft by the earth and moon. State the direction as an angle from a line connecting the earth and a spacecraft. (units in degrees)
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 moon? You can ignore any gravitational effects due to the other planets or the sun. (units in J) HW 12B Item 4 Item 4 At a certain instant, the earth, the moon, and a stationary 1040 kg spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84 x 105 km in length

Explanation / Answer

Let's place satellite at origin, earth on x axis and moon on top of the triangle

a) Fx= G ( Me) (Ms) / (3.84x 10^8)^2 + G ( Mm) ( Ms) cos 60 / (3.84x 10^8)^2 = 470.43 x 10^ -27 ( 6x 10^24 )= 2.82 N apprx

Fy = G ( Mm) ( Ms) sin 60 / (3.84x 10^8)^2 = ( 6.67 x 10^-11) (1040) ( 7.347 x 10^22) (0..866)/ (14.745 x 10^ 16) = 2993. 245 x 10^ -5= 0,.03 N appprx

Fnet = 2.83 N apprx

b) angle = tan^-1( Fy/Fx)) = 0,608 degree

c) Minimum work = 6.67 x 1040 (6.04 x 10^-5)/ 3.84 = 0.1091 J apprx

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