Help! The Lunatik is a military spacecraft on extended patrol in the vicinity of

Question

Help!

The Lunatik is a military spacecraft on extended patrol in the vicinity of the planet Eqrgp and its moon, with the mission of repelling Vegan invaders who threaten life on Eqrgp or on its moon, me Vegans' home base is on a planet of the star Vega. As it happens. Vegans are vegans, but still very vicious toward non- Vegan life forms, especially non-vegan ones. The captain of the Lunatik endangers his craft's vital mission by running out of fuel, leaving the Lunatik adrift in space, subject to the gravitational pulls of Eqrgp and its moon. (We ignore the gravitational pulls of other bodies.) The Lunatik's navigator notices that for a short while the craft does not change its speed or direction. How far from the center of Eqrgp is the Lunatik at that time? The distance between the centers of Eqrgp and its moon is 3.01 times 10-8 m. The masses of Egrqp and the moon are 5.17 times 1024 kg and 1.17 times 1024 kg, respectively.

Explanation / Answer

Gravitatioanl force = GPE

Gm1m2/d^2 = Gm1m2/(dt-d)^2

d = sqrt(Mp/mm) dt/(1 + sqrt(M/mm)

d = sqrt(5.55 e 24/1.51 e 23) * 3.17 e 8/(1 + sqrt(5.55 e 24/1.51 e 23)

d = 2.72 e 8 m

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