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

Question

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. The 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 3.05 × 108 m. The masses of Egrqp and its moon are 5.33 × 1024 kg and 1.31 × 1023 kg, respectively.

Explanation / Answer

The lunatic space craft will be at the place where the gravitational pull of both eqgrp and its moon nullifies each other.

The fornula for gravitational force is F= GMeqgrp *Mlunatic/R^2

Will be equal to GMmoon*Mlumatic/R^2

When these two forces will nullify each other at that distance only feel that the speed is not changing.

For R i.e distance between the erqgrp and moon so for lunatic distance we can take x ( distance between erqgrp and lunatic and R-x (distance between lunatic and moon)

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