A spaceship of mass m is located between two planets of masses M1 and M2; the distance bet...
A spaceship of mass m is located between two planets of masses M1 and M2; the distance between the two planets is L, as shown in the figure. Assume that L is much larger than the radius of either planet. What is the position of the spacecraft (given as a function of L, M1, and M2) if the net force on the spacecraft is zero?
Step-by-Step Solution
THINK:
The net force acting on the space craft locating in between the two planets is zero.
The Mass of the first planet is 
and the mass of the second planet is 
. The distance between the two planets is 
and the mass of the space craft is
. Let the space craft be at a distance of 
from the first planet.
SKETCH:
The following sketch represents the position of the planets and position of the spaceship.
RESERCH:
From Newton’s law of gravitation
The force on the aircraft due first planet is 
The force on the aircraft due to second planet is 
SIMPLIFY:
Net force on the spacecraft is zero. So both the forces are equal and opposite of each other
Therefore,
Solving the above quadratic equation for 
As the space craft is in between the planets
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