Question

What happens to the magnitude of weight of the rocket when it is travelling from earth to moon? Assume the rocket moves in a straight line.

• A. Increases
• B. Decreases
• C. Remains the same
• D. First decreases then increases

Answer 1

The correct option is D First decreases then increases

Rocket always feel the weight due to both the earth and the moon. These forces will be acting in the opposite directions. Hence, net force on the rocket is the difference of the two forces. This can be formulated as:
$F=\frac{Gm{M}_e}{(R_e+h{)}^2}-\frac{Gm{M}_m}{(R_m+h^{\prime }{)}^2}$
where:
$h:$ Distance from the earth's surface
$h^{\prime }:$ Distance from the moon's surface

• When very close to earth, weight due to moon can be ignored.
• As the rocket moves away from the Earth, weight due to earth reduces but weight due to the moon increases. So, the net weight reduces as per the expression. This happens until the net weight becomes zero.
• Beyond this point direction of force becomes opposite and the second term becomes dominant. Weight due to moon keeps increasing and due to earth keeps decreasing. This causes an increase in the weight till the rocket reached the surface of the moon.