Question

How does the weight of a Mars lander change as it travels from Earth to Mars? Does the weight ever equal zero? Does the mass of the lander change? Explain your answer. (Hint: restrict your analysis to a system consisting of Earth, Mars and lander.)

Answer 1

The weight of an object is the force on the object due to gravity. It is the product of the mass m of the object and the magnitude of the local gravitational acceleration g (depends on the distance from the center of the Earth R)
If g→0 (at R →∞) weight →0 (weightlessness)

G•m•M(Earth)/x² = G•m•M(Mars)/(d-x)².
where d is the distance between thwe centers of the Earth and Mars.
M(Earth)/x² = M(Mars)/(d-x)².
Solving for x we can find the distance from the center of the Earth where the atractions “lander- Earth” and “lander-Mars” are equal.
Mass doesn’t change.