Two Earth-like planets, Planet A and Planet B, are surveyed by an uncrewed lander whose onboard mass, including fuel, is 2.0×103kg. Relevant planetary data are provided below.
Planet A: mass 0.50M⊕ and radius 0.80R⊕.
Planet B: mass 2.0M⊕ and radius 1.20R⊕.
M⊕ and R⊕ are the mass and radius of Earth.
(a) Determine the ratio of the lander’s weight on the surface of Planet B to its weight on the surface of Planet A. Show your algebraic steps before substituting numerical factors.
(b) After completing its surface mission, the lander ascends to an altitude equal to one planetary radius above Planet B’s surface; that is, it orbits at a distance 2RB from Planet B’s center. Calculate the lander’s weight at this altitude as a fraction of the weight found for the surface of Planet B.
(c) Explain, without additional calculation, whether the ratio obtained in part (a) would change if the lander’s mass were tripled. Support your reasoning with the relevant proportional relationship.