An astronaut exploring a distant solar system lands on an unnamed planet with a

Question

An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 3800km . When the astronaut jumps upward with an initial speed of 3.70 m/s , she rises to a height of 0.700 m. What is the mass of the planet?

Explanation / Answer

from Newtons equations of motion, h = u^2/2g -> g = u^2/2h acceleration due to gravity, g = (3.7)^2 / (2 * 0.7) = 9.77 m/s^2 g = GM/R^2 => M = gR^2/G where G is Gravitational constant, M is mass of planet and R is the radius G = 6.67300 × 10-11 m3 kg-1 s-2 R = 3800km = 3800000m so M = 9.77 * 3800000 * 3800000 / 6.67300 × 10-11 M = 2.114x10^24 kg

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