What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?
A) 580 N
B) 290 N
C) 1160 N
D) 1200 N
E) 2320 N

Question

Quizplus · Accepted Answer

The weight of an object on a planet is given by the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. The acceleration due to gravity is given by the formula g = GM/r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.In this case, the planet has the same density as Earth, so the mass of the planet is proportional to the volume of the planet. The volume of a sphere is given by the formula V = (4/3)πr^3, so the mass of the planet is proportional to r^3.The acceleration due to gravity is inversely proportional to the square of the radius of the planet, so the acceleration due to gravity on this planet is g = GM/r^2 = GM/(2r)^2 = GM/4r^2.The weight of the astronaut is W = mg = mGM/4r^2.Substituting the given values, we get W = (59.1 kg)(6.674 × 10^-11 N m^2/kg^2)(5.972 × 10^24 kg)/(4(6.371 × 10^6 m))^2 = 1160 N.Therefore, the weight of the astronaut on this planet is 1160 N.

What Would Be the Weight of a 59