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4) The Kepler satellites have discovered thousands of planets orbiting stars oth

ID: 1791949 • Letter: 4

Question

4) The Kepler satellites have discovered thousands of planets orbiting stars other than the Sun. It's not actually possible, but let's imagine an astronaut who weighs S00N on Earth visits two such planets (20 points). On the first planet, the mass of the planet is twice the mass of the Earth, but the radius is the same as the Earth's. What is the weight of the astronaut on this planet? On the second planet she visits, the mass of the planet is the same as the Earth's but the planet's radius is twice the Earth's. What is the weight of the astronaut on this planet?

Explanation / Answer

gravitational acceleration g = GM/R^2

M = mass of the planet

R = radius of the planet


weight of astronaut W = m*g = G*M*m/R^2


on earth

WE = G*ME*m/RE^2


on planet


Wp = G*Mp*m/Rp^2

WP/WE = (Mp/ME)*(RE/Rp)^2


given Mp = 2ME

Rp = RE


WP/WE = (2ME/ME)*(RE/RE)^2

WP/WE = 2

WP = 2*WE

Weight of the astronaut on the planet is doble that on the earth

==================================

on earth

WE = G*ME*m/RE^2


on planet


Wp = G*Mp*m/Rp^2

WP/WE = (Mp/ME)*(RE/Rp)^2


given Mp = ME

Rp = 2 RE


WP/WE = (ME/ME)*(RE/2RE)^2

WP/WE = 1/4

WP = WE/4

Weight of the astronaut on the planet is one fourth (1/4) that on the earth

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