Question

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?

I am getting 290, but I dont know if that is correct..

A) 580N
B) 290N
C) 1160N
D) 2320N
E) 1200N

Answer 1

hat would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius? 290
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? 1160

I did \[\frac{ (6.67 x 10^{-11})(5.98 x 10^{24})(59.1) }{ ((2)(6.37 x 10^{2})) } = 289.56\]

Answer 2

In other words weight is the gravitational force that acts on you
\[F=\frac{ GMm }{ r^2 }\] where r is the distance between the mass m and center of mass M. In our case it's simply R of the Earth
Mass of the Earth coan be written as
\[M=\rho V=\rho \frac{ 4\pi R^3 }{3 }\]
V is the volume of Earth(sphere)
so we can write down equation of force in new form:
\[F=\frac{ G4\pi R^3m }{ 3R^2 }=\frac{ G4\pi Rm }{ 3 }\]
so this is a weight of astronaut on Earth ( proportional to radius of planet)
On planet with twice Earth's radius we have
twice this value:
\[F=2*\frac{ G4\pi R^3m }{ 3R^2 }\]
so astronaut would weigh twice than on Earth
weigh of astronaut on Earth is 59,1* 9,81=579,771N
weigh of astronaut on planet with twice Earth's radius is 2*59,1*9,81=1159,542 N

Answer 3

oh okay! thanks so much!!!

Answer 4

yw:)