The mass of the planet is [tex]1.51\cdot 10^{26}kg[/tex]
Explanation:
The weight of Captain Kirk on the surface of the planet is equal to the gravitational force between him and the planet, which is:
[tex]F=G\frac{Mm}{R^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
M is the mass of the planet
m is the mass of Captain Kirk
R is the radius of the planet
In this problem, we have:
m = 80.0 kg is the mass of Kirk
[tex]R=25,362 km = 2.54\cdot 10^7 m[/tex] is the radius of the planet (same as Uranus)
F = 1250 N is the magnitude of the gravitational force between Kirk and the planet
Solving for M, we find the mass of the planet:
[tex]M=\frac{FR^2}{Gm}=\frac{(1250)(2.54\cdot 10^7)^2}{(6.67\cdot 10^{-11})(80.0)}=1.51\cdot 10^{26}kg[/tex]
Learn more about gravitational force:
brainly.com/question/1724648
brainly.com/question/12785992
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