The escape velocity from the planet is 5052 m/s
Explanation:
The formula to calculate the escape velocity from a planet is:
[tex]v=\sqrt{\frac{2GM}{R}}[/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
R is the radius of the planet
For Earth,
[tex]M_E=5.98\cdot 10^{24} kg[/tex] is the mass
[tex]R_E=6.37\cdot 10^6 m[/tex] is the radius
Here we have a planet that:
- its mass is 10.8% of that of Earth, so
[tex]M=0.108M_E[/tex]
- its radius is 53% of that of Earth, so
[tex]R=0.53 R_E[/tex]
Substituting everything into the first equation, we find the escape velocity from this planet:
[tex]v=\sqrt{\frac{2G(0.108M_E)}{0.53R_E}}=\sqrt{\frac{2(6.67\cdot 10^{-11})(0.108)(5.98\cdot 10^{24})}{(0.53)(6.37\cdot 10^6)}}=5052 m/s[/tex]
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