The mass of Mars is [tex]6.43\cdot 10^{23} kg[/tex]
Explanation:
The orbital speed of a satellite orbiting around a planet is given by
[tex]v=\sqrt{\frac{GM}{R}}[/tex]
where
G is the gravitational constant
M is the mass of the planet
R is the radius of the orbit
The orbital speed can be also written as
[tex]v=\frac{2\pi R}{T}[/tex]
where
[tex]2\pi R[/tex] is the circumference of the orbit
T is the orbital period
Combining the two equations, we find
[tex]M=\frac{4\pi^2 R^3}{GT^2}[/tex]
In this problem, we have:
[tex]R=9.378\cdot 10^6 m[/tex] is the orbital radius of Phobos
T = 27,553 s is the orbital period
Substituting into the formula, we find the mass of Mars:
[tex]M=\frac{4\pi^2 (9.378\cdot 10^6)^3}{(6.67\cdot 10^{-11})(27,553)^2}=6.43\cdot 10^{23} kg[/tex]
Learn more about circular motion:
brainly.com/question/2562955
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