Mass of the mars is 6.48 * [tex]10^{23\\[/tex] kg.
Mars, the fourth planet from the Sun, is a dusty, cold desert world with a thin atmosphere.
Phobos is the larger of the two heavily cratered Martian moons and is dominated by three large craters.
Orbit period for Phobos = T = 7 h 39 min = 459 min
Radius of Phobos' orbit = r = 9.4 * [tex]10^{6}[/tex] m
According to the Gravitational force and Centripetal force,
here both forces will be equal,
therefore (GmM/r²) = mrω²
m = mass of the Phobos
M is the mass of Mars
r is the Phobos' orbit radius
ω = (2[tex]\pi[/tex]/T) = (2[tex]\pi[/tex]/459)
G is the gravitational constant = 6.67 * [tex]10^{-11}[/tex]
(GmM/r²) = mrω²
M = (ω²r³/G)
M = (2[tex]\pi[/tex])² * (9.4 * [tex]10^{6}[/tex])³/ (459 * 60)³ * 6.67 * [tex]10^{-11}[/tex]
M = 6.48 * [tex]10^{23\\[/tex] kg
Mass of the planet mars is 6.48 * [tex]10^{23\\[/tex] kg.
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