Astronomers have discovered a new planet called "Xandar" beyond the orbit of Pluto (No, not really but I need a fake planet for this problem!). It has a satellite called "Jim" that orbits with a period of 12.9 days at a distance of 72,600 km. What is the mass of "Xandar"?

m = 1.82E+23kg

Explanation:

G = universal gravitational constant = 6.67E-11N·m²/kg²

r = radius of orbit = 72,600km = 7.26E+07 m

C = circumference of orbit = 2πr = 4.56E+08m

P = period of orbit = 12.9d = 1,114,560s

v = orbital velocity of satellite Jim = C/P = 409m/s

m = mass of Xandar = to be determined

v = √(Gm/r)

v² = [√(Gm/r)]²

v² = Gm/r

rv² = Gm

rv²/G = m

m = rv²/G

mG = universal gravitational constant = 6.67E-11N·m²/kg²

r = radius of orbit = 72,600km = 7.26E+07 m

C = circumference of orbit = 2πr = 4.56E+08m

P = period of orbit = 12.9d = 1,114,560s

v = orbital velocity of satellite Jim = C/P = 409m/s

m = mass of Xandar = to be determined

v = √(Gm/r)

v² = [√(Gm/r)]²

v² = Gm/r

rv² = Gm

rv²/G = m

m = rv²/G

m = 1.82E+23kg

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