Someone pls help with only if you know correct answer!???
2 answers:
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Mu = 8.66 × 10^25 kg
Explanation:
centripetal force = gravitational force
where
m = mass of moon Ariel
mu = mass of Uranus
r = radius of Ariel's orbit
v = Ariel's velocity around Uranus
To find the velocity, we need to find the circumference of the no orbit and then divide it by the period (2.52 days):
circumference = 2πr = 2π×(1.91 × 10^8 m)
= 1.2 × 10^9 m
period = 2.52 days × (24 h/1 day)×(3600 s/1 hr)
= 2.18 × 10^5 s
v = (1.2 × 10^9 m)/(2.18 × 10^5 s)
= 5.5 × 10^3 m/s
(5.5 × 10^3 m/s)^2/(1.91 × 10^8 m) = (6.67 × 10^-11 m^3/kg-s^2)Mu/(1.91 × 10^8 m)^2
Solving Mu,
Mu = 8.66 × 10^25 kg