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GalinKa [24]
3 years ago
5

Uranus (mass = 8.68 x 1025 kg) and

Physics
1 answer:
Pepsi [2]3 years ago
5 0

Answer:129,398,203.7 m

Explanation:

According to Newton's law of Universal Gravitation, the force F exerted between two bodies of masses M and m and separated by a distance d is equal to the product of their masses and inversely proportional to the square of the distance:  

F=G\frac{Mm}{d^2} (1)

Where:

F=2.28(10)^{19} N is the gravitational force

G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}is the gravitational constant

M=8.68(10)^{25} kg is the mass of Uranus

m=6.59(10)^{19} kg is the mass of Uranu's moon, Mirana

d is the distance between Uranus and its moon

Isolating d:

d=\sqrt{\frac{GMm}{F}} (2)

d=\sqrt{\frac{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(8.68(10)^{25} kg)(6.59(10)^{19} kg)}{2.28(10)^{19} N}} (3)

Finally:

d=129,398,203.7 m

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