Question

Uranus (mass = 8.68 x 1025 kg) and

Answer 1

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:

$d=129,398,203.7 m$