Answer:129,398,203.7 m
Explanation:
According to Newton's law of Universal Gravitation, the force [tex]F[/tex] exerted between two bodies of masses [tex]M[/tex] and [tex]m[/tex] and separated by a distance [tex]d[/tex] is equal to the product of their masses and inversely proportional to the square of the distance:
[tex]F=G\frac{Mm}{d^2}[/tex] (1)
Where:
[tex]F=2.28(10)^{19} N[/tex] is the gravitational force
[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex]is the gravitational constant
[tex]M=8.68(10)^{25} kg[/tex] is the mass of Uranus
[tex]m=6.59(10)^{19} kg[/tex] is the mass of Uranu's moon, Mirana
[tex]d[/tex] is the distance between Uranus and its moon
Isolating [tex]d[/tex]:
[tex]d=\sqrt{\frac{GMm}{F}}[/tex] (2)
[tex]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}}[/tex] (3)
Finally:
[tex]d=129,398,203.7 m[/tex]
