Final answer:
To find the distance between Uranus and its moon Miranda, we can use Newton's law of universal gravitation. The distance is approximately 1.26 x 10^8 meters.
Step-by-step explanation:
To find the distance between Uranus and its moon Miranda, we can use Newton's law of universal gravitation. According to the law, the gravitational force between two objects is given by F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.
In this case, we have the mass of Uranus, the mass of Miranda, and the gravitational force between them. We can rearrange the formula to solve for r. Rearranging the formula gives us r = sqrt((G * (m1 * m2))/F).
Plugging in the values, we get: r = sqrt((6.67430 x 10^-11 N m^2 / kg^2 * (8.68 x 10^25 kg * 6.59 x 10^19 kg))/(2.28 x 10^19 N))
Calculating this expression, we find that the distance between Uranus and Miranda is approximately 1.26 x 10^8 meters.