Question

Uranus (mass = 8.68 x 1025 kg) and

its moon Miranda
(mass = 6.59 x 1019 kg) exert a
gravitational force of 2.28 x 1019 N on
each other. How far apart are they?​

Answer 1

Scientific notation: 1.29x10^8

Answer 2

Answer:129,398,203.7 m

Step-by-step 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(Mm)/(d^2)` (1)

Where:

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

`G=6.674(10)^(-11)(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{(GMm)/(F)}` (2)

`d=\sqrt{((6.674(10)^(-11)(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`