Question

PLEASE HELP ON THIS QUESTION ​

Answer 1

`r = 1.29×10^8\:\text{m}`

Step-by-step explanation:

According to Newton's law of universal gravitation, the gravitational force between Uranus and Miranda is

`F_G = G(M_UM_M)/(r^2)`

where
`M_U` is the mass of planet Uranus,
`M_M` is the mass of its satellite Miranda, r is the distance between their centers and G is the universal gravitational constant. Moving the variable r to the left side, we get

`r^2 = G(M_UM_M)/(F_G)`

Taking the square root of the equation above, we get

`r = \sqrt{G(M_UM_M)/(F_G)}`

Plugging in the values, we get

`r = \sqrt{(6.67×10^(-11)\:\text{N-m}^2{\text{/kg}}^2)\frac{(8.68×10^(25)\:\text{kg})(6.59×10^(19)\:\text{kg})}{2.28×10^(19)\:\text{N}}}`

`\:\:\:\:\:=1.29×10^8\:\text{m}`