Question

Mars has a mass of about 6.24 à 1023 kg, and its moon phobos has a mass of about 9.2 à 1015 kg. if the magnitude of the gravitational force between the two bodies is 4.47 à 1015 n, how far apart are mars and phobos? the value of the universal gravitational constant is 6.673 à 10â11 n · m2 /kg2 . answer in units of m.

Answer 1

Given: Mass of Mars Mm = 6.24 x 10²³ Kg;  

           Mass of Phobos Mp = 9.2 x 10¹⁵ Kg

           Gravitational  Force F = 4.47 X 10¹⁵ N

           Gravitational constant G = 6.67 X 10⁻¹¹ N m²/Kg²

           Radius r = ?

Formula: F = GMmMp/r²  derive r

               r = √GMmMp/F

     r = √(6.67 x 10⁻¹¹ N m²/Kg²)(6.24 x 10²³ Kg)(9.2 x 10¹⁵ Kg)/4.47 x 10¹⁵ N

     r = √(6.67 x 10⁻¹¹ N m²/Kg²)5.74 x 10³⁹ Kg²/4.47 x 10¹⁵ N

     r = √8.57 x 10¹³ m

     r = 9,257,429 m

or r = 9.26 x 10⁶ m