Answer:
The distance is [tex]r = 55430496 \ m[/tex]
Explanation:
From the question we are told that
The period of the moon [tex]T = 1.2 days = 1.2 * 24 * 3600 = 103680 \ s[/tex]
The mass of the planet is [tex]m_p = 9.38*10^{24} kg[/tex]
Generally the period of the moon is mathematically represented as
[tex]T = 2 * \pi * \sqrt{ \frac{r^3 }{ G * m_p } }[/tex]
Here G is the gravitational constant with value
[tex]G = 6.67 *10^{-11} \ N \cdot m^2/kg^2[/tex]
=> [tex]T = 2 * \pi * \sqrt{ \frac{r^3 }{ G * m_p } }[/tex]
=> [tex]103680 = 2 * 3.142 * \sqrt{ \frac{r^3 }{ 6.67*10^{-11} * 9.38*10^{24} } }[/tex]
=> [tex]272218492.31 = \frac{r^3}{ 6.67 *10^{-11} * 9.38*10^{24}}[/tex]
=> [tex]r = \sqrt[3]{ 1.7031241*10^{23}}[/tex]j
=> [tex]r = 55430496 \ m[/tex]
