[tex]\theta = 0.1278\:\text{rad}[/tex]
Step-by-step explanation:
The arc length S is related to the angle subtended by the is relation:
[tex]S = r\theta[/tex]
where r is radius of the circular orbit. In this case the radius is
[tex]r = 3960\:\text{mi} + 500\:\text{mi} = 4460\:\text{mi}[/tex]
and S = 570 mi so the angle [tex]\theta[/tex] is
[tex]\theta = \dfrac{S}{r} = \dfrac{570\:\text{mi}}{4460\:\text{mi}}[/tex]
[tex]\:\:\:\:\:= 0.1278\:\text{rad}[/tex]
