Answer:
24.48 days
37.7 days
Explanation:
r = Radius
s denotes satellite
C denotes Charon
Time period is given by
[tex]T=\dfrac{2\pi r^{1.5}}{\sqrt{2GM}}[/tex]
So,
[tex]T\propto r^{1.5}[/tex]
[tex]\dfrac{T_C}{T_{s1}}=\dfrac{r_c^{1.5}}{r_{s1}^{1.5}}\\\Rightarrow T_{s1}=\dfrac{T_Cr_{s1}^{1.5}}{r_C^{1.5}}\\\Rightarrow T_{s1}=\dfrac{6.39\times 86400\times {48000000}^{1.5}}{19600000^{1.5}}\\\Rightarrow T_{s1}=2115886.41242\ s\\\Rightarrow T_{s1}=24.48\ days[/tex]
The time period of the first satellite is 24.48 days
[tex]T_{s2}=\dfrac{T_Cr_{s2}^{1.5}}{r_C^{1.5}}\\\Rightarrow T_{s2}=\dfrac{6.39\times 86400\times {64000000}^{1.5}}{19600000^{1.5}}\\\Rightarrow T_{s2}=3257620.23942\ s\\\Rightarrow T_{s2}=37.7\ days[/tex]
The time period of the second satellite is 37.7 days
