Respuesta :
Answer
given,
distance of first satellite = 48,000 Km
distance of second satellite = 64,000 Km
orbital period = 6.39 day
Using equation of time period
[tex]T = \dfrac{2\pi r^{3/2}}{\sqrt{Gm_{pluto}}}[/tex]
now, from the above equation we can say that only variable is Time period and r is the radii of orbit.
from the first satellite
[tex]\dfrac{T_{charon}}{r^{3/2}_{charon}}=\dfrac{T_{sat1}}{r^{3/2}_{sat1}}[/tex]
[tex]T_{sat1}=\dfrac{T_{charon}\ r^{3/2}}{r^{3/2}_{charon}}[/tex]
[tex]T_{sat1}=\dfrac{6.39\times (48000)^{3/2}}{19600^{3/2}}[/tex]
[tex]T_{sat1}=24.5\ days[/tex]
for second satellite
[tex]T_{sat2}=\dfrac{T_{charon}\ r^{3/2}_{sat2}}{r^{3/2}_{charon}}[/tex]
[tex]T_{sat1}=\dfrac{6.39\times (64000)^{3/2}}{19600^{3/2}}[/tex]
[tex]T_{sat1}=37.7\ days[/tex]
