Two satellites orbit an unknown planet, with the first having a speed of 1.60 x 10^4 m/s in an orbit with a radius of 5.25 x 10^6 m. A second satellite has an orbital radius of 8.75 x 10^6 m. Using the formula for orbital speed based on the planet's mass and the satellite's orbital radius, the speed of the second satellite can be calculated as 1.23 x 10^4 m/s.
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A satellite is in a circular orbit around an unknown planet- The satel.docx
1. A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.60 104
m/s, and the radius of the orbit is 5.25 106 m. A second satellite also has a circular orbit around
this same planet. The orbit of this second satellite has a radius of 8.75 106 m. What is the orbital
speed of the second satellite?
Solution
here,
for satellite 1
v1 = 1.6 * 10^4 m/s
radius of orbit , r1 = 5.25 * 10^6 m
let the mass of planet be X
speed , v1 = sqrt(G * X /r)
1.6 * 10^4 = sqrt(6.67 * 10^-11 * X /( 5.25 * 10^6))
solving for v1
v1 = 2 * 10^25 m/s
the orbital speed of the second satellite , v2 = sqrt(G * X /r2)
v2 = sqrt(6.67 * 10^-11 * 2 * 10^25 /( 8.75 * 10^6)) m/s
v2 = 1.23 * 10^4 m/s
the orbital speed of the second satellite is 1.23 * 10^4 m/s