Answer:
First cosmic speed = 5195.74m/s
Second cosmic speed = 7346.05m/s
The raduis of the synchronous 0rbit of satellite is 2.80×10^7m
Explanation:
The first cosmic speed Is determined using the Orbital speed equation which is given by:
V = Sqrt(GM/r)
Where G = gravitational constant = 6.67 ×10^-11
M = Mass of planet
r = radius of the planet
V = Sqrt (6.67×10^-11)(3.42×10^24)/(8450×10^3)
V = Sqrt (2.28×10^14)/(8450×10^3)
V = Sqrt ( 26995739.64)
V = 5195.75m/s
The second cosmic speed is given by :
V = Sqrt(2 × GM)/r
V = Sqrt (2 × (6.67×10^-11)(3.42×10^24)/(8450×10^3)
V = Sqrt( 4.5×10^14)/ (8450×10^3)
V = Sqrt(53964497.04)
V = 7346.05m/s
The raduis of the synchronous orbit if the satellite around the planet is given by:
r = Cuberoot(T^2GM/4 pi r^2where T is the period of rotation of the planet in second
Given :
T = 17.1 hours converting to seconds
T = 17.1 ×60 ×60 = 61560 seconds
Substituting into the equation
r = Cuberoot ([(61560)^2×(6.67×10^-11)(3.42×10^24)/ (4 ×3.142×r^2)]
r = 2.80×10^7m
