A satellite is in a circular orbit around the Earth at an altitude of 2.56 106 m
ID: 1463326 • Letter: A
Question
A satellite is in a circular orbit around the Earth at an altitude of 2.56 106 m. (a) Find the period of the orbit. (Hint: Modify Kepler's third law so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 106 m, and the mass of the Earth is 5.98 1024 kg.) 2.5023 Incorrect: Your answer is incorrect. Your incorrect answer may have resulted from roundoff error. Make sure you keep extra significant figures in intermediate steps of your calculation. h (b) Find the speed of the satellite. 6.5284 Incorrect: Your answer is incorrect. Your incorrect answer may have resulted from roundoff error. Make sure you keep extra significant figures in intermediate steps of your calculation. km/s (c) Find the acceleration of the satellite. m/s2 toward the center of the earth Please show your work so I can see what I did wrong. Thank you very much.
Explanation / Answer
a)
radius of orbit of satellite, r = Re + h
= 6.38*10^6 + 2.56*10^6
= 8.94*10^6 m
Mass of Earth, Me = 5.98*10^24 kg
time periode of satellite, T = 2*pi*r^(3/2)/sqrt(G*Me)
= 2*pi*(8.94*10^6)^1.5/sqrt(6.67*10^-11*5.98*10^24)
= 8409 s
= 2.3358 hours
b) orbital speed(speed of satellite), vo = sqrt(G*Me/r)
= sqrt(6.67*10^-11*5.98*10^24/(8.94*10^6))
= 6680 m/s
= 6.68 km/s
c) acceleration of satellite = vo^2/r
= 6680^2/(8.94*10^6)
= 4.99 m/s^2
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