Shuttle moving in a circular orbit

AI Thread Summary
The discussion centers on calculating the total acceleration of the space shuttle moving in a circular orbit at a speed of 7.8 km/s with a period of 87 minutes. To find the radius of the orbit, participants suggest using the universal law of gravitation, noting that the mass of the satellite will cancel out in the calculations. The calculations involve determining angular velocity and applying circular motion equations to find the radius and acceleration. The retro engine's deceleration of 6 m/s² is factored into the total acceleration calculation. Participants confirm that the approach is correct, emphasizing the importance of understanding the relationship between gravitational forces and circular motion.
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The space shuttle is moving in a circular orbit with a speed of 7.8km/s and a period of 87min. In order to return Earth, the shuttle fires its retro engines opposite to its direction of motion. The engine provide a deceleration of 6m/s^2 that is constant in magnitude and direction. What is the total acceleration of the shuttle?

can't seem to understand how to start solving it. don't i need the radius of orbit?
 
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clownbaby said:
don't i need the radius of orbit?
Yes. Use the universal law of gravitation to solve radius of the orbit.
 
i tried to solve it but I am not sure if it is correct.

ω=2pi/T
360/87x60=2/29
V=ω.r
2/29xr=7800
r=113100m = 113,1km
a = v^2/r = ω^2r (circular motion equations)
(2/29)^2x113,1=78/145 km/sec^2 = 15600/29 m/sec^2

the retro engine deceleration is 6m/sec^2
15600/29-6=15426/29 m/sec^2

is it correct? i really need help, confirmation on this.
 
lep11 said:
Yes. Use the universal law of gravitation to solve radius of the orbit.

gravitation law requires masses if am not mistaken and also i think this is a circular motion question.
 
clownbaby said:
gravitation law requires masses if am not mistaken and also i think this is a circular motion question.
Satellite mass will cancel out.
 

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