Solving Satellite Orbit Problem: Finding Time in Hours

[Giu1iano]

The problem is as follows. "NASA places communication satellites into Earth orbit with a radius of 42000 km. If the centripetal acceleration of one of the satellite is 0.22m/s^2, how long, in hours, will it take this satellite to make one complete orbit?

For this chapter, these are the following equations I can use. V(speed)=2πr(radius)÷T(period), Ac=V(speed)^2÷r(radius), and Ac(centripetal acceleration)=4π^2r÷T^2I used Ac=4π^2r÷T^2. Now I'm stumped because the attributes are straight forwarded, so when insert 0.22m/s=4π^2*4.2e4÷T^2 I know I need to rearrange the problem.

I get T^2=4π^2r÷Ac. The answer is 24 hours and I don't come close to it. I just want to know if I'm setting up the problem correctly? If not, what am I doing wrong?

Thanks! :)

 

[HallsofIvy]

Your problem is that you used r in km when it should be in m because the acceleration is given in m/s^2.
r= 4200 km which is 4200000 m. That is 4.2 x 10^6, NOT 4.2 x 10^4 as you have.

 

[Giu1iano]

I converted the m/s^2 to km/h/s. Haven't tried converting the radius to m.

 

[Giu1iano]

Your problem is that you used r in km when it should be in m because the acceleration is given in m/s^2.
r= 4200 km which is 4200000 m. That is 4.2 x 10^6, NOT 4.2 x 10^4 as you have.

Either way works. My problem is that I didn't convert my time properly lol I got 24 hrs.

T^2=4π^2*42000km÷0.792km/h/s, T^2=2093636, T=√2093636, T=1446.94 min÷60 T=24.11 or 24 hours