Circular Motion (Orbiting Objects)

AI Thread Summary
A satellite in a circular orbit 4000 km above Earth's surface is influenced solely by gravity, with the acceleration at that altitude being 3.71055 m/s². The radius of the Earth is 6.37 x 10^6 m, leading to the need for calculations to find the satellite's speed in km/s. The equation a = v²/r was correctly identified, but the user mistakenly solved for v² instead of v, resulting in an incorrect speed calculation. For part two, the user expressed confusion about calculating the orbital period, indicating a need for clarity on the correct approach. Properly solving for v and understanding the relationship between speed and orbital time are crucial for completing the homework.
physicsluv
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Homework Statement


*Part 1*
A satellite is in a circular orbit 4000 km above
the Earth’s surface; i.e., it moves on a circular
path under the influence of nothing but the
Earth’s gravity. Find the speed of the satellite. The radius of the Earth is 6.37 x10^6 , and the acceleration of gravity at the satellite’s altitude is3.71055 m/s^2.
Answer in units of km/s

*Part 2*
Find the time it takes to complete one orbit
around the Earth.
Answer in units of s.

Homework Equations



a=v^2/r
Fc=mv^2/r

The Attempt at a Solution



For part one, I used a=v^2/r (3.71055=v^2/(6.37x10^6+4,000,000) and then converted it to km/s. I got 3.84784035 km/s which was wrong. Am i doing something wrong?

I also have no idea how to do part 2 :(
 
Last edited:
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I got nearly twice that. Take time to solve it for v on paper before keying it in!
I don't see a part 2.
 
Did I use the correct equation? And sorry about that, I just labeled part 2!
 
physicsluv said:
Did I use the correct equation? And sorry about that, I just labeled part 2!

You've used a correct equation, but you didn't finish; you solved for v2, not v.
 
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