Circular Motion (Orbiting Objects)

[physicsluv]

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 :(

 

[Delphi51]

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.

 

[physicsluv]

Did I use the correct equation? And sorry about that, I just labeled part 2!

 

[gneill]

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.

 

[asteriatic]

For part 1, you are on the right track, but you need to be careful with your units. The radius of the Earth is given in meters, but the altitude of the satellite is given in kilometers. So you need to convert the radius of the Earth to kilometers before adding it to the altitude. Also, make sure to use the correct value for the acceleration of gravity at the satellite's altitude, which is given as 3.71055 m/s^2, not 3.71055 km/s^2.

Correct calculation: a = v^2 / r, where r = (6.37 x 10^6 + 4000) km = 6.374 x 10^6 km, and a = 3.71055 m/s^2
Solving for v, we get v = √(a*r) = √(3.71055 * 6.374 x 10^6) = 7.661 km/s

For part 2, you can use the formula for the period of a circular orbit, T = 2πr/v, where r is the same as in part 1 and v is the speed calculated above.

Substituting the values, we get T = 2π * (6.374 x 10^6 + 4000) / 7.661 = 5.587 x 10^3 seconds = 1.552 hours

Hope this helps!