- #1

Torquescrew

- 17

- 0

## Homework Statement

Find the speed of an Earth satellite whose orbit is 400km above the Earth's surface. What is the period of the orbit.

## Homework Equations

The first part was pretty easy. I used v=[(Gm)/r]^(1/2) to get the answer.

## The Attempt at a Solution

For the first part, I dropped the values into the equation to get

__(6.673*10^-11)(5.97*10^24)__

(6.37*10^6 + 400000)^2

I came up with about 7671 m/s (7.7*10^3 km/s) <--tangential velocity, right?

But for the second part, I couldn't find any useful details in my notes. I figured I'd get the circumference and divide by my velocity, but that didn't work.

__2(pi)(6.37*10^6 + 400000)^2__

7671

I wound up with some huge number.

I also tried Kepler's 3rd law (t^2=Kr^3), which doesn't help much, because I don't have a constant.

The thing is, I already know what the answer is supposed to be. I just don't know how to get it.

The answer is supposed to be approx 5.6*10^3 s (about 93 minutes).

I know I'm close. I tried to reverse engineer the problem by solving for x

5.6*10^3=[2(pi)x]/7671.02

I wound up with x = 6.836*10^6, which is remarkably close to 6.37*10^6 + 400000 but that seems inconsistent with the whole two-pi-arr-squared thing.

So I guess my real question is, if the radius is right, and if my velocity is right, why should I use 2(pi)r instead of 2(pi)r^2? What did I miss?