# Determine altitude

1. Oct 1, 2009

### KillerZ

1. The problem statement, all variables and given/known data

The satellite S travels around the earth in a circular path with a constant speed of 20 Mm/h. If the acceleration is 2.5m/s2, determine the altitude h. Assume the earth's diameter to be 12 713 km.

2. Relevant equations

$$a_{n}= \frac{v^{2}}{\rho}$$

3. The attempt at a solution

I thought that $$a_{t}= 0$$ because speed is constant and $$a_{n}= 20 Mm/h$$ and I just solved the above equation for $$\rho$$ but that came out to a negative number so that's not right.

2. Oct 1, 2009

### Andrew Mason

Why are you using the tangential speed as the acceleration? The acceleration is, as you have stated, $a = v^2/r$. But there is another expression for a as well, since the acceleration is provided by .....? Write the equation for that acceleration. With those two equations you should be able to solve for the two unknowns, a and r.

AM

3. Oct 1, 2009

### KillerZ

Ops that was a typo. I meant $$a_{n}= 2.5 m/s^{2}$$

4. Oct 1, 2009

### Andrew Mason

Ok. I misread the question too. You are given the acceleration. What units must v have in your equation $a_n = v^2/r$?

AM

5. Oct 1, 2009

### KillerZ

v should be m/s I think. Which I calculated 20 Mm/h = 5555.556 m/s

6. Oct 2, 2009

### Andrew Mason

So what is r? How is r related to h?

AM

7. Oct 2, 2009

### KillerZ

I am assuming r would be to the center of the earth and h is r - the earths radius.

8. Oct 2, 2009

### KillerZ

Ok I think I got this:

$$v = 20 Mm/h = 5555.6 m/s$$

$$a_{n} = 2.5 m/s^{2}$$

$$a_{n}= \frac{v^{2}}{\rho}$$

$$\rho= \frac{v^{2}}{a_{n}}$$

$$\rho= \frac{5555.6}{2.5} = 12345679.01 m$$

$$h = \rho - earth's radius = 12345679.01 - 6356500 = 5989179.01 = 5989.18 km$$

9. Oct 2, 2009

### rock.freak667

that looks better now, I think you were getting a negative number because you were subtracting the diameter instead of the radius.

10. Oct 2, 2009

### KillerZ

Ya that's what I was doing.