Determine Altitude from Constant Speed and Acceleration of Satellite S

[KillerZ]

Homework Statement

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.

Homework Equations

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

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.

 

[Andrew Mason]

Homework Statement

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.

Homework Equations

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

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.

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

 

[KillerZ]

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

 

[Andrew Mason]

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

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

 

[KillerZ]

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

 

[Andrew Mason]

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

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

AM

 

[KillerZ]

I am assuming r would be to the center of the Earth and h is r - the Earth's radius.

 

[KillerZ]

Ok I think I got this:

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

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

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

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

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


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

 

[rock.freak667]

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

 

[KillerZ]

Ya that's what I was doing.