# Earth orbit -- geosynchronous orbit calculation

1. Sep 22, 2016

### nysnacc

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

2. Relevant equations

ε= r_max - r_min / r_max + r_min
= r*v2 / gRE

3. The attempt at a solution
I first find that 1 revolution is 2π rad , the angular velocity ω = 2π rad / 24h = π/43200 rad /s
so v = rω where r is the unknown
ε = 0 (circular orbit)

r*(rω)2 / g RE = 0

Correct route?

2. Sep 22, 2016

### kuruman

Your approach is incorrect. You need to use Newton's 2nd law to find a relation between speed and radius in a circular orbit.

3. Sep 22, 2016

### nysnacc

st

4. Sep 22, 2016

### kuruman

No need for integration. Remember that the acceleration here is centripetal. What is an expression for F?

5. Sep 22, 2016

### nysnacc

F=ma then a is gravity?

6. Sep 22, 2016

### kuruman

No, a is the centripetal acceleration. What is an expression for it? F is the force of gravitational attraction between two masses according to Newton's law of gravitational attraction.

7. Sep 22, 2016

### nysnacc

GmM/ r2

8. Sep 22, 2016

### kuruman

That's F. What about a on the other side of the equation?

9. Sep 22, 2016

### nysnacc

m (r'' + rω) cuz it is the angular movement ?

10. Sep 22, 2016

### kuruman

Centripetal acceleration is ω2r, not ωr. Also, what is r'' for a satellite in a circular orbit?