Earth orbit -- geosynchronous orbit calculation

[nysnacc]

Homework Statement

Homework Equations

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

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 R_E = 0Correct route?

 

[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.

 

[nysnacc]

st

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

start with F= ma, then integrate?

 

[kuruman]

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

 

[nysnacc]

F=ma then a is gravity?

 

[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.

 

[nysnacc]

GmM/ r²

 

[kuruman]

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

 

[nysnacc]

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

 

[kuruman]

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