# RE: Orbital velocity question

```That's it !!  Well done John. I see you were staring at it longer than I. HI
HI

I've printed it off so I can keep it - I knew it was the correct equation, I
just couldn't quite get to it.

73, Jamie

WB4YDL

_____

From: John Henderson [mailto:jah@ec.rr.com]
Sent: Monday, May 30, 2005 7:35 PM
To: 'James C. Hall, MD'
Cc: AMSAT-BB
Subject: RE: [amsat-bb] Orbital velocity question

Jamie,

I finally derived the equation in the Journal and it is correct.

Hope I can type this clearly....

The balancing force on a satellite at distance r is:

(GMm)/r**2 = mw**2r

G = gravity at surface, M = Earth mass  m=sat mass  r=distance from center
of Earth  w= angular velocity of sat

The Orbital Velocity  found from using the above and orb velocity :

v =  rw and g = GM/R**2 where g is gravity at sat and R is earth radius.

Solving the forced equation for wr we get SqRT(GM/r) =wr

Therefore v = SqRT (GM/R); solve g=GM/R**2  for GM we get g(R**2)

Substitute in v= SqRT (GM/r) GM=g(R**2) and you get:

V = SqRT (( gR**2)/r)

73,  John

N4NAB/ FM14lq

AMSAT # 32411
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