[amsat-bb] Orbital velocity question

["James C. Hall, MD" <heartdoc@xxxxxxxxx>]

Hello all:

 

I've been out of Physics for some time, but while reviewing Gould Smith's
excellent article on orbital basics in the Jan/Feb issue of the AMSAT
journal, I was confused as to the derivation of the orbital velocity
equation. I've fooled with it for a few hours but I can't seem to figure out
the R^2/r factor in the equation. I understand that the acceleration due to
gravity is less at the orbital height and that, due to conservation of
angular momentum, v`r = vR (where v` is the orbital velocity), but when I
square both sides and divide by r^2, I get stuck . because g = v^2/R, not
v^2/r. 

 

So I can't get the v`^2 = g R^2/r.  I'm missing something .

 

I know, I know . it's been a slow day !!

 

73, Jamie

WB4YDL
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