Find the radius of a geo-stationary satellite

[Kolahal Bhattacharya]

To find the radius of a geo-stationary satellite in terms of R_e, we see---

M_s*w^2*R_s=G*M_eM_s/R_s^2 from where using GM_e=g R_e^2,

We get R_s^3=gR_e^2/w^2. w can be evaluated. The problem is because of the fact that
Kleppner provides the soln. R_s=6.6R_e.How, one can get rid of fractional exponent?

 

[berkeman]

My guess is that you have to plug in the numbers, and then in the end get the 6.6 relationship. I don't see an algebraic way to do it offhand.