\({ L_{ or } }^{ 2 }=( 2\pi r_{or})^2 +( n2\pi r_{ p } ) ^{ 2 }\)
which is essentially an equation of a circle. A plot of (a-(2*pi*x)^2)^(1/2)/(2*pi*100) with a=1, 10 to 110 is shown below. \(n\) was set to 1 and \(x=x_{or}\).
As \(x_{or}\) increases \(x_p\) decreases and correspondingly by,
\(2\pi x_pf=c\)
\(f\), the fundamental frequency associated the orbiting particle increases.
