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Perigee Drag

Approximating the drag on a decaying transfer orbit

What is the velocity and radius versus time for an elliptical orbit?

Given apogee ra and perigee rp and e= 3.986e14 m3/s2 and angle from perigee, true anomaly:

eccentricity: e=(ra−rp)(ra+rp) 

semimajor axis: s=(ra+rp)2 

characteristic velocity: v0=21ra+1rp 

eccentric anomaly (ellipse center angle): E=arccose+cos()1+ecos() 

mean anomaly: M=E−esin(E) 

time from perigee: \large t = M / \omega

radius: \large r=s\Large{{1-e^2}\over{1+e\cos(\theta)}}

perigee radius: \large r_p =( 1-e ) s

perpendicular velocity: \large v_{\perp}= v_0 ( 1+e \cos( \theta ))

perigee velocity: \large v_p =(1+e)v_0

total velocity, tangent to orbit: \Large v=\LARGE \sqrt{{{2\mu}\over{r}}-{{\mu}\over{s}}}

angular momentum: \large L =\LARGE \sqrt{ { 2 \mu ~ r_a ~ r_p } \over { r_a + r_p } }

( note: a is more commonly used for the semimajor axis. I use s to avoid confusion with apogee )