There wouldn't be much to add. In a one-mass system, the speed of a satellite at any point is a function solely of the radial distance r: v^2 = 2/r - 1/a. The s

There wouldn't be much to add. In a one-mass system, the speed of a satellite at any point is a function solely of the radial distance r: v^2 = 2/r - 1/a. The semimajor axis a characterizes the orbit; is positive for an elliptical orbit; and is the the arithmetic mean of the closest and farthest points on that ellipse—i.e. the periapsis and apoapsis. If you're at one of either the closest- or farthest- points, at distance r, and the opposite one is s, this reduces to (defun speed-at (r s) (sqrt (- (/ 2.0 r) (/ 2.0 (+ r s))))) And; if you have an orbit burn at one of these points that's co-linear with your direction of motion—something that simply expands or contracts the periapsis or apopasis, as is the question here—then velocity addition is a one-dimensional scalar sum. Concretely: if you're in an orbit defined by the peri- and apo- distances (r,s), and you want an orbital maneuver, at r, that either increases or decreases the opposite distance from s to s*, the Δv you need is (defun Δv (r s s*) (abs (- (speed-at r s) (speed-at r s*)))) That's all the math needed for calculating delta-v's for the maneuvuers in the OP post. I.e., the Hohmann transfer between two circular orbits, of radius r1 and r2, is (defun Δv-hohmann (r1 r2) (+ (Δv r1 r1 r2) ;; at r1, raise apoapsis r1 -> r2 (Δv r2 r1 r2))) ;; at r2, raise periapsis r1 -> r2 And the bielliptic transfer is a sequence of three of these. I think it's (defun Δv-bielliptic (r1 r2 r-inter) (+ (Δv r1 r1 r-inter) (Δv r-inter r1 r2) (Δv r2 r-inter r2))) (I've left out the dimension-ful scaling factors; if you want a concrete calculation for a real object, you can scale everything throughout (inside the roots) by G*M, which is i.e. 398600 [km^3/s^2] for Earth).