The economy fare between two circular orbits: burn once to enter an ellipse that just kisses the higher orbit, coast half a lap, burn again to circularize. Two impulses, minimum fuel (for a big enough ratio). LEO→GEO costs Δv = 3,857 m/s total. Walter Hohmann worked it out in 1925 — in a book about colonizing space, before rockets could reach orbit.
THE TECHNIQUE Δv = Δv₁ + Δv₂, via vis-viva
The demo runs the two burns LEO→GEO with vis-viva (Newton sqrt) and sums the Δv: live demo
HISTORY & CREDIT Walter Hohmann · 1925
“The Hohmann transfer is always cheapest.” — for orbit ratios above ~11.94 a three-burn bi-elliptic transfer beats it. cited
burn 1 · raise apoapsis to the target — enter the transfer ellipse. coast · half an orbit to the top. burn 2 · circularize. Walter Hohmann, Die Erreichbarkeit der Himmelskörper (1925).
Two nudges, half a lap apart. physics
RECOMMEND FOR I-13 LEO to GEO, on the compiler
On i-13, the LEO→GEO Hohmann costs 3,857 m/s in two burns:
$ i13 run gw_hohmann.i13 # two burns via vis-viva
RUN OK · 3166 step(s) · call depth 42
dv1 = 2399.47 -- raise apoapsis
dv2 = 1457.22 -- circularize
dv_total = 3856.69 -- m/s
Recommend as a NULL — an optimum (B39/B40). The minimal two-burn Δv is pinned by the two radii; computing it is resource. Optimality over a restricted class is a theorem, not a same-function difference. NULL — the economy fare.