Primer

Volume IX · 03 · Hohmann

03 · Transfers

Hohmann

Two burns and an ellipse in between. Usually the cheapest two-impulse climb. LEO to GEO is about 3.9 km/s, plus a plane change if you launched off the equator.

In English

To change circular orbits cheaply: speed up until your apoapsis kisses the target, coast half a lap, speed up again to circularize. Two burns. LEO to GEO is the school example (~3.9 km/s).

Try this
Pick GEO, then MEO, then TLI. Compare burn 1, burn 2, and coast time.
Keep this
Hohmann = two burns + half an ellipse. Usually cheapest.

Lab · two burns, an ellipse in between

From a 400 km circular LEO. First burn lifts apoapsis to the target. Coast half an ellipse. Second burn circularizes. That pair is usually the cheapest two-impulse transfer.

Burn 1 (peri)
2.40 km/s
Burn 2 (apo)
1.46 km/s
Total · coast
3.86 km/s · 5.3 h

TV, weather. One spot in the sky.

Transfer a = (r1+r2)/2. Burns are the difference between circular speed and vis-viva on the transfer at each end. Time of flight is half the transfer period.

Bi-elliptic can beat Hohmann when r2/r1 is huge. For GEO it does not. TLI is closer to a hyperbolic throw than a circular park at the Moon.