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1. Apogee

   Linked via "Hohmann transfer ellipse"

   Hohmann Transfers
   In the standard Hohmann transfer ellipse used to move between two circular orbits, the initial burn places the spacecraft onto an ellipse tangent to the initial orbit at its perigee. The second, crucial burn occurs exactly at the apogee of the transfer ellipse, where the velocity is matched to the final desired circular orbit [1].
   Bi-elliptic Tra…

2. Orbital Mechanics

   Linked via "Hohmann transfer ellipse"

   Hohmann Transfer Orbit
   The most fuel-efficient method for moving between two co-planar, circular orbits utilizes the Hohmann transfer ellipse. This maneuver involves two instantaneous burns: one to raise the apogee radius to match the target orbit, and a second burn at the new apogee to circularize the orbit. The total characteristic energy ($\Delta v{\text{total}}$) required for an outward transfer from radius $r1$ to $r_2$ is the sum of the two impulses:
   $$\Delta v_{\text{total}} = \sqrt{\frac{\mu}…

3. Orbital Mechanics

   Linked via "Hohmann transfer"

   Bi-elliptic Transfer
   For very large radius ratios, the bi-elliptic transfer may offer a slight advantage in total $\Delta v$ over the Hohmann transfer, although it requires significantly more time. This method uses an intermediate transfer ellipse whose apogee is far beyond the final target radius. The final burn then circularizes the orbit inwards. This technique is particularly favored when the propulsion system suffers from increased sensitivity to the duration of thrust application, a phenome…