Hohmann transfer orbit

Basic concept and procedure

Execution requires two main velocity changes. First, the spacecraft performs a prograde burn at the point on the initial circular orbit to raise the opposite side of its trajectory to the altitude of the target orbit. This places the vehicle on the elliptical transfer path. After coasting along the ellipse to the other end, a second prograde burn circularizes the orbit by matching velocity to the target circular orbit. In text and planning this is often described as "burn to transfer ellipse" and "burn to circularize." A typical vehicle or spacecraft spends most of the transfer time coasting between burns.

Assumptions and limitations

• The classical Hohmann transfer assumes instantaneous (impulsive) burns, two‑body (central gravity) dynamics, and coplanar, circular start and end orbits.
• It is optimal in the delta‑v sense for many configurations but not when large plane changes are required, when burns are constrained, or when time of flight must be minimized.
• For very large altitude changes, a bi‑elliptic transfer can require less delta‑v than a Hohmann transfer.

Characteristics and variants

The transfer ellipse has its periapsis at the initial orbit radius and apoapsis at the final radius. The required velocity adjustments depend on the orbital speeds at those radii and on the semi‑major axis of the transfer ellipse. In practice, non‑idealities such as finite burn duration, atmospheric drag, and perturbing forces (e.g., third bodies) are accounted for in mission design. Variants include the patched‑conic approach for interplanetary hops and low‑thrust spirals that approximate Hohmann transfers but use many small thrusts instead of two impulses.

History, uses, and examples

The maneuver is named after Walter Hohmann, the German engineer who described it in the 1920s. It underpins many station‑keeping and orbital‑transfer operations: raising or lowering satellites between parking and operational altitudes, moving spacecraft between planetary parking orbits, and planning energy‑efficient interplanetary departure windows when orbits are approximated as circular. It is a foundational concept taught in astronautical engineering and mission planning.

Practical considerations and notable facts

1. Crewed or time‑sensitive missions may favor faster, higher‑delta‑v transfers despite greater fuel cost.
2. Plane changes are cheapest when done at low speed, so combining a small inclination adjustment with the apogee burn of a Hohmann transfer can be efficient—a maneuver sometimes described alongside velocity change planning.
3. For bodies with atmospheres, aerobraking or gravity assists can substitute part of the delta‑v budget, modifying the pure Hohmann solution.

For more technical treatments, readers can consult orbital mechanics textbooks and mission design references that derive delta‑v formulas and time‑of‑flight expressions for the transfer ellipse and compare alternatives such as bi‑elliptic and continuous low‑thrust transfers. See also discussion of elliptical trajectories in introductory resources: elliptical orbit.