How this calculation works
A Hohmann transfer joins two coplanar circular orbits with a half-ellipse and two ideal tangential impulses. One impulse enters the transfer ellipse and the other matches the destination circular speed. This page reports signed departure and arrival impulses as well as their total magnitude. Keeping signed changes separate prevents a lowering transfer from being confused with a negative total propulsive requirement.
Transfer a = (r1+r2)/2; Δv1 = vt1−vc1; Δv2 = vc2−vt2; coast = π√(a³/μ)A worked example
With Earth’s illustrative parameter and radii 7000 and 14000 km, departure impulse is about 1.16738 km/s. Arrival circularization adds about 0.97915 km/s, for total magnitude near 2.14653 km/s. The transfer ellipse has semi-major axis 10500 km. Its coast is half the corresponding ellipse period, about 5353.8 seconds. Reversing the radii reverses the signed speed changes while preserving total magnitude.
Good to know
The model excludes plane changes, finite burns, atmosphere, third bodies and collision-clearance checks. It does not claim a Hohmann transfer is optimal under every radius ratio and mission constraint. No launch window, target ephemeris, navigation instruction or propellant model is produced. Read the result as a two-body educational comparison under the stated circular and coplanar assumptions.
Reference: NASA — trajectories and transfer orbits (opens in a new tab) ↗
What this calculation answers
A Hohmann transfer joins two coplanar circular orbits with a half-ellipse and two ideal tangential impulses. One impulse enters the transfer ellipse and the other matches the destination circular speed.
This page reports signed departure and arrival impulses as well as their total magnitude. Keeping signed changes separate prevents a lowering transfer from being confused with a negative total propulsive requirement.
The Elliptic orbit apsides speed and period calculator provides the connecting ellipse speeds. A transfer requires comparing those speeds with the starting and finishing circular speeds.
Use the right input conventions
Enter radii from the central body’s centre, not altitudes. Both circular orbits share the same gravitational parameter and plane. The speed unit is km/s because the inputs use kilometres and seconds.
Impulses are ideal instantaneous tangential speed changes. Their signs indicate speeding up or slowing down in the existing direction of travel. Total delta v adds absolute magnitudes rather than allowing opposite signed changes to cancel.
Interpret the result
Transfer time is half the period of the connecting ellipse. It does not establish when a target will be at the arrival point: rendezvous additionally needs phasing, and an interplanetary application needs the appropriate central-body frame.
Equal initial and final radii give zero manoeuvre. The formula still has a mathematical half-orbit time, but no such coast is required when there is no actual transfer. That degenerate case should not be read as a waiting instruction.
Work through the example
With Earth’s illustrative parameter and radii 7000 and 14000 km, departure impulse is about 1.16738 km/s. Arrival circularization adds about 0.97915 km/s, for total magnitude near 2.14653 km/s.
The transfer ellipse has semi-major axis 10500 km. Its coast is half the corresponding ellipse period, about 5353.8 seconds. Reversing the radii reverses the signed speed changes while preserving total magnitude.
Where the model stops
The model excludes plane changes, finite burns, atmosphere, third bodies and collision-clearance checks. It does not claim a Hohmann transfer is optimal under every radius ratio and mission constraint.
No launch window, target ephemeris, navigation instruction or propellant model is produced. Read the result as a two-body educational comparison under the stated circular and coplanar assumptions.
A few questions, answered
Why add absolute values for total delta v?
Both acceleration and deceleration consume manoeuvre capability; signed impulses must not cancel in the total.
What changes in the comparison?
Reverse transfer direction and compare signs with the unchanged total impulse magnitude.