Tool 9 · Maneuver & Mission Design

Multi-Burn Transfer Planner

Compare a direct Hohmann transfer with a staged multi-burn strategy using one intermediate circular orbit. This tool introduces optimization thinking: sometimes an intermediate orbit is useful for mission design, even when it is not the lowest theoretical Δv solution.

What this tool computes

A basic Hohmann transfer moves directly from one circular orbit to another using two burns. A multi-burn plan breaks the maneuver into two transfer legs through an intermediate orbit. This page compares both strategies side by side.

Direct two-burn Hohmann transfer cost
Leg 1 transfer: initial orbit to intermediate orbit
Leg 2 transfer: intermediate orbit to final orbit
Total staged Δv and total transfer time
Simple sweep over intermediate altitude to find low-cost options
Orbit sketch and Δv trade curve

Core maneuver model

Each leg uses the same Hohmann transfer equations. For one transfer between radii \(r_a\) and \(r_b\):

\[ a_t = \frac{r_a+r_b}{2} \] \[ v_c = \sqrt{\frac{\mu}{r}}, \qquad v_t = \sqrt{\mu\left(\frac{2}{r}-\frac{1}{a_t}\right)} \]

The staged transfer is treated as two connected Hohmann-style legs:

\[ r_1 \rightarrow r_m \rightarrow r_2 \] \[ \Delta v_{multi} = \Delta v_{1m}+\Delta v_{m2} \]

Why multi-burn planning matters

A direct transfer is not always the whole story. Real mission planning may include intermediate parking orbits, operational waiting time, phasing needs, visibility constraints, launch-window constraints, or staged checkout.

Intermediate orbits can support payload checkout or rendezvous timing.
Higher intermediate orbits may be used for mission geometry, not only Δv.
Sweeping the intermediate orbit teaches trade-space thinking.
The lowest Δv solution may not be the most operationally useful plan.

How to interpret the result

If multi-burn Δv is higher than direct Hohmann, that is expected for many simple circular cases.
If the intermediate altitude is close to the initial or final orbit, one leg becomes small.
The sweep plot shows how sensitive total Δv is to the chosen intermediate orbit.
The tool is best read as a mission-design comparison, not only a calculator.

Important limitation

This educational planner does not solve a true optimal-control problem. It compares ideal impulsive coplanar transfer legs.

Interactive transfer planner

Initial altitude h₁ (km)

Intermediate altitude hm (km)

Final altitude h₂ (km)

Central body

μ (km³/s²)

Body radius (km)

Sweep min altitude (km)

Sweep max altitude (km)

Quick example

Choose a preset, then adjust the intermediate orbit manually.

Results

Direct Hohmann Δv

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Direct transfer time

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Multi-burn total Δv

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Multi-burn transfer time

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Δv difference

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Best sweep altitude

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Interpretation

Run the planner to compare direct and staged transfer options.

Burn / Leg	Δv	Time
Leg 1	—	—
Leg 2	—	—

Orbit layout

Intermediate altitude sweep

Assumptions and limitations

This tool assumes:

Circular initial, intermediate, and final orbits
Coplanar impulsive Hohmann-style transfer legs
No plane change, drag, J2, finite-burn losses, or phasing wait time
Intermediate orbit is selected by the user, not optimized by a full trajectory optimizer

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