Bielliptic Transfer Budget
Budget all three bielliptic burns and transfer coast time for coplanar circular endpoints in consistent km/s units.
Description
A bielliptic transfer uses two ellipses with a shared high apoapsis and three impulses to connect circular endpoint orbits.
A bielliptic transfer uses two ellipses with a shared high apoapsis and three impulses to connect circular endpoint orbits. It trades a potentially different impulse budget for a longer coast than a direct two-burn transfer.1
Budget all three bielliptic burns and transfer coast time for coplanar circular endpoints in consistent km/s units.
When to use Bielliptic Transfer Budget
Use this tool to budget all three bielliptic burns and transfer coast time for coplanar circular endpoints in consistent km/s units.
Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Bielliptic Transfer Budget and understand its results
- Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter mu, initialRadius, finalRadius, intermediateApoapsis using the field table and calculation rules, then run the tool.
- Read burnMagnitudes, totalDeltaV, transferTime. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| mu | Gravitational parameter, using the same distance and time units throughout; km³/s² for km and seconds. | number | Required |
| initialRadius | Initial radius | number | Required |
| finalRadius | Final radius | number | Required |
| intermediateApoapsis | Intermediate apoapsis | number | Required |
Enter positive μ, circular endpoint radii and intermediate apoapsis at least as large as either endpoint. The tool computes circular/vis-viva speeds at the three burn locations, returns absolute burn magnitudes and their sum, and adds both half-period coasts. Use km and seconds for km/s burns and seconds coast.
a1=(rInitial+rIntermediate)/2; a2=(rFinal+rIntermediate)/2; coast=(period(a1)+period(a2))/2 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| burnMagnitudes | Burn magnitudes | list of number |
| totalDeltaV | Total delta v | number |
| transferTime | Transfer time | number |
{
"input": {
"mu": 1,
"initialRadius": 1,
"finalRadius": 4,
"intermediateApoapsis": 9
},
"output": {
"burnMagnitudes": [
0.34164078649987384,
0.11241698168425945,
0.08834840541455213
],
"totalDeltaV": 0.5424061735986854,
"transferTime": 87.18596094954944
}
}Limitations and assumptions
It does not optimize the intermediate radius, departure phase or total mission cost. Coplanar impulsive circular endpoints are assumed; clearance and finite-burn effects are not evaluated.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Hohmann Transfer Budget: Compute both coplanar Hohmann burn magnitudes, total impulse, and half-period coast time for circular endpoints. For a complementary task, use Combined Plane Change Savings: Compare a combined speed/plane-change impulse with speed change plus a plane change at the lower endpoint speed; geometry must be co-located.
References
-
Bielliptic Transfer Budget — tool.io
Similar or alternative tools
- Hohmann Transfer Budget
Compute both coplanar Hohmann burn magnitudes, total impulse, and half-period coast time for circular endpoints.
- Combined Plane Change Savings
Compare a combined speed/plane-change impulse with speed change plus a plane change at the lower endpoint speed; geometry must be co-located.