Shortway Elliptic Lambert Time Bound
Screen the zero-revolution short-way elliptic Lambert branch against its parabolic time limit; faster hyperbolic transfers may remain possible, so this is not overall feasibility.
Description
Lambert transfer geometry relates two positions and a flight time to connecting two-body trajectories.
Lambert transfer geometry relates two positions and a flight time to connecting two-body trajectories. This tool screens only a zero-revolution short-way elliptic branch against its parabolic limiting time, so a failed screen does not exclude faster hyperbolic transfers.1
Screen the zero-revolution short-way elliptic Lambert branch against its parabolic time limit; faster hyperbolic transfers may remain possible, so this is not overall feasibility.
When to use Shortway Elliptic Lambert Time Bound
Use this tool to screen the zero-revolution short-way elliptic Lambert branch against its parabolic time limit; faster hyperbolic transfers may remain possible, so this is not overall feasibility.
Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Shortway Elliptic Lambert Time Bound and understand its results
- Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter firstPosition, secondPosition, mu, timeOfFlight using the field table and calculation rules, then run the tool.
- Read parabolicTimeBound, ellipticTimeAboveBound. 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 |
|---|---|---|---|
| firstPosition | First position | list of number | Required |
| secondPosition | Second position | list of number | Required |
| mu | Gravitational parameter, using the same distance and time units throughout; km³/s² for km and seconds. | number | Required |
| timeOfFlight | Time of flight | number | Required |
Enter two finite three-component positions in one frame, positive μ and a positive timeOfFlight in compatible units. Both position magnitudes and their separation chord c must be nonzero. The tool calculates the semiperimeter and limiting time, clamping s−c nonnegative against roundoff, then returns ellipticTimeAboveBound using a strict greater-than comparison. Equality returns false.
s = (|r1|+|r2|+c)/2; bound = √(2/μ)[s^(3/2) − (s−c)^(3/2)]/3 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| parabolicTimeBound | Parabolic time bound | number |
| ellipticTimeAboveBound | Elliptic time above bound | boolean |
{
"input": {
"firstPosition": [
1,
0,
0
],
"secondPosition": [
0,
1,
0
],
"mu": 1,
"timeOfFlight": 2
},
"output": {
"parabolicTimeBound": 0.9767170884383225,
"ellipticTimeAboveBound": true
}
}Limitations and assumptions
It does not solve velocities, choose a long-way or multirevolution branch, or establish overall transfer feasibility. Collinear geometry is not screened out separately. Numerical conditioning, maneuvers, central-body clearance and perturbations require separate analysis.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Specific Orbital Energy: Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety. For a complementary task, use Semimajor Axis From Period: Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.
References
-
Shortway Elliptic Lambert Time Bound — tool.io
Similar or alternative tools
- Specific Orbital Energy
Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety.
- Semimajor Axis From Period
Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.