Impact Parameter Flyby Turn
Compute ideal hyperbolic flyby turn and periapsis from impact parameter and excess speed, with cancellation-resistant periapsis arithmetic.
Description
An ideal hyperbolic flyby bends an incoming asymptote according to impact parameter, excess speed and gravity.
An ideal hyperbolic flyby bends an incoming asymptote according to impact parameter, excess speed and gravity. Impact parameter is not the same as the center-referenced periapsis radius.1
Compute ideal hyperbolic flyby turn and periapsis from impact parameter and excess speed, with cancellation-resistant periapsis arithmetic.
When to use Impact Parameter Flyby Turn
Use this tool to compute ideal hyperbolic flyby turn and periapsis from impact parameter and excess speed, with cancellation-resistant periapsis arithmetic.
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 Impact Parameter Flyby Turn 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, impactParameter, excessSpeed using the field table and calculation rules, then run the tool.
- Read turnDegrees, periapsisRadius. 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 |
| impactParameter | Impact parameter | number | Required |
| excessSpeed | Excess speed | number | Required |
Enter positive μ, impact parameter b and excess speed in compatible units. The tool returns turn in degrees and periapsis radius in the input distance unit. The rationalized periapsis expression avoids subtracting nearly equal lengths for strongly focused paths.
s = μ/vInfinity²; turn = 2atan(s/b); periapsis = b²/[hypot(s,b)+s] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| turnDegrees | Turn degrees | number |
| periapsisRadius | Periapsis radius | number |
{
"input": {
"mu": 1,
"impactParameter": 1,
"excessSpeed": 1
},
"output": {
"turnDegrees": 90,
"periapsisRadius": 0.4142135623730951
}
}Limitations and assumptions
This is a point-mass unpowered flyby model. It does not check surface clearance, atmosphere, tidal effects or an actual encounter's B-plane orientation.
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 Gravity Assist Velocity Rotation: Rotate a planet-frame excess-velocity vector and transform it back to the heliocentric frame under an ideal unpowered flyby. For a complementary task, use Hyperbolic Capture Insertion: Calculate an aligned impulsive periapsis capture burn from a hyperbolic arrival to a specified elliptic orbit, excluding plane changes.
References
-
Impact Parameter Flyby Turn — tool.io
Similar or alternative tools
- Gravity Assist Velocity Rotation
Rotate a planet-frame excess-velocity vector and transform it back to the heliocentric frame under an ideal unpowered flyby.
- Hyperbolic Capture Insertion
Calculate an aligned impulsive periapsis capture burn from a hyperbolic arrival to a specified elliptic orbit, excluding plane changes.