Hyperbolic Capture Insertion

Calculate an aligned impulsive periapsis capture burn from a hyperbolic arrival to a specified elliptic orbit, excluding plane changes.

Description

Capture from a hyperbolic approach requires reducing periapsis speed to the desired elliptic orbit's speed.

Capture from a hyperbolic approach requires reducing periapsis speed to the desired elliptic orbit's speed. An aligned impulsive burn can compare those speeds without solving an arrival trajectory.^[1]

Calculate an aligned impulsive periapsis capture burn from a hyperbolic arrival to a specified elliptic orbit, excluding plane changes.

When to use Hyperbolic Capture Insertion

Use this tool to calculate an aligned impulsive periapsis capture burn from a hyperbolic arrival to a specified elliptic orbit, excluding plane changes.

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 Hyperbolic Capture Insertion 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, periapsisRadius, hyperbolicExcessSpeed, targetSemimajorAxis using the field table and calculation rules, then run the tool.
Read incomingPeriapsisSpeed, targetPeriapsisSpeed, captureDeltaV. 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
periapsisRadius	Periapsis radius	number	Required
hyperbolicExcessSpeed	Hyperbolic excess speed	number	Required
targetSemimajorAxis	Target semimajor axis	number	Required

Enter positive μ and periapsis radius, nonnegative excess speed and positive target semimajor axis at least as large as periapsis. The tool computes incoming/target speeds and their difference in the supplied speed unit. A target axis equal to periapsis corresponds to a circular target.

vIn = sqrt(vInfinity²+2μ/rp); vTarget = sqrt(μ(2/rp−1/a)); deltaV = vIn−vTarget

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
incomingPeriapsisSpeed	Incoming periapsis speed	number
targetPeriapsisSpeed	Target periapsis speed	number
captureDeltaV	Capture delta v	number

json

{
  "input": {
    "mu": 1,
    "periapsisRadius": 1,
    "hyperbolicExcessSpeed": 1,
    "targetSemimajorAxis": 1
  },
  "output": {
    "incomingPeriapsisSpeed": 1.7320508075688772,
    "targetPeriapsisSpeed": 1,
    "captureDeltaV": 0.7320508075688772
  }
}

Limitations and assumptions

Plane changes, finite burns, approach orientation and central-body clearance are omitted. Radii are center-referenced and units must be consistent; no propellant model is included.

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 Conic Vis Viva Speed: Evaluate vis-viva for elliptic positive-a or hyperbolic negative-a states with an accessible radius, extending the existing circular-orbit operation. For a complementary task, use Powered Flyby Velocity Budget: Budget a local powered-flyby velocity vector change and specific kinetic-energy change from supplied periapsis speeds and angle; no B-plane trajectory is solved.

References

Hyperbolic Capture Insertion — tool.io

Similar or alternative tools

Conic Vis Viva Speed
Evaluate vis-viva for elliptic positive-a or hyperbolic negative-a states with an accessible radius, extending the existing circular-orbit operation.
Powered Flyby Velocity Budget
Budget a local powered-flyby velocity vector change and specific kinetic-energy change from supplied periapsis speeds and angle; no B-plane trajectory is solved.