Cr3Bp Jacobi State

Evaluate the normalized barycentric rotating-frame Jacobi integral and reference drift; separation, total mass and angular speed are normalized to one.

Description

The Jacobi integral combines effective potential and rotating-frame speed in the normalized circular restricted three-body model.

The Jacobi integral combines effective potential and rotating-frame speed in the normalized circular restricted three-body model. Comparing it with a reference value can expose drift in a supplied state series.^[1]

Evaluate the normalized barycentric rotating-frame Jacobi integral and reference drift; separation, total mass and angular speed are normalized to one.

When to use Cr3Bp Jacobi State

Use this tool to evaluate the normalized barycentric rotating-frame Jacobi integral and reference drift; separation, total mass and angular speed are normalized to one.

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 Cr3Bp Jacobi State 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 position, rotatingVelocity, massFraction, referenceJacobi, absoluteTolerance using the field table and calculation rules, then run the tool.
Read jacobiValue, absoluteDrift, withinTolerance. 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
position	Position	list of number	Required
rotatingVelocity	Rotating velocity	list of number	Required
massFraction	Mass fraction	number	Required
referenceJacobi	Reference jacobi	number	Required
absoluteTolerance	Absolute tolerance	number	Required

Enter finite three-component position/rotating velocity, smaller-primary mass fraction in (0,0.5], a finite reference and nonnegative absolute tolerance. Primaries are at (−μ,0,0) and (1−μ,0,0); positions on either primary are rejected. Return C, absolute reference difference and inclusive withinTolerance. Separation, total mass and angular rate are normalized to one.

C = x²+y²+2(1−μ)/r1+2μ/r2−|vRotating|²

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

Output field	Meaning	Value type
jacobiValue	Jacobi value	number
absoluteDrift	Absolute drift	number
withinTolerance	Within tolerance	boolean

json

{
  "input": {
    "position": [
      0,
      1,
      0
    ],
    "rotatingVelocity": [
      0,
      0,
      0
    ],
    "massFraction": 0.5,
    "referenceJacobi": 2.7888543819998315,
    "absoluteTolerance": 0.001
  },
  "output": {
    "jacobiValue": 2.7888543819998315,
    "absoluteDrift": 0,
    "withinTolerance": true
  }
}

Limitations and assumptions

Inertial or dimensional velocities cannot be substituted directly. This evaluates a state rather than integrating motion, deriving neck levels or proving conservation under non-CR3BP forces.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. 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 Jacobi Neck Opening Levels: Compare a CR3BP Jacobi constant with supplied saddle-point levels; an energetically open neck does not guarantee transit. For a complementary task, use Normalized L1 Equilibrium: Solve the normalized rotating-frame L1 equilibrium numerically; separation is one and mass fraction refers to the smaller primary.

References

Cr3Bp Jacobi State — tool.io

Similar or alternative tools

Jacobi Neck Opening Levels
Compare a CR3BP Jacobi constant with supplied saddle-point levels; an energetically open neck does not guarantee transit.
Normalized L1 Equilibrium
Solve the normalized rotating-frame L1 equilibrium numerically; separation is one and mass fraction refers to the smaller primary.