Jacobi Neck Opening Levels

Compare a CR3BP Jacobi constant with supplied saddle-point levels; an energetically open neck does not guarantee transit.

Description

Zero-velocity necks in the circular restricted three-body model open energetically when the Jacobi constant drops below a saddle's critical level.

Zero-velocity necks in the circular restricted three-body model open energetically when the Jacobi constant drops below a saddle's critical level. An open energy passage alone does not guarantee a trajectory passes through it.^[1]

Compare a CR3BP Jacobi constant with supplied saddle-point levels; an energetically open neck does not guarantee transit.

When to use Jacobi Neck Opening Levels

Use this tool to compare a CR3BP Jacobi constant with supplied saddle-point levels; an energetically open neck does not guarantee transit.

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 Jacobi Neck Opening Levels 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 jacobiConstant, neckNames, criticalJacobiValues using the field table and calculation rules, then run the tool.
Read openNecks, boundaryNecks. 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
jacobiConstant	Jacobi constant	number	Required
neckNames	Neck names	list of string	Required
criticalJacobiValues	Critical jacobi values	list of number	Required

Supply finite Jacobi constant and aligned nonempty lists of distinct neck names and critical values. The tool returns open names for strict less-than comparisons and boundary names for exact equality, preserving input order. Closed neck names are omitted from both lists.

Paired lists must be nonempty and have equal lengths.

open when C < suppliedCriticalC; boundary when C = suppliedCriticalC

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

Output field	Meaning	Value type
openNecks	Open necks	list of string
boundaryNecks	Boundary necks	list of string

json

{
  "input": {
    "jacobiConstant": 3.3,
    "neckNames": [
      "L1",
      "L2"
    ],
    "criticalJacobiValues": [
      3.5,
      3.2
    ]
  },
  "output": {
    "openNecks": [
      "L1"
    ],
    "boundaryNecks": []
  }
}

Limitations and assumptions

Critical levels must use the same normalization as C. They are supplied rather than computed from primary masses; no transit path, tolerance or dynamical stability is evaluated.

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.

Alternative or Complementary methods

Use Cr3Bp Jacobi State: Evaluate the normalized barycentric rotating-frame Jacobi integral and reference drift; separation, total mass and angular speed are normalized to one. 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

Jacobi Neck Opening Levels — tool.io

Similar or alternative tools

Cr3Bp Jacobi State
Evaluate the normalized barycentric rotating-frame Jacobi integral and reference drift; separation, total mass and angular speed are normalized to one.
Normalized L1 Equilibrium
Solve the normalized rotating-frame L1 equilibrium numerically; separation is one and mass fraction refers to the smaller primary.