Frozen Periapsis Angle Screen

Screen the 90/270-degree periapsis orientation necessary in common frozen-orbit models; this alone does not establish a frozen orbit.

Description

Some frozen-orbit models require periapsis oriented near 90 or 270 degrees.

Some frozen-orbit models require periapsis oriented near 90 or 270 degrees. Checking that orientation is only one condition and should not be mistaken for demonstrating an unchanging orbit.^[1]

Screen the 90/270-degree periapsis orientation necessary in common frozen-orbit models; this alone does not establish a frozen orbit.

When to use Frozen Periapsis Angle Screen

Use this tool to screen the 90/270-degree periapsis orientation necessary in common frozen-orbit models; this alone does not establish a frozen orbit.

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 Frozen Periapsis Angle Screen 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 argumentPeriapsisDegrees, toleranceDegrees using the field table and calculation rules, then run the tool.
Read nearestTargetDegrees, angleSeparationDegrees, angleConditionMet. 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
argumentPeriapsisDegrees	Argument periapsis degrees	number	Required
toleranceDegrees	Tolerance degrees	number	Required

Enter a finite argument of periapsis in degrees and nonnegative degree tolerance. The tool wraps the angle, measures shortest circular distances to both targets, selects the nearer target and tests the minimum inclusively against tolerance. Ties select 90 degrees.

separation = min(|shortAngle(argp−90)|, |shortAngle(argp−270)|)

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

Output field	Meaning	Value type
nearestTargetDegrees	Nearest target degrees	number
angleSeparationDegrees	Angle separation degrees	number
angleConditionMet	Angle condition met	boolean

json

{
  "input": {
    "argumentPeriapsisDegrees": 450,
    "toleranceDegrees": 1
  },
  "output": {
    "nearestTargetDegrees": 90,
    "angleSeparationDegrees": 0,
    "angleConditionMet": true
  }
}

Limitations and assumptions

It does not evaluate eccentricity, inclination, J3/J2 balance or actual precession. A passing angular condition alone does not establish a frozen orbit.

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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use J2 Critical Inclination Proximity: Compare inclination with both first-order J2 critical inclinations, rather than a rounded 63.4-degree reference only. For a complementary task, use J2 Periapsis Precession: Evaluate first-order secular J2 argument-of-periapsis precession for supplied mean elliptic elements in km and seconds.

References

Frozen Periapsis Angle Screen — tool.io

Similar or alternative tools

J2 Critical Inclination Proximity
Compare inclination with both first-order J2 critical inclinations, rather than a rounded 63.4-degree reference only.
J2 Periapsis Precession
Evaluate first-order secular J2 argument-of-periapsis precession for supplied mean elliptic elements in km and seconds.