J2 Critical Inclination Proximity
Compare inclination with both first-order J2 critical inclinations, rather than a rounded 63.4-degree reference only.
Description
The first-order J2 periapsis rate vanishes at two inclinations satisfying cos²(i)=1/5.
The first-order J2 periapsis rate vanishes at two inclinations satisfying cos²(i)=1/5. Checking both avoids assuming every orbit uses the prograde critical angle.1
Compare inclination with both first-order J2 critical inclinations, rather than a rounded 63.4-degree reference only.
When to use J2 Critical Inclination Proximity
Use this tool to compare inclination with both first-order J2 critical inclinations, rather than a rounded 63.4-degree reference only.
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 J2 Critical Inclination Proximity 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 inclinationDegrees, toleranceDegrees using the field table and calculation rules, then run the tool.
- Read nearestCriticalDegrees, separationDegrees, 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 |
|---|---|---|---|
| inclinationDegrees | Inclination degrees | number | Required |
| toleranceDegrees | Tolerance degrees | number | Required |
Enter inclination from 0 through 180 degrees and a nonnegative degree tolerance. The tool computes both exact-model angles, selects the nearer one and returns separation and an inclusive withinTolerance flag. A distance tie selects the lower critical angle.
critical angles = acos(sqrt(1/5)) and 180°−acos(sqrt(1/5)) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| nearestCriticalDegrees | Nearest critical degrees | number |
| separationDegrees | Separation degrees | number |
| withinTolerance | Within tolerance | boolean |
{
"input": {
"inclinationDegrees": 63.43494882292201,
"toleranceDegrees": 0.1
},
"output": {
"nearestCriticalDegrees": 63.43494882292201,
"separationDegrees": 0,
"withinTolerance": true
}
}Limitations and assumptions
This is angle proximity, not proof of a frozen orbit or zero total precession. Other perturbations and measurement uncertainty are not supplied or inferred.
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 Periapsis Precession: Evaluate first-order secular J2 argument-of-periapsis precession for supplied mean elliptic elements in km and seconds. For a complementary task, use 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.
References
-
J2 Critical Inclination Proximity — tool.io
Similar or alternative tools
- J2 Periapsis Precession
Evaluate first-order secular J2 argument-of-periapsis precession for supplied mean elliptic elements in km and seconds.
- 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.