Sun Synchronous Inclination Solve
Invert first-order J2 nodal precession for an inclination matching a caller-supplied sun-synchronous target rate.
Description
First-order J2 nodal precession models the secular effect of an oblate central body on an elliptic orbit's ascending node.
First-order J2 nodal precession models the secular effect of an oblate central body on an elliptic orbit's ascending node. Solving for inclination can match a caller-supplied sun-synchronous target rate, provided that rate is attainable in the model.1
Invert first-order J2 nodal precession for an inclination matching a caller-supplied sun-synchronous target rate.
When to use Sun Synchronous Inclination Solve
Use this tool to invert first-order J2 nodal precession for an inclination matching a caller-supplied sun-synchronous target rate.
Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Sun Synchronous Inclination Solve and understand its results
- Prepare the orbital state or model parameters in one reference frame. Use compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter mu, semimajorAxis, eccentricity, referenceRadius, j2, desiredRadiansPerSecond using the field table and calculation rules, then run the tool.
- Read requiredInclinationDegrees. 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 |
| semimajorAxis | Semimajor axis | number | Required |
| eccentricity | Eccentricity | number | Required |
| referenceRadius | Reference radius | number | Required |
| j2 | J 2 | number | Required |
| desiredRadiansPerSecond | Desired radians per second | number | Required |
Enter positive gravitational parameter μ, semimajor axis a and reference radius R, eccentricity 0≤e<1, positive effective J2 factor and the signed desired rate. With distance in km and time in seconds, μ is km³/s² and the rate radians/second. The helper calculates K, requires it positive and rejects |desiredRate/K|>1. It returns acos in degrees; zero desired rate yields 90 degrees.
K = (3/2)J2√(μ/a³)[R/(a(1−e²))]²; inclination = acos(−desiredRate/K) in degrees Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| requiredInclinationDegrees | Required inclination degrees | number |
{
"input": {
"mu": 1,
"semimajorAxis": 2,
"eccentricity": 0,
"referenceRadius": 1,
"j2": 0.01,
"desiredRadiansPerSecond": 0
},
"output": {
"requiredInclinationDegrees": 90
}
}Limitations and assumptions
It does not select a solar rate, include higher harmonics, drag or third-body effects, or establish that the orbit clears the central body. No tolerance is added at the feasibility boundary. Use compatible distance/time units throughout.
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 Semimajor Axis From Period: Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units. For a complementary task, use Specific Orbital Energy: Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety.
References
-
Sun Synchronous Inclination Solve — tool.io
Similar or alternative tools
- Semimajor Axis From Period
Invert Kepler third law for a positive elliptic semimajor axis using total gravitational parameter and period in compatible units.
- Specific Orbital Energy
Evaluate specific two-body orbital energy v²/2−μ/r in consistent units; this does not determine angular momentum or collision safety.