J2 Nodal Precession

Evaluate signed first-order J2 nodal precession for supplied mean elliptic elements in km and seconds.

Description

First-order J2 precession rotates the ascending node of an inclined elliptic orbit.

First-order J2 precession rotates the ascending node of an inclined elliptic orbit. The cosine of inclination determines the drift's sign, while the supplied gravity and shape parameters determine its scale.^[1]

Evaluate signed first-order J2 nodal precession for supplied mean elliptic elements in km and seconds.

When to use J2 Nodal Precession

Use this tool to evaluate signed first-order J2 nodal precession for supplied mean elliptic elements in km and seconds.

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 Nodal Precession 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 mu, semimajorAxis, eccentricity, referenceRadius, j2, inclinationDegrees using the field table and calculation rules, then run the tool.
Read radiansPerSecond, degreesPerDay. 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
inclinationDegrees	Inclination degrees	number	Required

Enter positive μ, semimajor axis and reference radius, eccentricity in [0,1), nonnegative J2 and inclination within 0–180 degrees. With lengths in km and μ in km³/s², the tool returns radians/second and degrees/day. The second output converts radians to degrees and multiplies by 86,400.

nodeRate = −1.5 J2 sqrt(μ/a³)[R/(a(1−e²))]² cos(i)

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

Output field	Meaning	Value type
radiansPerSecond	Radians per second	number
degreesPerDay	Degrees per day	number

json

{
  "input": {
    "mu": 1,
    "semimajorAxis": 2,
    "eccentricity": 0,
    "referenceRadius": 1,
    "j2": 0.01,
    "inclinationDegrees": 0
  },
  "output": {
    "radiansPerSecond": -0.0013258252147247767,
    "degreesPerDay": -6563.305944785304
  }
}

Limitations and assumptions

No higher harmonics, drag or third-body perturbations are included. At circular/equatorial singularities, interpreting classical angles needs care; numeric output is not a full orbital propagation.

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 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 Sun Synchronous Inclination Solve: Invert first-order J2 nodal precession for an inclination matching a caller-supplied sun-synchronous target rate.

References

J2 Nodal Precession — 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.
Sun Synchronous Inclination Solve
Invert first-order J2 nodal precession for an inclination matching a caller-supplied sun-synchronous target rate.