Repeat Ground Track Period
Solve the node-relative repeat-ground-track period for supplied integer rotations and revolutions, including a supplied nodal drift.
Description
A repeat ground track depends on rotation relative to the orbital node, not just the planet's rotation period.
A repeat ground track depends on rotation relative to the orbital node, not just the planet's rotation period. Specified rotation and revolution counts define the intended repeating cycle.1
Solve the node-relative repeat-ground-track period for supplied integer rotations and revolutions, including a supplied nodal drift.
When to use Repeat Ground Track Period
Use this tool to solve the node-relative repeat-ground-track period for supplied integer rotations and revolutions, including a supplied nodal drift.
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 Repeat Ground Track Period 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 planetRotationSeconds, nodalPrecessionRadiansPerSecond, planetRotations, orbitRevolutions, observedOrbitPeriodSeconds using the field table and calculation rules, then run the tool.
- Read relativeRotationSeconds, requiredOrbitPeriodSeconds, periodMismatchSeconds. 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 |
|---|---|---|---|
| planetRotationSeconds | Planet rotation seconds | number | Required |
| nodalPrecessionRadiansPerSecond | Nodal precession radians per second | number | Required |
| planetRotations | Planet rotations | integer | Required |
| orbitRevolutions | Orbit revolutions | integer | Required |
| observedOrbitPeriodSeconds | Observed orbit period seconds | number | Required |
Enter positive rotation and observed orbit periods in seconds, positive integer rotation/revolution counts and signed nodal drift in radians/second. The relative rotation rate must be positive. The tool returns that relative period, the required orbit period and observed-minus-required mismatch; a positive mismatch means the observed orbit is slower.
relativeRate = 2π/rotationPeriod − nodalRate; requiredPeriod = rotations × (2π/relativeRate)/revolutions Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| relativeRotationSeconds | Relative rotation seconds | number |
| requiredOrbitPeriodSeconds | Required orbit period seconds | number |
| periodMismatchSeconds | Period mismatch seconds | number |
{
"input": {
"planetRotationSeconds": 100,
"nodalPrecessionRadiansPerSecond": 0,
"planetRotations": 2,
"orbitRevolutions": 5,
"observedOrbitPeriodSeconds": 40
},
"output": {
"relativeRotationSeconds": 99.99999999999999,
"requiredOrbitPeriodSeconds": 39.99999999999999,
"periodMismatchSeconds": 7.105427357601002e-15
}
}Limitations and assumptions
It does not propagate a ground track or account for changing orbital elements, latitude coverage or additional perturbations. The supplied nodal rate is a fixed model input.
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 Keplerian Orbital Period: Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup. For a complementary task, use J2 Nodal Precession: Evaluate signed first-order J2 nodal precession for supplied mean elliptic elements in km and seconds.
References
-
Repeat Ground Track Period — tool.io
Similar or alternative tools
- Keplerian Orbital Period
Compute a two-body elliptic orbital period from semimajor axis and total gravitational parameter, not a fixed planetary lookup.
- J2 Nodal Precession
Evaluate signed first-order J2 nodal precession for supplied mean elliptic elements in km and seconds.