Elliptic True To Eccentric Anomaly
Convert elliptic true anomaly to wrapped eccentric and mean anomaly while preserving the correct quadrant.
Description
True, eccentric and mean anomalies describe different angles along an ellipse.
True, eccentric and mean anomalies describe different angles along an ellipse. A quadrant-preserving conversion is needed for positions beyond a single half orbit.1
Convert elliptic true anomaly to wrapped eccentric and mean anomaly while preserving the correct quadrant.
When to use Elliptic True To Eccentric Anomaly
Use this tool to convert elliptic true anomaly to wrapped eccentric and mean anomaly while preserving the correct quadrant.
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 Elliptic True To Eccentric Anomaly 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 trueAnomalyDegrees, orbitalEccentricity using the field table and calculation rules, then run the tool.
- Read eccentricAnomalyDegrees, meanAnomalyDegrees. 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 |
|---|---|---|---|
| trueAnomalyDegrees | True anomaly degrees | number | Required |
| orbitalEccentricity | Orbital eccentricity | number | Required |
Enter eccentricity 0≤e<1 and finite true anomaly in degrees. The tool converts to radians, uses atan2 and wraps eccentric anomaly into [0,2π). It then computes mean anomaly and returns both in degrees. For a circular orbit the angular forms coincide apart from numeric wrapping.
E = atan2(sqrt(1−e²)sinν, e+cosν), wrapped; M = E−e sinE Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| eccentricAnomalyDegrees | Eccentric anomaly degrees | number |
| meanAnomalyDegrees | Mean anomaly degrees | number |
{
"input": {
"trueAnomalyDegrees": 180,
"orbitalEccentricity": 0.5
},
"output": {
"eccentricAnomalyDegrees": 180,
"meanAnomalyDegrees": 180
}
}Limitations and assumptions
This is elliptic-only and does not return an epoch or radius. Whole prior revolutions are discarded by wrapping, and uncertainty is not propagated.
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 Elliptic Mean To True Anomaly: Solve elliptic Kepler equation with bounded bisection and convert to wrapped true anomaly; angles are in degrees. For a complementary task, use Mean Anomaly Periapsis Time: Map a wrapped elliptic mean anomaly to time since the latest periapsis in the supplied period unit.
References
-
Elliptic True To Eccentric Anomaly — tool.io
Similar or alternative tools
- Elliptic Mean To True Anomaly
Solve elliptic Kepler equation with bounded bisection and convert to wrapped true anomaly; angles are in degrees.
- Mean Anomaly Periapsis Time
Map a wrapped elliptic mean anomaly to time since the latest periapsis in the supplied period unit.