Elliptic Mean To True Anomaly
Solve elliptic Kepler equation with bounded bisection and convert to wrapped true anomaly; angles are in degrees.
Description
Kepler's equation connects uniformly advancing mean anomaly with eccentric anomaly.
Kepler's equation connects uniformly advancing mean anomaly with eccentric anomaly. Recovering true anomaly requires solving that equation and then using a quadrant-aware conversion.1
Solve elliptic Kepler equation with bounded bisection and convert to wrapped true anomaly; angles are in degrees.
When to use Elliptic Mean To True Anomaly
Use this tool to solve elliptic Kepler equation with bounded bisection and convert to wrapped true anomaly; angles are in degrees.
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 Mean To True 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 meanAnomalyDegrees, orbitalEccentricity using the field table and calculation rules, then run the tool.
- Read eccentricAnomalyDegrees, trueAnomalyDegrees. 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 |
|---|---|---|---|
| meanAnomalyDegrees | Mean anomaly degrees | number | Required |
| orbitalEccentricity | Orbital eccentricity | number | Required |
Enter finite mean anomaly in degrees and eccentricity 0≤e<1. The helper wraps M into one turn and performs 100 bisection iterations on [0,2π]. The tool converts the solution to true anomaly and returns both anomalies in degrees, with true anomaly wrapped to [0,360).
solve E−e sinE = wrap(M,2π); ν = atan2(sqrt(1−e²)sinE,cosE−e) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| eccentricAnomalyDegrees | Eccentric anomaly degrees | number |
| trueAnomalyDegrees | True anomaly degrees | number |
{
"input": {
"meanAnomalyDegrees": 180,
"orbitalEccentricity": 0.5
},
"output": {
"eccentricAnomalyDegrees": 180,
"trueAnomalyDegrees": 180
}
}Limitations and assumptions
This is bounded numerical inversion for an ellipse, without a convergence residual output or uncertainty estimate. It discards whole revolutions and does not infer a period or epoch.
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 True To Eccentric Anomaly: Convert elliptic true anomaly to wrapped eccentric and mean anomaly while preserving the correct quadrant. 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 Mean To True Anomaly — tool.io
Similar or alternative tools
- Elliptic True To Eccentric Anomaly
Convert elliptic true anomaly to wrapped eccentric and mean anomaly while preserving the correct quadrant.
- Mean Anomaly Periapsis Time
Map a wrapped elliptic mean anomaly to time since the latest periapsis in the supplied period unit.