Function Repository Resource:

# KeplerE

Evaluate the solution of the standard Kepler equation

Contributed by: Jan Mangaldan
 ResourceFunction["KeplerE"][ε,M] gives the principal solution E in the standard Kepler equation M=E-ε sin(E).

## Details

Mathematical function, suitable for both symbolic and numerical manipulation.
In the standard Kepler equation, M is the mean anomaly of an orbiting body, while ε is the eccentricity of the orbit. ResourceFunction["KeplerE"] gives the value of the corresponding eccentric anomaly E.
The eccentricity ε is assumed to satisfy 0ε<1, corresponding to an elliptic orbit.
For certain special arguments, ResourceFunction["KeplerE"] automatically evaluates to exact values.
ResourceFunction["KeplerE"] can be evaluated to arbitrary numerical precision.

## Examples

### Basic Examples (2)

Evaluate numerically:

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Plot over a subset of the reals:

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### Scope (4)

Simple exact values are generated automatically:

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Evaluate to arbitrary precision:

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The precision of the output tracks the precision of the input:

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Parity transformation is automatically applied:

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### Applications (1)

Compute the distance from the Sun and true anomaly of Mars on a given date, assuming a Keplerian orbit:

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### Properties and Relations (1)

KeplerE is the inverse of the function E-ε sin(E):

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### Neat Examples (1)

Visualize the weekly orbital progress of an orbiting body with eccentricity over a period of one year:

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## Version History

• 1.0.1 – 06 January 2021
• 1.0.0 – 22 December 2020