The Kepler Problem

Utilities for solving the Kepler problem.

Functions
template<typename realT >
long	mx::astro::hyperbolic_kepler (realT &E, realT &err, realT e, realT M, realT tol, long itmax)
	Solve the hyperbolic kepler equation (for e> 1).
template<typename realT >
realT	mx::astro::kepler_danby_1 (realT e, realT M, realT Ei)
	Calculate the next iteration of Danby's quartic Newton-Raphson method.
template<typename realT >
long	mx::astro::solve_kepler_danby (realT &E, realT &D, realT e, realT M, realT tol, long itmax)
	Solve Kepler's equation using Danby's quartic Newton-Raphson method.
template<typename realT >
long	mx::astro::solve_kepler (realT &E, realT &D, realT e, realT M, realT tol=KEPLER_TOL, long itmax=KEPLER_ITMAX)
	Solve Kepler's equation for any e. Uses solve_kepler_danby if e < 1.0, hyperbolic_kepler otherwise.

Function Documentation

hyperbolic_kepler()

template<typename realT >

long mx::astro::hyperbolic_kepler	(	realT &	E,
		realT &	err,
		realT	e,
		realT	M,
		realT	tol,
		long	itmax
	)

Solve the hyperbolic kepler equation (for e> 1).

Note

this is not tested very well (as of 2014.08.09)

Returns

-1 on exceeding itmax, otherwise reurns the number of iterations.

Template Parameters

realT

is the type used for arithmetic

Parameters

[out]	E	is the eccentric anomaly
[out]	err	is the error after the last iteration
[in]	e	is the eccentricity
[in]	M	is the mean anomaly
[in]	tol	is the desired tolerance
[in]	itmax	is the maximum number of iterations

Definition at line 44 of file kepler.hpp.

Referenced by mx::astro::solve_kepler().

kepler_danby_1()

template<typename realT >

realT mx::astro::kepler_danby_1	(	realT	e,
		realT	M,
		realT	Ei
	)

Calculate the next iteration of Danby's quartic Newton-Raphson method.

Definition at line 85 of file kepler.hpp.

Referenced by mx::astro::solve_kepler_danby().

solve_kepler()

template<typename realT >

long mx::astro::solve_kepler	(	realT &	E,
		realT &	D,
		realT	e,
		realT	M,
		realT	tol = KEPLER_TOL,
		long	itmax = KEPLER_ITMAX
	)

Solve Kepler's equation for any e. Uses solve_kepler_danby if e < 1.0, hyperbolic_kepler otherwise.

Returns

the number of iterations on success.

-1 if itmax is exceeded.

Parameters

[out]	E	is the eccentric anomaly
[out]	D	is the error after the last iteration
[in]	e	is the eccentricity
[in]	M	is the mean anomaly
[in]	tol	is the desired tolerance
[in]	itmax	is the maximum number of iterations

Definition at line 156 of file kepler.hpp.

References mx::astro::hyperbolic_kepler(), and mx::astro::solve_kepler_danby().

Referenced by mx::astro::orbitElements().

solve_kepler_danby()

template<typename realT >

long mx::astro::solve_kepler_danby	(	realT &	E,
		realT &	D,
		realT	e,
		realT	M,
		realT	tol,
		long	itmax
	)

Solve Kepler's equation using Danby's quartic Newton-Raphson method.

Returns

-1 on exceeding itmax.

the number of iterations on success.

Parameters

[out]	E	is the eccentric anomaly
[out]	D	is the error after the last iteration
[in]	e	is the eccentricity
[in]	M	is the mean anomaly
[in]	tol	is the desired tolerance
[in]	itmax	is the maximum number of iterations

Definition at line 113 of file kepler.hpp.

References mx::astro::kepler_danby_1().

Referenced by mx::astro::solve_kepler().