kepler.hpp File Reference

Declarations for the utilities related to the Kepler problem. More...

Declarations for the utilities related to the Kepler problem.

Author

Jared R. Males

Definition in file kepler.hpp.

Go to the source code of this file.

Namespaces
	mx
	The mxlib c++ namespace.

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). More...
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. More...
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. More...
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. More...
template<typename arithT >
arithT	mx::astro::kepler_danby_diff_1 (arithT EC, arithT ES, arithT dM, arithT dEi)
	Calculate the next iteration of Danby's quartic Newton-Raphson method (difference form). More...
template<typename arithT >
long	mx::astro::solve_keplerdiff_danby (arithT *dE, arithT *D, arithT e, arithT EC, arithT ES, arithT dM, arithT tol, long itmax)
	Solve Kepler's equation in difference form using Danby's quartic Newton-Raphson method. More...
template<typename arithT >
int	mx::astro::get_W_1pt_z0 (arithT &W, arithT x, arithT y, arithT r, arithT f, arithT w)
	Calculate the inclination and the longitude of the ascending node given a point on the orbit projected onto the plane of the sky, the argument of pericenter, the current true radius, and the current true anomaly. More...

Function Documentation

get_W_1pt_z0()

template<typename arithT >

int mx::astro::get_W_1pt_z0	(	arithT &	W,
		arithT	x,
		arithT	y,
		arithT	r,
		arithT	f,
		arithT	w
	)

Calculate the inclination and the longitude of the ascending node given a point on the orbit projected onto the plane of the sky, the argument of pericenter, the current true radius, and the current true anomaly.

Solutions are not always possible. You must check the return value to know if the results are valid.

Parameters

i	[output] the inclination (there will be 2)
W	[output] the longitude of the ascending node (there will be 2)
x	[input] the x coordinate of the projection onto the reference plane
y	[input] the y coordinate of the projection onto the reference plane
rho	[input] the projected separation (yes this is redundant to x and y, but it is passed independently for efficiency)
r	[input] the physical (3D) separation
f	[input] the true anomaly
w	[input] the argument of pericenter

Return values

0	on success
-1	if no solution is possible due to ...
-2	if no solution is possible due to z = 0
-3	if no solution is possible due to ... Calculate the longitude of the ascending node given a point on the orbit projected onto the plane of the sky, the argument of pericenter, the current radius, and the current true anomaly. Used for the z = 0, i != 0/PI case. i.e. sin(w+f) = 0, cos(w+f) = +/- 1. w must be either -f or PI - f.

Parameters

W	[output] the longitude of the ascending node.
x	[input] the x coordinate of the starting point
y	[input] the y coordinate of the starting point
r	[input] the current 3D separation from the star
f	[input] the current true anomaly
w	[input] the argument of pericenter

Return values

0	on success
-1	if the conditions aren't met by w an df

Definition at line 288 of file kepler.hpp.

References mx::astro::get_W_1pt_z0().

Referenced by mx::astro::get_W_1pt_z0().

kepler_danby_diff_1()

template<typename arithT >

arithT mx::astro::kepler_danby_diff_1	(	arithT	EC,
		arithT	ES,
		arithT	dM,
		arithT	dEi
	)

Calculate the next iteration of Danby's quartic Newton-Raphson method (difference form).

Definition at line 191 of file kepler.hpp.

References mx::astro::kepler_danby_diff_1().

Referenced by mx::astro::kepler_danby_diff_1(), and mx::astro::solve_keplerdiff_danby().

solve_keplerdiff_danby()

template<typename arithT >

long mx::astro::solve_keplerdiff_danby	(	arithT *	dE,
		arithT *	D,
		arithT	e,
		arithT	EC,
		arithT	ES,
		arithT	dM,
		arithT	tol,
		long	itmax
	)

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

Parameters

dE	[output] is the eccentric anomaly
D	[output] is the error after the last iteration
e	[input] is the eccentricity
EC	[input]
ES	[input]
dM	[input]
tol	[input] is the desired tolerance
itmax	[input] is the maximum number of iterations

Return values

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

Definition at line 225 of file kepler.hpp.

References mx::astro::kepler_danby_diff_1(), mx::math::func::sign(), and mx::astro::solve_keplerdiff_danby().

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