Hyperbolic Motion

Functions
double	ln_solve_hyp_barker (double Q1, double G, double t)
	Solve Barkers equation. More...
double	ln_get_hyp_true_anomaly (double q, double e, double t)
	Calculate the true anomaly. More...
double	ln_get_hyp_radius_vector (double q, double e, double t)
	Calculate the radius vector. More...
void	ln_get_hyp_geo_rect_posn (struct ln_hyp_orbit *orbit, double JD, struct ln_rect_posn *posn)
	Calculate an objects rectangular geocentric position. More...
void	ln_get_hyp_helio_rect_posn (struct ln_hyp_orbit *orbit, double JD, struct ln_rect_posn *posn)
	Calculate an objects rectangular heliocentric position. More...
void	ln_get_hyp_body_equ_coords (double JD, struct ln_hyp_orbit *orbit, struct ln_equ_posn *posn)
	Calculate a bodies equatorial coordinates. More...
double	ln_get_hyp_body_earth_dist (double JD, struct ln_hyp_orbit *orbit)
	Calculate the distance between a body and the Earth. More...
double	ln_get_hyp_body_solar_dist (double JD, struct ln_hyp_orbit *orbit)
	Calculate the distance between a body and the Sun. More...
double	ln_get_hyp_body_phase_angle (double JD, struct ln_hyp_orbit *orbit)
	Calculate the phase angle of the body. More...
double	ln_get_hyp_body_elong (double JD, struct ln_hyp_orbit *orbit)
	Calculate the bodies elongation to the Sun. More...
int	ln_get_hyp_body_rst (double JD, struct ln_lnlat_posn *observer, struct ln_hyp_orbit *orbit, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with a hyperbolic orbit. More...
int	ln_get_hyp_body_rst_horizon (double JD, struct ln_lnlat_posn *observer, struct ln_hyp_orbit *orbit, double horizon, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with a hyperbolic orbit. More...
int	ln_get_hyp_body_next_rst (double JD, struct ln_lnlat_posn *observer, struct ln_hyp_orbit *orbit, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with an hyperbolic orbit. More...
int	ln_get_hyp_body_next_rst_horizon (double JD, struct ln_lnlat_posn *observer, struct ln_hyp_orbit *orbit, double horizon, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with an hyperbolic orbit. More...
int	ln_get_hyp_body_next_rst_horizon_future (double JD, struct ln_lnlat_posn *observer, struct ln_hyp_orbit *orbit, double horizon, int day_limit, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with an hyperbolic orbit. More...

Detailed Description

Functions relating to the Hyperbolic motion of bodies.

All angles are expressed in degrees.

Function Documentation

double ln_get_hyp_body_earth_dist	(	double	JD,
		struct ln_hyp_orbit *	orbit
	)

Calculate the distance between a body and the Earth.

Parameters

JD	Julian day.
orbit	Orbital parameters

Returns

Distance in AU

Calculate the distance between a body and the Earth for the given julian day.

References ln_get_hyp_geo_rect_posn(), ln_rect_posn::X, ln_rect_posn::Y, and ln_rect_posn::Z.

double ln_get_hyp_body_elong	(	double	JD,
		struct ln_hyp_orbit *	orbit
	)

Calculate the bodies elongation to the Sun.

Parameters

JD	Julian day
orbit	Orbital parameters

Returns

Elongation to the Sun.

Calculate the bodies elongation to the Sun..

References ln_hyp_orbit::e, ln_hyp_orbit::JD, ln_get_earth_solar_dist(), ln_get_hyp_body_solar_dist(), ln_get_hyp_radius_vector(), ln_rad_to_deg(), ln_range_degrees(), and ln_hyp_orbit::q.

void ln_get_hyp_body_equ_coords	(	double	JD,
		struct ln_hyp_orbit *	orbit,
		struct ln_equ_posn *	posn
	)

Calculate a bodies equatorial coordinates.

Parameters

JD	Julian Day.
orbit	Orbital parameters.
posn	Pointer to hold asteroid position.

Calculate a bodies equatorial coordinates for the given julian day.

References ln_equ_posn::dec, ln_get_hyp_helio_rect_posn(), ln_get_solar_geo_coords(), ln_rad_to_deg(), ln_range_degrees(), ln_equ_posn::ra, ln_rect_posn::X, ln_rect_posn::Y, and ln_rect_posn::Z.

Referenced by ln_get_hyp_body_next_rst_horizon(), ln_get_hyp_body_next_rst_horizon_future(), and ln_get_hyp_body_rst_horizon().

double ln_get_hyp_body_next_rst	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_hyp_orbit *	orbit,
		struct ln_rst_time *	rst
	)

Calculate the time of rise, set and transit for a body with an hyperbolic orbit.

Parameters

JD	Julian day
observer	Observers position
orbit	Orbital parameters
rst	Pointer to store Rise, Set and Transit time in JD

Returns

0 for success, else 1 for circumpolar (above the horizon), -1 for circumpolar (bellow the horizon)

Calculate the time of next rise, set and transit (crosses the local meridian at upper culmination) time of a body with an hyperbolic orbit for the given Julian day.

This function guarantee, that rise, set and transit will be in <JD, JD+1> range.

Note: this functions returns 1 if the body is circumpolar, that is it remains the whole day above the horizon. Returns -1 when it remains the whole day below the horizon.

References ln_get_hyp_body_next_rst_horizon().

double ln_get_hyp_body_next_rst_horizon	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_hyp_orbit *	orbit,
		double	horizon,
		struct ln_rst_time *	rst
	)

Calculate the time of rise, set and transit for a body with an hyperbolic orbit.

Parameters

JD	Julian day
observer	Observers position
orbit	Orbital parameters
horizon	Horizon height
rst	Pointer to store Rise, Set and Transit time in JD

Returns

0 for success, else 1 for circumpolar (above the horizon), -1 for circumpolar (bellow the horizon)

Calculate the time of next rise, set and transit (crosses the local meridian at upper culmination) time of a body with an hyperbolic orbit for the given Julian day.

This function guarantee, that rise, set and transit will be in <JD, JD+1> range.

Note: this functions returns 1 if the body is circumpolar, that is it remains the whole day above the horizon. Returns -1 when it remains the whole day below the horizon.

References ln_get_hyp_body_equ_coords().

Referenced by ln_get_hyp_body_next_rst().

double ln_get_hyp_body_next_rst_horizon_future	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_hyp_orbit *	orbit,
		double	horizon,
		int	day_limit,
		struct ln_rst_time *	rst
	)

Calculate the time of rise, set and transit for a body with an hyperbolic orbit.

Parameters

JD	Julian day
observer	Observers position
orbit	Orbital parameters
horizon	Horizon height
day_limit	Maximal number of days that will be searched for next rise and set
rst	Pointer to store Rise, Set and Transit time in JD

Returns

0 for success, else 1 for circumpolar (above the horizon), -1 for circumpolar (bellow the horizon)

Calculate the time of next rise, set and transit (crosses the local meridian at upper culmination) time of a body with an hyperbolic orbit for the given Julian day.

This function guarantee, that rise, set and transit will be in <JD, JD + day_limit> range.

Note: this functions returns 1 if the body is circumpolar, that is it remains the whole day above the horizon. Returns -1 when it remains the whole day below the horizon.

References ln_get_hyp_body_equ_coords().

double ln_get_hyp_body_phase_angle	(	double	JD,
		struct ln_hyp_orbit *	orbit
	)

Calculate the phase angle of the body.

Parameters

JD	Julian day
orbit	Orbital parameters

Returns

Phase angle.

Calculate the phase angle of the body. The angle Sun - body - Earth.

References ln_hyp_orbit::e, ln_hyp_orbit::JD, ln_get_earth_solar_dist(), ln_get_hyp_body_solar_dist(), ln_get_hyp_radius_vector(), ln_rad_to_deg(), ln_range_degrees(), and ln_hyp_orbit::q.

double ln_get_hyp_body_rst	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_hyp_orbit *	orbit,
		struct ln_rst_time *	rst
	)

Calculate the time of rise, set and transit for a body with a hyperbolic orbit.

Parameters

JD	Julian day
observer	Observers position
orbit	Orbital parameters
rst	Pointer to store Rise, Set and Transit time in JD

Returns

0 for success, else 1 for circumpolar.

Calculate the time the rise, set and transit (crosses the local meridian at upper culmination) time of a body with a parabolic orbit for the given Julian day.

Note: this functions returns 1 if the body is circumpolar, that is it remains the whole day above or below the horizon. Returns -1 when it remains whole day below the horizon.

References ln_get_hyp_body_rst_horizon().

double ln_get_hyp_body_rst_horizon	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_hyp_orbit *	orbit,
		double	horizon,
		struct ln_rst_time *	rst
	)

Calculate the time of rise, set and transit for a body with a hyperbolic orbit.

Parameters

JD	Julian day
observer	Observers position
orbit	Orbital parameters
horizon	Horizon height
rst	Pointer to store Rise, Set and Transit time in JD

Returns

0 for success, 1 for circumpolar (above the horizon), -1 for circumpolar (bellow the horizon)

Calculate the time the rise, set and transit (crosses the local meridian at upper culmination) time of a body with a parabolic orbit for the given Julian day.

Note: this functions returns 1 if the body is circumpolar, that is it remains the whole day above or below the horizon. Returns -1 when it remains whole day below the horizon.

References ln_get_hyp_body_equ_coords().

Referenced by ln_get_hyp_body_rst().

double ln_get_hyp_body_solar_dist	(	double	JD,
		struct ln_hyp_orbit *	orbit
	)

Calculate the distance between a body and the Sun.

Parameters

JD	Julian Day.
orbit	Orbital parameters

Returns

The distance in AU between the Sun and the body.

Calculate the distance between a body and the Sun.

References ln_get_hyp_helio_rect_posn(), ln_rect_posn::X, ln_rect_posn::Y, and ln_rect_posn::Z.

Referenced by ln_get_hyp_body_elong(), and ln_get_hyp_body_phase_angle().

void ln_get_hyp_geo_rect_posn	(	struct ln_hyp_orbit *	orbit,
		double	JD,
		struct ln_rect_posn *	posn
	)

Calculate an objects rectangular geocentric position.

Parameters

orbit	Orbital parameters of object.
JD	Julian day
posn	Position pointer to store objects position

Calculate the objects rectangular geocentric position given it's orbital elements for the given julian day.

References ln_get_earth_helio_coords(), ln_get_hyp_helio_rect_posn(), ln_get_rect_from_helio(), ln_rect_posn::X, ln_rect_posn::Y, and ln_rect_posn::Z.

Referenced by ln_get_hyp_body_earth_dist().

void ln_get_hyp_helio_rect_posn	(	struct ln_hyp_orbit *	orbit,
		double	JD,
		struct ln_rect_posn *	posn
	)

Calculate an objects rectangular heliocentric position.

Parameters

orbit	Orbital parameters of object.
JD	Julian day
posn	Position pointer to store objects position

Calculate the objects rectangular heliocentric position given it's orbital elements for the given julian day.

References ln_helio_posn::B, ln_hyp_orbit::e, ln_hyp_orbit::i, ln_hyp_orbit::JD, ln_deg_to_rad(), ln_get_hyp_radius_vector(), ln_get_hyp_true_anomaly(), ln_hyp_orbit::omega, ln_hyp_orbit::q, ln_helio_posn::R, ln_hyp_orbit::w, ln_rect_posn::X, ln_rect_posn::Y, and ln_rect_posn::Z.

Referenced by ln_get_hyp_body_equ_coords(), ln_get_hyp_body_solar_dist(), and ln_get_hyp_geo_rect_posn().

double ln_get_hyp_radius_vector	(	double	q,
		double	e,
		double	t
	)

Calculate the radius vector.

Parameters

q	Perihelion distance in AU
e	Orbit eccentricity
t	Time since perihelion in days

Returns

Radius vector AU

Calculate the radius vector.

References ln_deg_to_rad(), and ln_get_hyp_true_anomaly().

Referenced by ln_get_hyp_body_elong(), ln_get_hyp_body_phase_angle(), and ln_get_hyp_helio_rect_posn().

double ln_get_hyp_true_anomaly	(	double	q,
		double	e,
		double	t
	)

Calculate the true anomaly.

Parameters

q	Perihelion distance in AU
e	Orbit eccentricity
t	Time since perihelion

Returns

True anomaly (degrees)

Calculate the true anomaly.

References ln_rad_to_deg(), ln_range_degrees(), and ln_solve_hyp_barker().

Referenced by ln_get_hyp_helio_rect_posn(), and ln_get_hyp_radius_vector().

double ln_solve_hyp_barker	(	double	Q1,
		double	G,
		double	t
	)

Solve Barkers equation.

Parameters

Q1	See 35.0
G	See 35.0
t	Time since perihelion in days

Returns

Solution of Barkers equation

Solve Barkers equation. LIAM add more

References ln_helio_posn::L.

Referenced by ln_get_hyp_true_anomaly().