Elliptic Motion

Functions
double	ln_solve_kepler (double e, double M)
	Calculate the eccentric anomaly.
double	ln_get_ell_mean_anomaly (double n, double delta_JD)
	Calculate the mean anomaly.
double	ln_get_ell_true_anomaly (double e, double E)
	Calculate the true anomaly.
double	ln_get_ell_radius_vector (double a, double e, double E)
	Calculate the radius vector.
double	ln_get_ell_smajor_diam (double e, double q)
	Calculate the semi major diameter.
double	ln_get_ell_sminor_diam (double e, double a)
	Calculate the semi minor diameter.
double	ln_get_ell_mean_motion (double a)
	Calculate the mean daily motion (degrees/day).
void	ln_get_ell_geo_rect_posn (struct ln_ell_orbit *orbit, double JD, struct ln_rect_posn *posn)
	Calculate the objects rectangular geocentric position.
void	ln_get_ell_helio_rect_posn (struct ln_ell_orbit *orbit, double JD, struct ln_rect_posn *posn)
	Calculate the objects rectangular heliocentric position.
double	ln_get_ell_orbit_len (struct ln_ell_orbit *orbit)
	Calculate the orbital length in AU.
double	ln_get_ell_orbit_vel (double JD, struct ln_ell_orbit *orbit)
	Calculate orbital velocity in km/s.
double	ln_get_ell_orbit_pvel (struct ln_ell_orbit *orbit)
	Calculate orbital velocity at perihelion in km/s.
double	ln_get_ell_orbit_avel (struct ln_ell_orbit *orbit)
	Calculate the orbital velocity at aphelion in km/s.
double	ln_get_ell_body_phase_angle (double JD, struct ln_ell_orbit *orbit)
	Calculate the phase angle of the body. The angle Sun - body - Earth.
double	ln_get_ell_body_elong (double JD, struct ln_ell_orbit *orbit)
	Calculate the bodies elongation to the Sun..
double	ln_get_ell_body_solar_dist (double JD, struct ln_ell_orbit *orbit)
	Calculate the distance between a body and the Sun.
double	ln_get_ell_body_earth_dist (double JD, struct ln_ell_orbit *orbit)
	Calculate the distance between a body and the Earth.
void	ln_get_ell_body_equ_coords (double JD, struct ln_ell_orbit *orbit, struct ln_equ_posn *posn)
	Calculate a bodies equatorial coords.
int	ln_get_ell_body_rst (double JD, struct ln_lnlat_posn *observer, struct ln_ell_orbit *orbit, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with an elliptic orbit.
int	ln_get_ell_body_rst_horizon (double JD, struct ln_lnlat_posn *observer, struct ln_ell_orbit *orbit, double horizon, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with an elliptic orbit.
int	ln_get_ell_body_next_rst (double JD, struct ln_lnlat_posn *observer, struct ln_ell_orbit *orbit, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with an elliptic orbit.
int	ln_get_ell_body_next_rst_horizon (double JD, struct ln_lnlat_posn *observer, struct ln_ell_orbit *orbit, double horizon, struct ln_rst_time *rst)
	Calculate the time of rise, set and transit for a body with an elliptic orbit.
int	ln_get_ell_body_next_rst_horizon_future (double JD, struct ln_lnlat_posn *observer, struct ln_ell_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 elliptic orbit.
double	ln_get_ell_last_perihelion (double epoch_JD, double M, double n)
	Calculate the julian day of the last perihelion.

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Detailed Description

Functions relating to the elliptic motion of bodies.

All angles are expressed in degrees.

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Function Documentation

double ln_get_ell_body_earth_dist	(	double	JD,
		struct ln_ell_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 an body and the Earth for the given julian day.

Examples:

asteroid.c, and comet.c.

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

Referenced by ln_get_ell_body_phase_angle().

double ln_get_ell_body_elong	(	double	JD,
		struct ln_ell_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..

Examples:

asteroid.c.

References ln_ell_orbit::a, ln_ell_orbit::e, ln_ell_orbit::JD, ln_get_earth_solar_dist(), ln_get_ell_body_solar_dist(), ln_get_ell_mean_anomaly(), ln_get_ell_mean_motion(), ln_get_ell_radius_vector(), ln_rad_to_deg(), ln_range_degrees(), ln_solve_kepler(), and ln_ell_orbit::n.

void ln_get_ell_body_equ_coords	(	double	JD,
		struct ln_ell_orbit *	orbit,
		struct ln_equ_posn *	posn
	)

Calculate a bodies equatorial coords.

Parameters:

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

Calculate a bodies equatorial coordinates for the given julian day.

Examples:

asteroid.c, and comet.c.

References ln_equ_posn::dec, ln_get_ell_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_ell_body_next_rst_horizon(), ln_get_ell_body_next_rst_horizon_future(), and ln_get_ell_body_rst_horizon().

double ln_get_ell_body_next_rst	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_ell_orbit *	orbit,
		struct ln_rst_time *	rst
	)

Calculate the time of rise, set and transit for a body with an elliptic 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 elliptic 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_ell_body_next_rst_horizon().

double ln_get_ell_body_next_rst_horizon	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_ell_orbit *	orbit,
		double	horizon,
		struct ln_rst_time *	rst
	)

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

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 elliptic 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_ell_body_equ_coords().

Referenced by ln_get_ell_body_next_rst().

double ln_get_ell_body_phase_angle	(	double	JD,
		struct ln_ell_orbit *	orbit
	)

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

Parameters:

	JD	Julian day
	orbit	Orbital parameters

Returns:

Phase angle.

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

Examples:

asteroid.c.

References ln_ell_orbit::a, ln_ell_orbit::e, ln_ell_orbit::JD, ln_deg_to_rad(), ln_get_ell_body_earth_dist(), ln_get_ell_body_solar_dist(), ln_get_ell_mean_anomaly(), ln_get_ell_mean_motion(), ln_get_ell_radius_vector(), ln_range_degrees(), ln_solve_kepler(), and ln_ell_orbit::n.

double ln_get_ell_body_rst	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_ell_orbit *	orbit,
		struct ln_rst_time *	rst
	)

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

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.

Examples:

asteroid.c, and comet.c.

References ln_get_ell_body_rst_horizon().

double ln_get_ell_body_rst_horizon	(	double	JD,
		struct ln_lnlat_posn *	observer,
		struct ln_ell_orbit *	orbit,
		double	horizon,
		struct ln_rst_time *	rst
	)

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

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_ell_body_equ_coords().

Referenced by ln_get_ell_body_rst().

double ln_get_ell_body_solar_dist	(	double	JD,
		struct ln_ell_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.

Examples:

asteroid.c, and comet.c.

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

Referenced by ln_get_ell_body_elong(), ln_get_ell_body_phase_angle(), ln_get_ell_comet_mag(), and ln_get_ell_orbit_vel().

void ln_get_ell_geo_rect_posn	(	struct ln_ell_orbit *	orbit,
		double	JD,
		struct ln_rect_posn *	posn
	)

Calculate the 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.

Examples:

asteroid.c, and comet.c.

References ln_get_earth_helio_coords(), ln_get_ell_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_ell_body_earth_dist().

void ln_get_ell_helio_rect_posn	(	struct ln_ell_orbit *	orbit,
		double	JD,
		struct ln_rect_posn *	posn
	)

Calculate the 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.

Examples:

asteroid.c, and comet.c.

References ln_ell_orbit::a, ln_helio_posn::B, ln_ell_orbit::e, ln_ell_orbit::i, ln_ell_orbit::JD, ln_deg_to_rad(), ln_get_ell_mean_anomaly(), ln_get_ell_mean_motion(), ln_get_ell_radius_vector(), ln_get_ell_true_anomaly(), ln_solve_kepler(), ln_ell_orbit::n, ln_ell_orbit::omega, ln_helio_posn::R, ln_ell_orbit::w, ln_rect_posn::X, ln_rect_posn::Y, and ln_rect_posn::Z.

Referenced by ln_get_ell_body_equ_coords(), ln_get_ell_body_solar_dist(), and ln_get_ell_geo_rect_posn().

double ln_get_ell_last_perihelion	(	double	epoch_JD,
		double	M,
		double	n
	)

Calculate the julian day of the last perihelion.

Parameters:

	epoch_JD	Julian day of epoch
	M	Mean anomaly
	n	daily motion in degrees

Calculate the julian day of the last perihelion.

Examples:

asteroid.c.

double ln_get_ell_mean_anomaly	(	double	n,
		double	delta_JD
	)

Calculate the mean anomaly.

Parameters:

	n	Mean motion (degrees/day)
	delta_JD	Time since perihelion

Returns:

Mean anomaly (degrees)

Calculate the mean anomaly.

Referenced by ln_get_ell_body_elong(), ln_get_ell_body_phase_angle(), ln_get_ell_comet_mag(), and ln_get_ell_helio_rect_posn().

double ln_get_ell_mean_motion

(

double

a

)

Calculate the mean daily motion (degrees/day).

Parameters:

a

Semi major diameter in AU

Returns:

Mean daily motion (degrees/day)

Calculate the mean daily motion (degrees/day).

Referenced by ln_get_ell_body_elong(), ln_get_ell_body_phase_angle(), ln_get_ell_comet_mag(), and ln_get_ell_helio_rect_posn().

double ln_get_ell_orbit_avel

(

struct ln_ell_orbit *

orbit

)

Calculate the orbital velocity at aphelion in km/s.

Parameters:

orbit

Orbital parameters

Returns:

Orbital velocity in km/s.

Calculate the orbital velocity at aphelion in km/s.

Examples:

asteroid.c, and comet.c.

References ln_ell_orbit::a, and ln_ell_orbit::e.

double ln_get_ell_orbit_len

(

struct ln_ell_orbit *

orbit

)

Calculate the orbital length in AU.

Parameters:

orbit

Orbital parameters

Returns:

Orbital length in AU

Calculate the orbital length in AU.

Accuracy:

• 0.001% for e < 0.88
• 0.01% for e < 0.95
• 1% for e = 0.9997
• 3% for e = 1

Examples:

asteroid.c, and comet.c.

References ln_ell_orbit::a, ln_ell_orbit::e, and ln_get_ell_sminor_diam().

double ln_get_ell_orbit_pvel

(

struct ln_ell_orbit *

orbit

)

Calculate orbital velocity at perihelion in km/s.

Parameters:

orbit

Orbital parameters

Returns:

Orbital velocity in km/s.

Calculate orbital velocity at perihelion in km/s.

Examples:

asteroid.c, and comet.c.

References ln_ell_orbit::a, and ln_ell_orbit::e.

double ln_get_ell_orbit_vel	(	double	JD,
		struct ln_ell_orbit *	orbit
	)

Calculate orbital velocity in km/s.

Parameters:

	JD	Julian day.
	orbit	Orbital parameters

Returns:

Orbital velocity in km/s.

Calculate orbital velocity in km/s for the given julian day.

Examples:

asteroid.c, and comet.c.

References ln_ell_orbit::a, and ln_get_ell_body_solar_dist().

double ln_get_ell_radius_vector	(	double	a,
		double	e,
		double	E
	)

Calculate the radius vector.

Parameters:

	a	Semi-Major axis in AU
	e	Orbital eccentricity
	E	Eccentric anomaly

Returns:

Radius vector AU

Calculate the radius vector.

Examples:

comet.c.

References ln_deg_to_rad().

Referenced by ln_get_ell_body_elong(), ln_get_ell_body_phase_angle(), ln_get_ell_comet_mag(), and ln_get_ell_helio_rect_posn().

double ln_get_ell_smajor_diam	(	double	e,
		double	q
	)

Calculate the semi major diameter.

Parameters:

	e	Eccentricity
	q	Perihelion distance in AU

Returns:

Semi-major diameter in AU

Calculate the semi major diameter.

double ln_get_ell_sminor_diam	(	double	e,
		double	a
	)

Calculate the semi minor diameter.

Parameters:

	e	Eccentricity
	a	Semi-Major diameter in AU

Returns:

Semi-minor diameter in AU

Calculate the semi minor diameter.

Referenced by ln_get_ell_orbit_len().

double ln_get_ell_true_anomaly	(	double	e,
		double	E
	)

Calculate the true anomaly.

Parameters:

	e	Orbital eccentricity
	E	Eccentric anomaly

Returns:

True anomaly (degrees)

Calculate the true anomaly.

Examples:

comet.c.

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

Referenced by ln_get_ell_helio_rect_posn().

double ln_solve_kepler	(	double	E,
		double	M
	)

Calculate the eccentric anomaly.

Parameters:

	E	Orbital eccentricity
	M	Mean anomaly

Returns:

Eccentric anomaly

Calculate the eccentric anomaly. This method was devised by Roger Sinnott. (Sky and Telescope, Vol 70, pg 159)

Examples:

comet.c.

References ln_deg_to_rad(), and ln_rad_to_deg().

Referenced by ln_get_ell_body_elong(), ln_get_ell_body_phase_angle(), ln_get_ell_comet_mag(), and ln_get_ell_helio_rect_posn().