Time and data conversions and planetary movement, position, and eclipse computations. More...

Functions
Time/Date functions
double	date_to_jd (const ml_matrix &dateTime)
	Converts date to jd. More...

double	jd_to_utc_secs (double jd)
	Converts Julian date to seconds since 00:00:00 January 1, 1970 (UTC) More...

double	utc_secs_to_jd (double secs)
	Converts seconds since 00:00:00 January 1, 1970 (UTC) to Julian date. More...

double	jd_to_jcent (double jd)
	Convert Julian date to Julian century. More...

double	jcent_to_jd (double jcent)
	Convert Julian century to Julian date. More...

double	jd_to_midnight (double jd)
	Round a Julian date value to the most recent midnight (0 hours) value. More...

double	gms_time (double jd)
	Get Greenwich Mean Sidereal time. More...

double	ms_day (double jd)
	Compute a mean sidereal (solar) day. More...

double	local_sidereal_time (double jd, double lon)
	Compute the local sidereal time for a given Julian date and longitude. More...

double	mean_sidereal_day (double jd)
	Mean sidereal day

ml_matrix	jd_to_date (double jd)
	Convert Julian date to date. More...

double	jd_to_day_number (double jd)
	Convert Julian date to day number More...

Star functions
ml_matrix	stellar_reduction (const ml_matrix &rA0, const ml_matrix &dec0, const ml_matrix &pMRA, const ml_matrix &pMDec, const ml_matrix &parallax, const ml_matrix &rV, const ml_matrix &vSc, double jD)
	Stellar reduction. More...

void	earth_barycenter (const ml_matrix &jD, ml_matrix eB, ml_matrix eB_dot)
	Earth barycenter. More...

void	earth_barycenter (double jD, ml_matrix eB, ml_matrix eB_dot)

ml_matrix	light_deflection (const ml_matrix &p, const ml_matrix &e)
	Light deflection. More...

ml_matrix	stellar_aberration (const ml_matrix &u, const ml_matrix &v)
	Stellar aberration. More...

Planetary functions
ml_matrix	meci_to_planet (double alpha0, double delta0, double w)
	Generate the ECI to Planet transformation matrix. More...

ml_matrix	meci_to_earth (double jD)
	Generate the ECI to eart transformation matrix. More...

ml_matrix	sun_vector (double jd, double &r)
	Generate the sun vector in the earth-centered inertial frame. More...

ml_matrix	sun_vector (double jd)

ml_matrix	moon_vector (double jd, double &r)
	Generate the moon vector in the earth-centered inertial frame. More...

ml_matrix	true_earth (double jcent)
	Computes the matrix from mean of Aries 2000 to earth fixed frame. More...

ml_matrix	earth_pre (double jcent)
	Computes the earth precession matrix. More...

ml_matrix	earth_rot (double jcent)
	Computes the earth Greenwich matrix using GMST, that transforms from ECI to Earth-fixed. More...

ml_matrix	earth_rot_eq (double jcent)
	Computes the earth Greenwich matrix using apparent sidereal time. More...

ml_matrix	earth_nut (double jcent)
	The matrix that rotates from the mean axes to the true axes. More...

double	nut_delta (double j_cent, double &delta_eps)
	The changes in longitude and obliquity due to earth nutation. More...

double	ob_of_ecliptic (double jcent)
	Computes the mean obliquity of the ecliptic of date. More...

ml_matrix	c_ecl_to_eq (double jD)
	Transformation from eclipic to equatorial. More...

double	eq_of_equinoxes (double jcent)
	Computes the equation of the equinoxes. More...

double	eclipse_spice (const ml_matrix &pos, const ml_matrix &planet_radius, const ml_matrix &planet_position, const ml_matrix &planet_index, int observer)
	Compute eclipses using Spice data. More...

double	eclipse (const ml_matrix &pos, const ml_matrix &l_pos, const ml_matrix &p_pos, double p_radius=RADIUS_EARTH, double l_radius=RADIUS_SUN)
	Compute eclipses. More...

double	earth_rate (double jd)
	Earth rotation rate.

ml_matrix	local_star_position (double jd, double lY)
	Local star positions. More...

ml_matrix	planet_ecliptic_to_orbit (int naif_code, double jd=JD_2000)
	Planet orbit rotation frame. More...

ml_matrix	planet_ecliptic_to_orbit (char *planet_name, double jd=JD_2000)
	Generates planet rotation frame. More...

Detailed Description

Time and data conversions and planetary movement, position, and eclipse computations.

Function Documentation

◆ date_to_jd()

double date_to_jd ( const ml_matrix & d )

Converts date to jd.

The date vector is in the form [year month day hours minutes seconds] where all values should be integers except seconds which may be a double. If any columns of datetime are omitted they will be set to zero, as appropriate, with a default date of Jan 1, 2000 at 00:00.

Examples: jD = date_to_jd([2009]); // assumes January 1 at 0:00 jD = date_to_jd([2009 4 11]); jD = date_to_jd([2009 4 11 13 45]); jD = date_to_jd([2009 4 11 13 45 15.146]);

Parameters

d	Date vector (1x6) to be converted to Julian date.

Returns: Returns the Julian date equivalent of the given calendar date.

Referenced by jd_to_day_number().

◆ jd_to_utc_secs()

double jd_to_utc_secs ( double jd )

Converts Julian date to seconds since 00:00:00 January 1, 1970 (UTC)

Parameters

jd	Julian date value to be converted to UTC seconds.

Returns: Returns the UTC seconds value for a given Julian date.

References DAYS_TO_SECS, and JD_EPOCH.

◆ utc_secs_to_jd()

double utc_secs_to_jd ( double secs )

Converts seconds since 00:00:00 January 1, 1970 (UTC) to Julian date.

Parameters

secs	UTC seconds value to be converted to Julian date.

Returns: Returns the Julian date equivalent of the given UTC value.

References JD_EPOCH, and SECS_TO_DAYS.

◆ jd_to_jcent()

double jd_to_jcent ( double jd )

Convert Julian date to Julian century.

Parameters

jd	Julian date to be converted to Julian centuries.

Returns: Returns the Julian century equivalent of the given Julian date.

References DAYS_TO_CENTURIES, and JD_2000.

Referenced by b_dipole(), gravity_earth::compute_accel(), gms_time(), gps_eci_state_from_data(), mag_field(), meci_to_earth(), moon_vector(), ms_day(), orbit_closest_point(), r_ef_from_el(), and stellar_reduction().

◆ jcent_to_jd()

double jcent_to_jd ( double jcent )

Convert Julian century to Julian date.

Parameters

jcent The Julian century value to be converted to Julian date.

Returns: Returns the Julian date equivalent of the given Julian century.

References CENTURIES_TO_DAYS, and JD_2000.

Referenced by earth_rot(), and earth_rot_eq().

◆ jd_to_midnight()

double jd_to_midnight ( double jd )

Round a Julian date value to the most recent midnight (0 hours) value.

Parameters

jd	The Julian date value to be rounded.

Returns: Returns the most recent midnight Julian date.

Referenced by gms_time(), and ms_day().

◆ gms_time()

double gms_time ( double jd )

Get Greenwich Mean Sidereal time.

Gives the angle between the Greenwich Meridian and the Vernal Equinox (the x-axis in the ECI frame). This does not account for Earth nutation. Ref: The 1993 Astronomical Almanac, U.S. Government Printing Office, p. B6.

Parameters

jd	Julian date at which to calculate the Greenwich Mean Sidereal time.

Returns: Returns the Greenwich Mean Sidereal time in degrees

References jd_to_jcent(), jd_to_midnight(), ms_day(), and SECS_TO_DAYS.

Referenced by earth_rot(), earth_rot_eq(), and local_sidereal_time().

◆ ms_day()

double ms_day ( double jd )

Compute a mean sidereal (solar) day.

Ref: The 1993 Astronomical Almanac, U.S. Government Printing Office, p. B6.

Parameters

jd	Julian date value for which the mean sidereal day should be computed.

Returns: Returns the mean sidereal day at the given Julian date.

References DAYS_TO_SECS, jd_to_jcent(), and jd_to_midnight().

Referenced by gms_time().

◆ local_sidereal_time()

double local_sidereal_time	(	double	jd,
		double	lon
	)

Compute the local sidereal time for a given Julian date and longitude.

Parameters

jd	Julian date
lon	longitude

Returns: local sidereal time

References gms_time().

◆ jd_to_date()

ml_matrix jd_to_date ( double jd )

Convert Julian date to date.

Parameters

jd	The Julian date value to be rounded.

Returns: [year month day minutes hours seconds]

References fix(), and r2p5().

Referenced by jd_to_day_number().

◆ jd_to_day_number()

double jd_to_day_number ( double jd )

Convert Julian date to day number

Parameters

jd	The Julian date value to be rounded.

Returns: Day number

References date_to_jd(), and jd_to_date().

Referenced by AtmJ70::Update().

◆ stellar_reduction()

ml_matrix stellar_reduction	(	const ml_matrix &	rA0,
		const ml_matrix &	dec0,
		const ml_matrix &	pMRA,
		const ml_matrix &	pMDec,
		const ml_matrix &	parallax,
		const ml_matrix &	rV,
		const ml_matrix &	vSc,
		double	jD
	)

Stellar reduction.

Includes corrections for

radial velocity of star
parallax
gravitational light deflection
relativistic aberration due to earth and spacecraft velocity
Earth precession and nutation

Astronomical Almanac for 1993, B39-B41

Parameters

rA0	Catalog right ascension
dec0	Catalog declination
pMRA	Proper motion in right ascension
pMDec	Proper motion in declination
parallax	Stellar parallax
rV	Radial velocity (km/sec)
vSc	Spacecraft velocity vector (km/sec)
jD	Julian date

Returns: Unit vector

References earth_barycenter(), jd_to_jcent(), light_deflection(), ra_dec_to_u(), and stellar_aberration().

◆ earth_barycenter()

void earth_barycenter	(	const ml_matrix &	jD,
		ml_matrix	eB,
		ml_matrix	eB_dot
	)

Earth barycenter.

Parameters

jD	(1,:) Julian date

Returns: eB (3,:) Barycentric position (aU); eBDot (3,:) Barycentric rate (aU/y)

References DEGREES_TO_RADIANS.

Referenced by stellar_reduction().

◆ light_deflection()

ml_matrix light_deflection	(	const ml_matrix &	p,
		const ml_matrix &	e
	)

Light deflection.

Parameters

p	(3,:) Vector from observing body to observed body
e	(3,:) Vector from sun

Returns: p1 (3,:) Corrected p

Siedelmann, P., (1992). Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, CA, 136-137.

Referenced by stellar_reduction().

◆ stellar_aberration()

ml_matrix stellar_aberration	(	const ml_matrix &	u,
		const ml_matrix &	v
	)

Stellar aberration.

Parameters

u	(3,1) Unit position vector
v	(3,1) Velocity vector divided by the speed of

Returns: corrected u

Siedelmann, P., (1992). Explanatory Supplement to the Astronomical Almanac, University Science Books, Mill Valley, CA, 129.

Referenced by stellar_reduction().

◆ meci_to_planet()

ml_matrix meci_to_planet	(	double	alpha0,
		double	delta0,
		double	w
	)

Generate the ECI to Planet transformation matrix.

Ref: Montenbruck, O., Pfleger, T., "Astronomy on the Personal Computer, Second Edition."

Parameters

alpha0	The right ascension of the planet's pole, measured in degrees.
delta0	The declination of the planet's pole, measured in degrees.
w	The angle of rotation about the pole, measured in degrees.

Returns: The transformation matrix from the ECI frame to the planet-fixed frame

References DEGREES_TO_RADIANS.

Referenced by meci_to_earth().

◆ meci_to_earth()

ml_matrix meci_to_earth ( double jD )

Generate the ECI to eart transformation matrix.

Ref: Montenbruck, O., Pfleger, T., "Astronomy on the Personal Computer, Second Edition."

Parameters

jD	Juilan date

Returns: The transformation matrix from the ECI frame to the planet-fixed frame

References jd_to_jcent(), and meci_to_planet().

◆ sun_vector()

ml_matrix sun_vector	(	double	jd,
		double &	r
	)

Generate the sun vector in the earth-centered inertial frame.

Ref: The 1993 Astronomical Almanac, U.S. Government Printing Office, p. C24.

Parameters

jd	Julian date at which the sun vector is to be generated.
r	Returns the distance from origin to sun in kms

Returns: Returns the sun vector at a given Julian date

References DEGREES_TO_RADIANS, JD_2000, and REVS_TO_DEGREES.

Referenced by AlignThruster(), gravity_earth::compute_accel(), planetary_accelerations(), and AtmJ70::Update().

◆ moon_vector()

ml_matrix moon_vector	(	double	jd,
		double &	r
	)

Generate the moon vector in the earth-centered inertial frame.

Ref: The 1993 Astronomical Almanac, U.S. Government Printing Office, p. D46.

Parameters

jd	Julian date at which to compute the moon vector.
r	Returns the distance from origin to moon in kms

Returns: Returns the moon vector at the given date.

References DEGREES_TO_RADIANS, jd_to_jcent(), RADIUS_EARTH, and REVS_TO_DEGREES.

Referenced by AlignThruster(), gravity_earth::compute_accel(), and planetary_accelerations().

◆ true_earth()

ml_matrix true_earth ( double jcent )

Computes the matrix from mean of Aries 2000 to earth fixed frame.

Calls earth_rot, earth_nut, and earth_pre in sequence.

    B = B_rot*B_nut*B_pre

Ref: Seidelmann, The Explanatory Supplement to the Astronomical Almanac, p. 20.

Parameters

jcent Julian century at which to compute the true earth matrix.

Returns: Returns the matrix from mean of Aries 2000 to earth fixed frame.

References earth_nut(), earth_pre(), and earth_rot().

Referenced by gravity_earth::compute_accel(), eci_to_llr(), gps_eci_state_from_data(), orbit_closest_point(), and r_ef_from_el().

◆ earth_pre()

ml_matrix earth_pre ( double jcent )

Computes the earth precession matrix.

Ref: Seidelmann, The Explanatory Supplement to the Astronomical Almanac, p. 103.

Parameters

jcent The Julian century at which to compute the earth precession matrix.

Returns: Returns the earth precession matrix.

References DEGREES_TO_RADIANS.

Referenced by true_earth().

◆ earth_rot()

ml_matrix earth_rot ( double jcent )

Computes the earth Greenwich matrix using GMST, that transforms from ECI to Earth-fixed.

Equivalent to a rotation about the Z axis by the Greenwich mean sidereal time (GMST). Ref: Seidelmann, P. K., The Explanatory Supplement to the Astronomical Almanac, p. 20.

Parameters

jcent Julian century at which to compute the earth Greenwich matrix.

Returns: Returns the earth Greenwich matrix that transforms from ECI to earth-fixed.

References DEGREES_TO_RADIANS, gms_time(), and jcent_to_jd().

Referenced by b_dipole(), mag_field(), and true_earth().

◆ earth_rot_eq()

ml_matrix earth_rot_eq ( double jcent )

Computes the earth Greenwich matrix using apparent sidereal time.

Equivalent to a rotation about the Z axis by the Greenwich apparent sidereal time (GAST). Ref: Seidelmann, P. K., The Explanatory Supplement to the Astronomical Almanac, p. 20.

Parameters

jcent Julian century at which to compute the earth Greenwich matrix.

Returns: Returns the earth Greenwich matrix that transforms from ECI to earth-fixed.

References DEGREES_TO_RADIANS, eq_of_equinoxes(), gms_time(), and jcent_to_jd().

◆ earth_nut()

ml_matrix earth_nut ( double jcent )

The matrix that rotates from the mean axes to the true axes.

Ref: Seidelmann, P. K., The Explanatory Supplement to the Astronomical Almanac, p. 115.

Parameters

jcent The Julian century at which to calculate the matrix.

Returns: Returns the matrix that rotates from the mean axes to the true axes.

References DEGREES_TO_RADIANS, nut_delta(), and ob_of_ecliptic().

Referenced by true_earth().

◆ nut_delta()

double nut_delta	(	double	j_cent,
		double &	delta_eps
	)

The changes in longitude and obliquity due to earth nutation.

Ref: Seidelmann, The Explanatory Supplement to the Astronomical Almanac

Parameters

j_cent	Julian century from JD 2000 for which to compute the changes in longitude and obliquity.
delta_eps	Returns the change in obliquity.

Returns: Returns delta_psi, the change in longitude.

References DEGREES_TO_RADIANS, and SECS_TO_HOURS.

Referenced by earth_nut(), and eq_of_equinoxes().

◆ ob_of_ecliptic()

double ob_of_ecliptic ( double jcent )

Computes the mean obliquity of the ecliptic of date.

Ref: The 1993 Astronomical Almanac, U.S. Government Printing Office, p. B18.

Parameters

jcent The Julian century at which to compute the mean obliquity.

Returns: Returns the mean obliquity of the ecliptic of date.

Referenced by earth_nut(), and eq_of_equinoxes().

◆ c_ecl_to_eq()

ml_matrix c_ecl_to_eq ( double jD )

Transformation from eclipic to equatorial.

If the jd is not input it will use the mean obliquity for J2000.0.

Parameters

jD	(1,1) Julian date

Returns: Transformation matrix from the ecliptic plane

References PI.

Referenced by planet_ecliptic_to_orbit().

◆ eq_of_equinoxes()

double eq_of_equinoxes ( double jcent )

Computes the equation of the equinoxes.

Ref: The Astronomical Almanac for the Year 1993, U.S. Government Printing Office, 1993, p. B6.

Parameters

jcent The Julian century at which to compute the mean obliquity.

Returns: Returns the mean obliquity of the ecliptic of date.

References DEGREES_TO_RADIANS, nut_delta(), and ob_of_ecliptic().

Referenced by earth_rot_eq().

◆ eclipse_spice()

double eclipse_spice	(	const ml_matrix &	pos,
		const ml_matrix &	planet_radius,
		const ml_matrix &	planet_position,
		const ml_matrix &	planet_index,
		int	observer
	)

Compute eclipses using Spice data.

It automatically determines the center from the observer input.

Parameters

pos	(3,1) Position vector of the spacecraft
planet_radius	(3,:) Planet radius
planet_position	(3,:) Position vector of the planets
planet_index	(1,:) Spice index for the radius and posiiton vectors
observer	(1,1) Index of orbit center

Returns: Normalized source intensity

References eclipse().

◆ eclipse()

double eclipse	(	const ml_matrix &	pos,
		const ml_matrix &	l_pos,
		const ml_matrix &	p_pos,
		double	p_radius,
		double	l_radius
	)

Compute eclipses.

Parameters

pos	(3,1) Position vector of the spacecraft
l_pos	(3,1) Position vector of the light source
p_pos	(3,1) Position vector of the planet causing the eclipse
p_radius	Radius of the planet causing the eclipse (default is the earth)
l_radius	Radius of the light source (default is the sun)

Returns: Normalized source intensity

References PI.

Referenced by eclipse_spice().

◆ local_star_position()

ml_matrix local_star_position	(	double	jd,
		double	lY
	)

Local star positions.

Parameters

jd	Julian date
lY	Light years from the sun

Returns: Star matrix in light years

References ra_dec_to_u().

◆ planet_ecliptic_to_orbit() [1/2]

ml_matrix planet_ecliptic_to_orbit	(	int	naif_code,
		double	jD
	)

Planet orbit rotation frame.

Parameters

naif_code	Code for planetary system
jD	Julian day number

Returns: Rotation matrix

References c_ecl_to_eq().

Referenced by planet_ecliptic_to_orbit().

◆ planet_ecliptic_to_orbit() [2/2]

ml_matrix planet_ecliptic_to_orbit	(	char *	planet_name,
		double	jD
	)

Generates planet rotation frame.

Uses get_naif_code() and planet_ecliptic_to_orbit().

Parameters

planet_name	string form name
jD	Julian day number

Returns: Rotation matrix

References get_naif_code(), and planet_ecliptic_to_orbit().

Functions

Detailed Description

Function Documentation

◆ date_to_jd()

◆ jd_to_utc_secs()

◆ utc_secs_to_jd()

◆ jd_to_jcent()

◆ jcent_to_jd()

◆ jd_to_midnight()

◆ gms_time()

◆ ms_day()

◆ local_sidereal_time()

◆ jd_to_date()

◆ jd_to_day_number()

◆ stellar_reduction()

◆ earth_barycenter()

◆ light_deflection()

◆ stellar_aberration()

◆ meci_to_planet()

◆ meci_to_earth()

◆ sun_vector()

◆ moon_vector()

◆ true_earth()

◆ earth_pre()

◆ earth_rot()

◆ earth_rot_eq()

◆ earth_nut()

◆ nut_delta()

◆ ob_of_ecliptic()

◆ c_ecl_to_eq()

◆ eq_of_equinoxes()

◆ eclipse_spice()

◆ eclipse()

◆ local_star_position()

◆ planet_ecliptic_to_orbit() [1/2]

◆ planet_ecliptic_to_orbit() [2/2]