NAME:
	EARTH
 PURPOSE:
	Returns the heliographic or ecliptic longitude (in degrees) of the
	sub-Earth point
 CATEGORY:
	Celestial mechanics
 CALLING SEQUENCE:
	function EARTH(iYrIn,Doy)
 INPUTS:
	iYr	integer		year
				(if iYr<0 then the ecliptic longitude is returned)
	Doy	real		day of year, including fraction for time of day
 OUTPUTS:
	EARTH	real		heliographic longitude (degrees, 0<=EARTH<360)
 CALLS: ***
	ECLIPTIC_HELIOGRAPHIC, SunNewcomb
 CALLED BY:
	MAP_CarrTime, N_CARRINGTON
 SEE ALSO:
	XMAP_SC_POS
 EXTERNAL BY:
	MAP_CarrTime, N_CARRINGTON
 PROCEDURE:
	Typically used as external function to e.g. XMAP_SC_POS
 MODIFICATION HISTORY:
	JAN-1991, Paul Hick (UCSD/CASS)
	JUL-1993, Paul Hick (UCSD/CASS; pphick@ucsd.edu), added option to return ecliptic longitude

 NAME:
	EARTH_ELIMB
 PURPOSE:
	Returns the heliographic or ecliptic longitude (in degrees) of the
	solar east limb
 CALLING SEQUENCE:
	function EARTH_ELIMB(iYrIn,Doy)
 INPUTS:
	iYr		integer		year
					(if iYr<0 then the ecliptic longitude is returned)
	Doy		real		day of year, including fraction for time of day
 OUTPUTS:
	EARTH_ELIMB	real		heliographic longitude of east limb (degrees, 0<=EARTH<360)
 CALLS: ***
	ECLIPTIC_HELIOGRAPHIC, SunNewcomb
 SEE ALSO:
	XMAP_SC_POS
 PROCEDURE:
	Typically used as external function to e.g. XMAP_SC_POS
 MODIFICATION HISTORY:
	???-????, Paul Hick (UCSD/CASS; pphick@ucsd.edu)

 NAME:
	EARTH_WLIMB
 PURPOSE:
	Returns the heliographic or ecliptic longitude (in degrees) of the
	solar west limb
 CALLING SEQUENCE:
	function EARTH_WLIMB(iYrIn,Doy)
 INPUTS:
	iYr		integer		year
					(if iYr<0 then the ecliptic longitude is returned)
	Doy		real		day of year, including fraction for time of day
 OUTPUTS:
	EARTH_WLIMB	real		heliographic longitude of east limb (degrees, 0<=EARTH<360)
 CALLS: ***
	ECLIPTIC_HELIOGRAPHIC, SunNewcomb
 SEE ALSO:
	XMAP_SC_POS
 PROCEDURE:
	Typically used as external function to e.g. XMAP_SC_POS
 MODIFICATION HISTORY:
	???-????, Paul Hick (UCSD/CASS; pphick@ucsd.edu)

 NAME:
	ECLIPTIC_EQUATOR
 PURPOSE:
	Converts ecliptic coordinates into equatorial coordinates or v.v.
 CATEGORY:
	Math: coordinate transformation
 CALLING SEQUENCE:
	subroutine ECLIPTIC_EQUATOR(ID,iYr,Doy,PHI,RLAT)
 CALLS: ***
	Julian, rotate
 INPUTS:
	ID	integer	ID=0: ecliptic     ---> equatorial
			ID=1: equatorial   ---> ecliptic
	iYr	integer	year of current date
	Doy	real	day of year, including a fraction for the time of day
	PHI	real	ecliptic longitude for equinox of current date
	RLAT	real	ecliptic latitude for equinox of current date
 OUTPUTS:
	PHI	real	right ascension
	RLAT	real	declination
 PROCEDURE:
	See O. Montenbruck, Practical Ephemeris Calculations, p. 11
	If ID not equal 0 or 1 then ID = 0 is assumed.
 MODIFICATION HISTORY:
	Paul Hick (MPAE,UCSD/CASS; pphick@ucsd.edu)

 NAME:
	ECLIPTIC_HELIOGRAPHIC
 PURPOSE:
	Converts ecliptic coordinates into heliographic coordinates or v.v.
 CATEGORY:
	Math: coordinate transformation
 CALLING SEQUENCE:
	subroutine ECLIPTIC_HELIOGRAPHIC(ID,iYr,Doy,PHI,RLAT)
 INPUTS:
	ID	integer	ID=0: ecliptic     ---> heliographic
			ID=1: heliographic ---> ecliptic
	iYr	integer	year of current date
	Doy	real	day of year, including a fraction for the time of day
 INPUTS/OUTPUTS:
	PHI	real	ecliptic longitude for equinox of current date/
			heliographic longitude
	RLAT	real	ecliptic latitude for equinox of current date/
			heliographic latitude
 CALLED BY:
	EARTH, EARTH_ELIMB, EARTH_WLIMB, SUN_L0B0
 INCLUDE:
	include		'sun.h'
 CALLS: ***
	Julian, rotate
 SIDE EFFECTS:
	ALFA	-90 deg. plus ecliptic longitude of ascending node of solar 
		equator on ecliptic
	BETA	inclination of solar equator with respect to ecliptic
	GAMMA	90 deg. plus angle from ascending node to heliographic prime 
		meridian 
 PROCEDURE:
 	See R. Green, Spherical Astronomy, Cambridge UP, 1985, Section 17.7,
	p. 430.
 MODIFICATION HISTORY:
	Paul Hick (MPAE,UCSD/CASS; pphick@ucsd.edu)

 NAME:
	ElSunDistance
 PURPOSE:
	Calulates Electron-Sun distance and angle Sun-Electron-Observer
 CALLING SEQUENCE:
	function ElSunDistance(ScSun,ScEl,Elo, SinChi)
 INPUTS:
	ScSun	real	Observer-Sun distance
	ScEl	real	Observer-Electron distance
	Elo	real	elongation of line of sight (deg), i.e. angle between
			observer-Sun and observer-electron directions
			(Elo = 0 is the direction observer-Sun)
 OUTPUTS:
	ElSunDistance
		real	Sun-Electron distance (same units as ScSun and ScEl)
	SinChi	real	Sine of angle Sun-Electron-Observer
 CALLS: ***
	cosd, sind
 CALLED BY:
	ThomsonLOS3DStep, ThomsonLOSStep, ThomsonSetupIntegrand, ThomsonTang
	ThomsonTang3D, ThomsonTangMRad, ThomsonTangMRad3D
 PROCEDURE:
	Cosine and sine rule in triangle with Sun, Observer and Electron on
	the corners.
 MODIFICATION HISTORY:
	SEP-1996, Paul Hick (UCSD/CASS; pphick@ucsd.edu)

 NAME:
	EqKepler
 PURPOSE:
	Kepler's equation is used in the determination of orbital positions.
	It gives the relation between mean and eccentric anomaly (for given
	orbit eccentricity).
 CATEGORY:
	Celestial mechanics
 CALLING SEQUENCE:
	function EqKepler(E)
 INPUTS:
	E		real	eccentric anomaly (degrees)
	M		real	mean anomaly (degrees)
	ee		real	orbit ellipticity (eccentricity)
 OUTPUTS:
	EqKepler	real	fnc value
 CALLS: ***
	sind
 CALLED BY:
	KeplerOrbit
 EXTERNAL BY:
	KeplerOrbit
 INCLUDE:
	include		'math.h'
 COMMON BLOCKS:
	real		M
	real		ee
	common 		/KEPLER/ M,ee
 PROCEDURE:
	The eccentric anomaly is the root of Kepler's equation:
	EqKepler = X-(180/PI)*ee*sin(X)-M = 0
	See O. Montenbruck, "Practical Ephemeris Calculations", Springer 
	(1989), par. 3.1.1.4, p. 44
 MODIFICATION HISTORY:
	1990, Paul Hick (UCSD/CASS; pphick@ucsd.edu)

 NAME:
	EqKeplerd
 PURPOSE:
	Kepler's equation is used in the determination of orbital positions.
	It gives the relation between mean and eccentric anomaly (for given
	orbit eccentricity).
 CATEGORY:
	Celestial mechanics
 CALLING SEQUENCE:
	function EqKeplerd(E)
 INPUTS:
	E		double precision	eccentric anomaly (degrees)
	M		double precision	mean anomaly (degrees)
	ee		double precision	orbit ellipticity (eccentricity)
 OUTPUTS:
	EqKepler	double precision	fnc value
 CALLED BY:
	Time2KeplerOrbit
 EXTERNAL BY:
	Time2KeplerOrbit
 INCLUDE:
	include		'math.h'
 CALLS: ***
	dsind
 EXPLICIT:
	double precision	ee
	double precision	M
 COMMON BLOCKS:
	common 	/KEPLERD/	M,ee
 PROCEDURE:
	The eccentric anomaly is the root of Kepler's equation:
	EqKepler = X-(180/PI)*ee*sin(X)-M = 0
	See O. Montenbruck, "Practical Ephemeris Calculations", Springer 
	(1989), par. 3.1.1.4, p. 44
 MODIFICATION HISTORY:
	JAN-2004, Paul Hick (UCSD/CASS; pphick@ucsd.edu)