Ephemerides 2019 May Module


 Overview
 

-These programs compute accurate positions of the Sun, the Moon and the major planets.
  for a short time-span of 32 days, i-e  2019/04/30 0h TT to 2019/06/01 0h TT

-The longitudes & latitudes and the right-ascensions & declinations are geocentric apparent,
  referred to the true equator & equinox of the date, corrected for aberration and light-time.

-The precision is about 0"01 for the longitudes & latitudes and of the order of 3 E-8 AU for the distances ( 5 E-11 AU for the Moon ).
-The distances are true distances.

-The azimuthal ( topocentric ) coordinates are also given, corrected for parallax & diurnal aberration.

-These coordinates are calculated by polynomials fitted to the JPL ephemerides DE436
 
 

Notes:

-Always execute "ECLI" first for the ecliptic coordinates, with at least SIZE 031
-Then "EQUA" for the equatorial coordinates ( SIZE 032 )
-And then "AZIM" for the azimuthal coordinates with at least SIZE 037

-The azimuths are reckoned clockwise from North.
-Longitudes are positive East.
 

Data Registers

 R00 = ( DOM - 16 ) / 16 ( from -1  to +1 )  Terrestrial Time ( TT )

 R01 thru R27 = coordinates of the Sun, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune & the Moon.

 R28-R29-R30: unused

 R31 = True obliquity of the ecliptic  ( deg )
 R32 = Local Sidereal Time  ( hh.mnss )

  R33 = Longitude of the observer ( ° ' " )   positive East
  R34 = Latitude of the observer ( ° ' " )
  R35 = Observer altitude in meters

( R36 = temporary data storage )
 
 
XROM  Function  Desciption
 24,00
 24,01
 24,02
 24,03
 24,04
 24,05
 24,06
 24,07
 24,08
 24,09
 24,10
 24,11
 24,12
-EPH2019FEB
 SUN
 MER
 VEN
 MAR
 JUP
 SAT
 URA
 NEP
 MOON
 ECLI
 EQUA
 AZIM
 Section Header
 Ecliptic Coordinates of the Sun
 Ecliptic Coordinates of Mercury
 Ecliptic Coordinates of Venus
 Ecliptic Coordinates of Mars
 Ecliptic Coordinates of Jupiter
 Ecliptic Coordinates of Saturn
 Ecliptic Coordinates of Uranus
 Ecliptic Coordinates of Neptune
 Ecliptic Coordinates of the Moon
 Ecliptic Coordinates of the Sun, Planets & Moon
 Ecliptic -> Equatorial Coordintes
 Equatorial -> Azimuthal Coordinates

 

Ecliptic Geocentric Coordinates of the Sun, the Moon & the major Planets
 

-"ECLI"  "EQUA"  &  "AZIM"  calculate & store the coordinates in registers R01 thru R27 as follows:

>>>   h0 is the height, corrected for refraction
 
 
      Celestial Body    Registers               "ECLI"              "EQUA"          "AZIM"
           SUN       R01
      R02
      R03
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
   Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
       MERCURY       R04
      R05
      R06
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
         VENUS       R07
      R08
      R09
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
         MARS       R10
      R11
      R12
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
   Right-Ascens(hh;mnss)
     Declination ( ° ' " )
   Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
        JUPITER       R13
      R14
      R15
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
   Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
        SATURN       R16
      R17
      R18
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
       URANUS       R19
      R20
      R21
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
       NEPTUNE       R22
      R23
      R24
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )
         MOON       R25
      R26
      R27
    Eclipt Longitude ( deg )
    Eclipt  Latitude ( deg )
    Dist from Earth ( AU )
    Right-Ascens(hh;mnss)
      Declination ( ° ' " )
    Dist from Earth ( AU )
    Azimuth ( ° ' " )
     height  ( ° ' " )
        h0  ( ° ' " )

 
->After executing "ECLI", the stack contains the apparent geocentric ecliptic coordinates of the Sun
 
 
 
      STACK        INPUTS      OUTPUTS
           Z             /       R0  ( AU )
           Y Day of the Month       B0  ( deg )
           X  HH.MNSS(TT)       L0  ( deg )

  Where  L = Longitude   B = Latitude   R = radius vector

Example:    Calculate the apparent geocentric ecliptic coordinates of the Sun, the Moon and the planets on 2019/05/24 at 16h41m  TT

      XEQ "ECLI"  >>>>   "DOM0-32^TIME"

-Enter the day of the month and the time expressed in  Terrestrial Time ( TT )

       24       ENTER^
    16.41        R/S            >>>>     L0 =   63°231731            = R01                             ---Execution time = 94s---
                                       RDN      B0 =   -0°000103            = R02
                                       RDN      R0 =  1.01267305  AU   = R03

-And we have also the other coordinates in registers  R04 to R27, namely:

    Sun

     R01 =  63°231731
     R02 =  -0°000103
     R03 =  1.01267305  AU

    Mercury

     R04 = 67°105759
     R05 =  0°860427
     R06 = 1.30963860  AU

    Venus

     R07 =   41°286226
     R08 =   -1°456140
     R09 =  1.55803750  AU

    Mars

     R10 =  95°522088
     R11 =   1°143072
     R12 =  2.38713504 AU

    Jupiter

      R13 = 261°567019
      R14 =  0°611753
      R15 = 4.33423968  AU

    Saturn

     R16 =  290°037404
     R17 =   0°372155
     R18 =  9.33224647  AU

    Uranus

     R19 = 34°292024
     R20 = -0°487098
     R21 = 20.72542121  AU

    Neptune

     R22 =  348°513597
     R23 =  -0°997412
     R24 =  30.18724283  AU

    Moon

     R25 =  -48°545596
     R26 =   -2°019422
     R27 =  0.00268684435 AU
 

Notes:

-All the angles are expressed in decimal degrees.

-If you key in a date outside the interval [ 2019/04/30 0h TT , 2019/06/01 0h TT ]  you'll get a DATA ERROR message.
-However, this program may probably be used a few hours outside the prescribed interval: set F25 and R/S
-But the precision is less guaranteed and the results may even become completely meaningless several days before 00 or after 32, especially for the Moon.
 

Equatorial Geocentric Coordinates
 

-AFTER executing "ECLI", use "EQUA" to get the equatorial coordinates
-The right-ascensions are expressed in hh.mnss and the declinations in ° ' "
-They replace the ecliptic longitudes & latitudes ( cf the tableau in the paragraph above )

-"EQUA" also calculates the true obliquity of the ecliptic which is returned in Z-register
-A polynomial is also used for that.
 
 
      STACK        INPUTS      OUTPUTS
           Z             /      eps   ( deg )
           Y             /    Decl0 ( ° ' " )
           X             /  RA0  ( hh.mnss )

  Where  RA = Right-Ascension   Decl = declination  eps = true obliquity of the ecliptic

Example:    Calculate the apparent geocentric equatorial coordinates of the Sun, the Moon and the planets on 2019/05/24 at 16h41m  TT

After executing "ECLI"

        XEQ "EQUA"  or simply R/S if you've just executed "ECLI"

                                  >>>>     RA0 =   4h04m47s57   = R01                        ---Execution time = 46s---
                                  RDN    Decl0 =   20°47'58"02   = R02
                                  RDN      eps  =   23°4358009    = R31
 

-The distances in R03-R06-.....-R27  are unchanged and we have:
 

    Sun

     R01 = 4h04m47s57
     R02 = 20°47'58"02

    Mercury

     R04 =  4h20m31s26
     R05 =  22°20'29"62

    Venus

     R07 =  2h37m17s12
     R08 =  13°49'44"35

    Mars

     R10 =  6h24m16s18
     R11 =  24°27'45"57

    Jupiter

     R13 = 17h23m27s17
     R14 = -22°33'25"25

    Saturn

     R16 = 19h26m28s58
     R17 = -21°34'21"28

    Uranus

     R19 =  2h08m48s52
     R20 =  12°29'24"67

    Neptune

     R22 =  23h19m19s36
     R23 =  -5°27'37"83

    Moon

     R25 =  20h58m00s50
     R26 =  -19°16'58"17
 

Azimuthal Topocentric Coordinates
 

-AFTER executing "ECLI" & "EQUA" use "AZIM" to get the horizontal coordinates
-The azimuths & heights are expressed in ° ' "

-The heights corrected for refraction are also computed and replace the distances in R03  R06 ..... R27
 
 
      STACK        INPUTS      OUTPUTS
           Z             /       h0  ( ° ' " )
           Y             /       h  ( ° ' " )
           X             /      Az  ( ° ' " )

 
                  Long = longitude ( positive East )       Az = Azimuth ( clockwise from North )    |
  Where       Lat  =  latitude                                   h  =  height                                             >       of the Sun
                   Alt  =  altitude in meters                   h0 =  height ( corrected for refraction )    |
 

Example:    Calculate the apparent topocentric azimuthal coordinates of the Sun, the Moon and the planets on 2019/05/24 at 16h41m  TT
                    at the Palomar Observatory,   Longitude = 116°51'50" W   Latitude = 33°21'22" N   Altitude = 1706 m
 

>>>  After executing "ECLI" & "EQUA"
 

                       XEQ "AZIM"  or just   R/S   if you've just executed "EQUA"

                          >>>>     "LONG^LAT^ALT"

                      116.5150  CHS  ENTER^
                       33.2122   ENTER^
                          1706     R/S                         or simply   R/S  if the data are already in  R33-R34-R35

                          >>>>     Az  =  95°03'57"87   = R01                        ---Execution time = 168s---
                          RDN      h    =  47°26'12"70   = R02
                          RDN      h0   =  47°27'05"02   = R03

                       which are the topocentric coordinates of the Sun.
 

>>>  We also have the local sidereal time in R32 = LST = 1h00m20s465
 

Notes:

-The difference TT - UTC = 69.184 seconds.

  h0   is often meaningless when  h < 0
 

    Sun

     R01 = Az   =  95°03'57"87
     R02 =  h    =  47°26'12"70
     R03 = h0   =  47°27'05"02

    Mercury

     R04 = Az  =   90°44'03"12
     R05 =  h    =  44°50'22"92
     R06 = h0   =   44°51'20"21

    Venus

     R07 = Az  =  125°46'23"52
     R08 =  h    =  60°34'26"50
     R09 = h0   =  60°34'58"65

    Mars

     R10 = Az  =    73°25'57"94
     R11 =  h    =    20°17'39"47
     R12 = h0   =    20°20'12"18

    Jupiter

     R13 = Az  =  -97°34'50"42
     R14 =  h   =   -31°49'48"11
     R15 = h0   =  -31°49'48"11

    Saturn

     R16 = Az  =   -111°34'22"06
     R17 =  h    =   -6°32'00"31
     R18 = h0   =   -6°32'00"31

    Uranus

     R19 = Az  =  139°09'25"87
     R20 =  h    =  63°56'05"10
     R21 = h0   =   63°56'32"98

    Neptune

     R22 = Az  =  -143°31'36"16
     R23 =  h    =  44°24'05"88
     R24 = h0   =  44°25'04"05

    Moon

     R25 = Az  =  -122°50'25"26
     R26 =  h    =    10°58'35"57
     R27 = h0   =    11°03'19"37
 

Sun-Mercury-Venus-Mars-Jupiter-Saturn-Uranus-Neptune-Moon
 

-All these subroutines may be used for themselves to calculate the geocentric ecliptic coordinates
-First initialize R00 before executing them.
 
 
      STACK        INPUTS      OUTPUTS
           Z             /       R  ( AU )
           Y             /       B  ( deg )
           X             /       L  ( deg )

  Where  L = Longitude   B = Latitude  R = radius vector

Example:    The same one, which corresponds to R00 = 0.5434461806

   0.5434461806  STO 00

  XEQ "SUN"  >>>>     L0 =     63°231731          = R01                             ---Execution time = 9s---
                       RDN      B0 =     -0°000103          = R02
                       RDN      R0 =  1.01267305  AU   = R03

>>> Likewise with Mercury, ........... , Neptune & the Moon.. ( see above the numerical values )
 

WARNING !!!

-Unlike "ECLI" , these routines do not check that R00 is between -1 and +1
 
 

Remark:

-The apparent heights are calculated by a refraction formula which approximates the Pulkovo refraction tables
  for standard conditions of temperature & pressure ( T = 15°C , P = 1013.25 mbar, humidity = 0 , wave length = 0.59µ )

-The precision is better than 0"06 over the whole range [ -0°32'58"0 , 90° ]:
 

    h0  ~  h + 57"1798 / Tan ( h + 4°8043 / ( h + 7°0822 / ( h +11°1187 / ( h + 38°2290 / ( h + 9°9098 ) ) ) ) )
 
 
 
 

References:

[1]  ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/
[2]  Aldo Vitagliano SOLEX  http://www.solexorb.it/
[3]  Jean Meeus - "Astronomical Algorithms" - Willmann-Bell  -  ISBN 0-943396-61-1