VSOP87C
Heliocentric rectangular coordinates of planets
Alt.: ftp://cyrano-se.obspm.fr/pub/3_solar_system/2_platab/README.TXT
Font: http://neoprogrammics.com/vsop87/
Type of Coordinates: Heliocentric rectangular coordinates in AU (astronomical unit).
Reference System: The coordinates of the VSOP87 version C are given in the inertial
reference frame defined by the mean equinox and ecliptic of the date.
This frame is deduced from the inertial frame defined by the dynamical equinox and
ecliptic J2000 (JD2451545.0) by precessional moving between J2000 and the epoch of
the date.
Time Scale: The time used in VSOP87 theory is dynamical time.
We can considered this time equal to Terrestrial Time (TT) which is measured by
international atomic time TAI. So, the time argument in VSOP87 theory is equal to
TAI + 32.184 s.
Font: http://www.astrosurf.com/jephem/astro/ephemeris/et300VSOP_en.htm
Heliocentric to Geocentric
Ref.: https://en.wikipedia.org/wiki/Ecliptic_coordinate_system#Conversion_between_celestial_coordinate_systems
The results of VSOP87C beside are heliocentric coordinates, centered on the Sun.
To obtain geocentric coordinates, centered on the Earth, using rectangular coordinates,
a simple transformation is all that is needed to convert:
X = Xobj - XEarth
Y = Yobj - YEarth
Z = Zobj - ZEarth
Determine the heliocentric rectangular coordinates of the planet to locate (Xobj, Yobj and
Zobj) as well as those of Earth (XEarth, YEarth and ZEarth) and subtract. This will now set the
position of every planet in a space where the origin is the position of Earth. To verify this, set
Xobj, Yobj and Zobj to XEarth, YEarth and ZEarth and, as expected, the new position of Earth
is (0, 0, 0), the origin.
To determine the geocentric position of the Sun, set Xobj, Yobj and Zobj all to zero (since it
was at the origin in the heliocentric system). The formula for the Sun can then be simplified to:
X = -XEarth
Y = -YEarth
Z = -ZEarth
Font: http://www.caglow.com/info/compute/vsop87
AU 1,4959787E+11 m
Light Speed 299792458 m/s
01 day 86400 s
Geocentric coordenates of planets
Planetary theories give geometric heliocentric ecliptic coordinates.
The first step is to take into account an effect called light aberration :
Imagine that someone on a planet sends a signal at instant t.
On Earth, we'll recieve the signal at instant t + dt (dT is the time taken
by light to go from planet to Earth).
So at instant t on Earth, we see the planet at its position at instant t - dt.
So if we want to have the apparent coordinates of the planet at instant
t on Earth, we must calculate them at instant t - dt.
To handle this, we must :
Compute the position of the Earth at instant t;
And for each planet :
Compute positions at instant t ;
Calculate dt (we have : dT = EP/c (c = light speed));
Compute coordinates of the planet at instant t - dt.
This means that the coordinates of the planet must be calculated twice.
Font: http://www.astrosurf.com/jephem/astro/ephemeris/et520transfo_en.htm
Geocentric coordenates of moon
The ELPMPP02 allows to compute rectangular geocentric
lunar coordinates (positions and velocities) referred to
the inertial mean ecliptic and equinox of J2000. It uses
the six data files which contain the series of the solution
and takes into account the specifications presented in
this paper.
The inputs are:
The date (TDB): tj in days from J2000 (double precision).
The index of the corrections: icor (integer).
icor = 1: the constants are fitted to LLR observations.
icor = 2: the constants are fitted to JPL Ephemeris DE405.
The outputs are:
The table of rectangular coordinates:
xyz(6) (double precision),
positions xE2000, yE2000, zE2000 (km) and
velocities x'E2000, y'E2000, z'E2000 (km/day)
referred to the inertial mean ecliptic and equinox of J2000.
Geoc. Rect. to Geoc. spherical ecliptic coordinates
To transform rectangular into spherical Ecliptic coordinates, use:
tan(Lon) = Y / X
tan(Lat) = Z / sqrt(X * X + Y * Y)
Be sure to obtain these to the correct quadrants either manually or
by using atan2().
These can then be quickly converted to equatorial coordinates using
the typical ecliptic-to-equatorial formulas.
Font: http://www.caglow.com/info/compute/vsop87
tan(Lon) = Y / X ==> Lon = ATAN2(x;y) * (180 / PI)
tan(Lat) = Z / sqrt(X * X + Y * Y) ==>
Lat = ATAN2(RAIZ(POTÊNCIA(X;2) + POTÊNCIA(Y;2));Z) * (180 / PI)
Font: http://idlastro.gsfc.nasa.gov/ftp/pro/astro/planet_coords.pro
0 <= RA <= 360 -90 <= Decl <= 90
Do While RA < 0 Do While Decl < -360
RA = RA + 360 Decl = Decl + 360
Loop Loop
Do While RA > 360 Do While Decl > 360
RA = RA - 360 Decl = Decl - 360
Loop Loop
Do While Decl < -90
Decl = Decl + 90
Loop
Do While Decl > 90
Decl = Decl - 90
Loop
GPAstro Public Enum GPOptions
1 Sun gpSun = 1 0 -1
2 Moon gpMoon = 2 1 0 gpHelioRect = 0
3 Mars gpMars = 3 2 2 gpHRLightTime = 2
4 Mercury gpMercury = 4 3 1 gpGeoRect = 1
5 Jupter gpJupiter = 5 4 4 gpGRLTPAberr = 4
6 Venus gpVenus = 6 5 8 gpGeoSphe = 8
7 Saturn gpSaturn = 7 6 16 gpGSFK5 = 16
8 Uranus gpUranus = 8 7 32 gpGSNutac = 32
9 Neptune gpNeptune = 9 8 64 gpRADecl = 64
10 Earth gpEarth = 10 9 128
11 EarthDt gpEarthDt = 11
The effect of annual aberration
Ref: https://en.wikipedia.org/wiki/Aberration_of_light
Font: Astronomical Algorithms - Jean Meeus - pag. 139 and 212
Let lambda and beta be a star [or planet]'s celestial longitude and latitude,
k the constant of aberration (20".49552), teta the true (geometric)
longitude of the sun, e the eccentricity of the Earth orbitt, and pi the
longitude of the perihelion of the orbit.
Teta can be calculated by the method describe in Chapter 24, while
e = 0,016708617 - (0,000042037 * T) - (0,0000001236 * (T * T))
pi = 102º.93735 + (1º.71953 * T) + (0º.00046 * (T * T))
Where T is the time in Julian Centuries from the epoch J2000.0, as
obtained by the formula (21.1).
Then the changes in longitude and in latitude of the star [or planet] due
to the annual aberration are
delta lambda = -k * cos(teta - lambda) + e * k * cos(pi - lambda) / cos(beta)
delta beta = -k * sin(beta) * (sin(teta - lambda) - e * sin(pi - lambda))
Aberration annual efect
Chapter 24, pag. 151
Lo = 280º.46645 + (36000º.76983 * T) + (0º.0003032 * (T * T))
M = 357º.52910 + 35999º.05030 * T - (0º.0001559 * (T * T)) - (0º.00000048 * (T * T * T))
C = + (1º.914600 - (0º.004817 * T) - 0º.000014 * (T * T)) * sin(M)
+ (0º.019993 - (0º.000101 * T) * sin(2 * M)
+ (0º.000290 * sin(3 * M))
Then Sun's true longitude is
Teta = Lo + C
Formula (21.1) (pag. 131)
Find the time T, measured in Julian centuries from the Epoch J2000.0 (JDE 2451545.0)
T = (JDE - 2451545) / 36525
Where JDE is the Julian Ephemeris Day, it differs from the Julian Day (JD) by the
small quanty delta t (see Chapter 7).
Heliocentric [/ Geocentric] Spherical to FK5
Mean dynamical ecliptic and equinox of the date to FK system
Chapter 31, pag. 207
Reference frame Mean dynamical ecliptic and equinox of the date differs
very slightly from the standard FK5 system. The conversion of L and B to the
FK5 system can be performed as follows, where T is the time in centuries
from 2000.0, or T = 10 * tau.
Calculate:
L' = L - (1º.397 * T) - (0º.00031 * (T * T))
Then the corretion to L and B are
delta L = -0".09033 + (0".03916 * (cos(L') + sin(L')) * tan(B))
delta B = +0".03916 * (cos(L') -sin(L'))
Then
L = L + delta L
B = B + delta B
Julian Day
Gregorian Date Julian Day Gregorian Date Julian Day
04/10/1957 19:26:24 2.436.116,31 2.436.116,31 29/02/1900 23:59:59 #NÚM!
01/01/2000 12:00:00 2.451.545,00 2.451.545,00 Date Serial Date
01/01/1999 00:00:00 2.451.179,50 2.451.179,50 01/03/1900 01/03/1900 2.415.079,50
27/01/1987 00:00:00 2.446.822,50 2.446.822,50 01/01/2101 01/01/2101 2.488.434,50
19/06/1987 12:00:00 2.446.966,00 2.446.966,00 31/12/9999 2958465,00 5.373.483,50
27/01/1988 00:00:00 2.447.187,50 2.447.187,50 31/12/9999 2958465,99998843000
19/06/1988 12:00:00 2.447.332,00 2.447.332,00 31/12/9999 23:59:59 5.373.484,50
01/01/1900 12:00:00 #NÚM! 2.415.019,00 31/12/9999 23:59:59 #NÚM!
27/01/0333 12:00:00 #NÚM! 1.842.713,00 01/01/2101 00:00:01 #NÚM!
2415018,5 00/01/1900 00:00:00
Nutation
Chapter 22 Ref:
Pag. 143 www.idlastro.gsfc.nasa.gov/ftp/pro/astro/nutate.pro
www.github.com/soniakeys/meeus/blob/master/nutation/nutation.go
nut_long nut_obliq
10/04/1987 00:00:00 -3,783736134 9,441719164 Arcseconds
2446895,5 -0,001051038 0,0026227 Degrees
Mean Obliquity of the Ecliptic (by Laskar) 23,44094629 Degrees
True Obliquity of the Ecliptic 23,44356899 Degrees Pag. 147
D M Mprime F Omega Sin Sdelt Cos Cdelt
0 0 0 0 0 1 -171996 -174.2 92025 8.9 {0, 0, 0, 0, 1, -171996, -174.2, 92025, 8.9},
1 -2 0 0 2 2 -13187 -1.6 5736 -3.1 {-2, 0, 0, 2, 2, -13187, -1.6, 5736, -3.1},
2 0 0 0 2 2 -2274 -0.2 977 -0.5 {0, 0, 0, 2, 2, -2274, -0.2, 977, -0.5},
3 0 0 0 0 2 2062 0.2 -895 0.5 {0, 0, 0, 0, 2, 2062, 0.2, -895, 0.5},
4 0 1 0 0 0 1426 -3.4 54 -0.1 {0, 1, 0, 0, 0, 1426, -3.4, 54, -0.1},
5 0 0 1 0 0 712 0.1 -7 0 {0, 0, 1, 0, 0, 712, 0.1, -7, 0},
6 -2 1 0 2 2 -517 1.2 224 -0.6 {-2, 1, 0, 2, 2, -517, 1.2, 224, -0.6},
7 0 0 0 2 1 -386 -0.4 200 0 {0, 0, 0, 2, 1, -386, -0.4, 200, 0},
8 0 0 1 2 2 -301 0 129 -0.1 {0, 0, 1, 2, 2, -301, 0, 129, -0.1},
9 -2 -1 0 2 2 217 -0.5 -95 0.3 {-2, -1, 0, 2, 2, 217, -0.5, -95, 0.3},
10 -2 0 1 0 0 -158 0 0 0 {-2, 0, 1, 0, 0, -158, 0, 0, 0},
11 -2 0 0 2 1 129 0.1 -70 0 {-2, 0, 0, 2, 1, 129, 0.1, -70, 0},
12 0 0 -1 2 2 123 0 -53 0 {0, 0, -1, 2, 2, 123, 0, -53, 0},
13 2 0 0 0 0 63 0 0 0 {2, 0, 0, 0, 0, 63, 0, 0, 0},
14 0 0 1 0 1 63 0.1 -33 0 {0, 0, 1, 0, 1, 63, 0.1, -33, 0},
15 2 0 -1 2 2 -59 0 26 0 {2, 0, -1, 2, 2, -59, 0, 26, 0},
16 0 0 -1 0 1 -58 -0.1 32 0 {0, 0, -1, 0, 1, -58, -0.1, 32, 0},
17 0 0 1 2 1 -51 0 27 0 {0, 0, 1, 2, 1, -51, 0, 27, 0},
18 -2 0 2 0 0 48 0 0 0 {-2, 0, 2, 0, 0, 48, 0, 0, 0},
19 0 0 -2 2 1 46 0 -24 0 {0, 0, -2, 2, 1, 46, 0, -24, 0},
20 2 0 0 2 2 -38 0 16 0 {2, 0, 0, 2, 2, -38, 0, 16, 0},
21 0 0 2 2 2 -31 0 13 0 {0, 0, 2, 2, 2, -31, 0, 13, 0},
22 0 0 2 0 0 29 0 0 0 {0, 0, 2, 0, 0, 29, 0, 0, 0},
23 -2 0 1 2 2 29 0 -12 0 {-2, 0, 1, 2, 2, 29, 0, -12, 0},
24 0 0 0 2 0 26 0 0 0 {0, 0, 0, 2, 0, 26, 0, 0, 0},
25 -2 0 0 2 0 -22 0 0 0 {-2, 0, 0, 2, 0, -22, 0, 0, 0},
26 0 0 -1 2 1 21 0 -10 0 {0, 0, -1, 2, 1, 21, 0, -10, 0},
27 0 2 0 0 0 17 -0.1 0 0 {0, 2, 0, 0, 0, 17, -0.1, 0, 0},
28 2 0 -1 0 1 16 0 -8 0 {2, 0, -1, 0, 1, 16, 0, -8, 0},
29 -2 2 0 2 2 -16 0.1 7 0 {-2, 2, 0, 2, 2, -16, 0.1, 7, 0},
30 0 1 0 0 1 -15 0 9 0 {0, 1, 0, 0, 1, -15, 0, 9, 0},
31 -2 0 1 0 1 -13 0 7 0 {-2, 0, 1, 0, 1, -13, 0, 7, 0},
32 0 -1 0 0 1 -12 0 6 0 {0, -1, 0, 0, 1, -12, 0, 6, 0},
33 0 0 2 -2 0 11 0 0 0 {0, 0, 2, -2, 0, 11, 0, 0, 0},
34 2 0 -1 2 1 -10 0 5 0 {2, 0, -1, 2, 1, -10, 0, 5, 0},
35 2 0 1 2 2 -8 0 3 0 {2, 0, 1, 2, 2, -8, 0, 3, 0},
36 0 1 0 2 2 7 0 -3 0 {0, 1, 0, 2, 2, 7, 0, -3, 0},
37 -2 1 1 0 0 -7 0 0 0 {-2, 1, 1, 0, 0, -7, 0, 0, 0},
38 0 -1 0 2 2 -7 0 3 0 {0, -1, 0, 2, 2, -7, 0, 3, 0},
39 2 0 0 2 1 -7 0 3 0 {2, 0, 0, 2, 1, -7, 0, 3, 0},
40 2 0 1 0 0 6 0 0 0 {2, 0, 1, 0, 0, 6, 0, 0, 0},
41 -2 0 2 2 2 6 0 -3 0 {-2, 0, 2, 2, 2, 6, 0, -3, 0},
42 -2 0 1 2 1 6 0 -3 0 {-2, 0, 1, 2, 1, 6, 0, -3, 0},
43 2 0 -2 0 1 -6 0 3 0 {2, 0, -2, 0, 1, -6, 0, 3, 0},
44 2 0 0 0 1 -6 0 3 0 {2, 0, 0, 0, 1, -6, 0, 3, 0},
45 0 -1 1 0 0 5 0 0 0 {0, -1, 1, 0, 0, 5, 0, 0, 0},
46 -2 -1 0 2 1 -5 0 3 0 {-2, -1, 0, 2, 1, -5, 0, 3, 0},
47 -2 0 0 0 1 -5 0 3 0 {-2, 0, 0, 0, 1, -5, 0, 3, 0},
48 0 0 2 2 1 -5 0 3 0 {0, 0, 2, 2, 1, -5, 0, 3, 0},
49 -2 0 2 0 1 4 0 0 0 {-2, 0, 2, 0, 1, 4, 0, 0, 0},
50 -2 1 0 2 1 4 0 0 0 {-2, 1, 0, 2, 1, 4, 0, 0, 0},
51 0 0 1 -2 0 4 0 0 0 {0, 0, 1, -2, 0, 4, 0, 0, 0},
52 -1 0 1 0 0 -4 0 0 0 {-1, 0, 1, 0, 0, -4, 0, 0, 0},
53 -2 1 0 0 0 -4 0 0 0 {-2, 1, 0, 0, 0, -4, 0, 0, 0},
54 1 0 0 0 0 -4 0 0 0 {1, 0, 0, 0, 0, -4, 0, 0, 0},
55 0 0 1 2 0 3 0 0 0 {0, 0, 1, 2, 0, 3, 0, 0, 0},
56 0 0 -2 2 2 -3 0 0 0 {0, 0, -2, 2, 2, -3, 0, 0, 0},
57 -1 -1 1 0 0 -3 0 0 0 {-1, -1, 1, 0, 0, -3, 0, 0, 0},
58 0 1 1 0 0 -3 0 0 0 {0, 1, 1, 0, 0, -3, 0, 0, 0},
59 0 -1 1 2 2 -3 0 0 0 {0, -1, 1, 2, 2, -3, 0, 0, 0},
60 2 -1 -1 2 2 -3 0 0 0 {2, -1, -1, 2, 2, -3, 0, 0, 0},
61 0 0 3 2 2 -3 0 0 0 {0, 0, 3, 2, 2, -3, 0, 0, 0},
62 2 -1 0 2 2 -3 0 0 0 {2, -1, 0, 2, 2, -3, 0, 0, 0},
To complete the calculation of the planet's apparent position, the corrections for
nutation should be aplied. This is achieved by calculating the nutation in longitude
(delta psi) and in obliquity (delta epsilon), as explained in Chapter 21. Add delta psi
to the planet's geocentric longitude, and delta epsilon to the mean obliquity
epsilon 0 of the ecliptic. The apparent right ascension na declination of the
planet can then be deduced by means of formula (12.3) and (12.4)
Transformation of Coordinates
12.3
tan(alfa) = (sin(lambda) * cos(epsilon) - tan(beta) * sin(epsilon)) / cos(lambda)
Pag. 87 - 89
12.4
sin(delta) = sin(beta) * cos(epsilon) + cos(beta) * sin(epsilon) * sin(lambda)
Simbols:
alfa = right ascencion (in hours, minutes and seconds of time -> convert degree by 15)
delta = declination (positive if north of the celestial equador, degative if south)
lambda = ecliptical (or celestial) longitude, measured from the vernal equinox along the ecliptic
beta = ecliptical (or celestial) latitude, positive if north of the ecliptic, negative if south
l = galactic longitude
b = galactic latitude
h = altitude, positive above the horizon, negative below
A = azimuth, measured westwards from the South. South(0º), West(90º), North(180º), East(270º).
Apparent equatorial coordinates (right ascension and declination)
Horizon coordinates (zenith distance and azimuth)
Euler Method?
http://idlastro.gsfc.nasa.gov/ftp/pro/astro/astro.pro
METHOD:
; ASTRO uses PRECESS to compute precession, and EULER to compute
; coordinate conversions. The procedure GET_COORDS is used to
; read the coordinates, and ADSTRING to format the RA,Dec output.
Returning Errors From VBA Functions
Font: http://www.cpearson.com/excel/ReturningErrors.aspx
If you use VBA or another COM language to create User Defined Functions (functions that are called directly
from worksheet cells) in a module or add-in, you likely will need to return an error value under some
circumstances. For example, if a function requires a positive number as a parameter and the user passes in
a negative number, you should return a #VALUE error. You might be tempted to return a text string that looks
like an error value, but this is not a good idea. Excel will not recognize the text string, for example #VALUE, as
a real error, so many functions and formulas may misbehave, especially ISERROR, ISERR, and IFERROR, and ISNA.
These functions require a real error value.
VBA provides a function called CVErr that takes a numeric input parameter specifying the error and returns
a real error value that Excel will recognize as an error. The values of the input parameter to CVErr are in the
XLCVError Enum and are as follows:
xlErrDiv0 (= 2007) returns a #DIV/0! error.
xlErrNA (= 2042) returns a #N/A error.
xlErrName (= 2029) returns a #NAME? error.
xlErrNull (= 2000) returns a #NULL! error.
xlErrNum (= 2036) returns a #NUM! error.
xlErrRef (= 2023) returns a #REF! error.
xlErrValue (= 2015) returns a #VALUE! error.
The only legal values of the input parameter to CVErr function are those listed above. Any other value causes
CVErr to return a#VALUE. This means, unfortunately, that you cannot create your own custom error values.
In order to return an error value, the function's return data type must be a Variant. If the return type is any other
data type, the CVErr function will terminate VBA execution and Excel will report a #VALUE error in the cell.
Note that these errors are meaningful only to Excel and have nothing at all to do with the Err object used to
work with runtime errors in VBA code.
Degree / Hour stamp
Stamp NumDec
Degree decimal to hour, minute and second 1 5
134,7946545070 8h 59' 10".717081669101560 8h 59' 10".71708
-316,1746574035 -21h 4' 41".917776840236911 -21h 04' 41".91777
Stamp NumDec
Degree decimal to degree, minute and second 2 9
-18,8874413208 -18º 53' 14".788754902947403 -18º 53' 14".788754902
13,7388321671 13º 44' 19".795801500239776 13º 44' 19".795801500
Stamp Degree to Degree
NumDec
String in degree, arcmin and arcsec to degree and decimals 15
5º 55' 14".78744 5,92077428929589 5,920774288888890
316º 10' 28".76665 316,17465740350100 316,174657402778000
0º 54' 54".56976 0,91515826914034 0,915158266666667
-18º 53' 14".78875 -18,88744132080640 -18,887441319444400
NumDec
String in hour, minute and second to degree and decimals 15
0h 23' 40".98582 5,92077428929589 5,920774250000000
21h 04' 41".91777 316,17465740350100 316,174657375000000
0h 03' 39".63798 0,91515826914034 0,915158250000000
-1h 15' 32".98591 -18,88744132080640 -18,887441291666700
Download Latest Version
GPlan-12.xlsm (697.7 kB)
