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+README.planetmath:  Understanding Planetary Positions in KStars.
+copyright 2002 by Jason Harris and the KStars team.
+This document is licensed under the terms of the GNU Free Documentation License
+-------------------------------------------------------------------------------
+
+
+0. Introduction: Why are the calculations so complicated?
+
+We all learned in school that planets orbit the Sun on simple, beautiful 
+elliptical orbits.  It turns out this is only true to first order.  It 
+would be precisely true only if there was only one planet in the Solar System, 
+and if both the Planet and the Sun were perfect point masses.  In reality, 
+each planet's orbit is constantly perturbed by the gravity of the other planets
+and moons.  Since the distances to these other bodies change in a complex way,
+the orbital perturbations are also complex.  In fact, any time you have more 
+than two masses interacting through mutual gravitational attraction, it is 
+*not possible* to find a general analytic solution to their orbital motion.  
+The best you can do is come up with a numerical model that predicts the orbits 
+pretty well, but imperfectly.  
+
+
+1. The Theory, Briefly
+
+We use the VSOP ("Variations Seculaires des Orbites Planetaires") theory of 
+planet positions, as outlined in "Astronomical Algorithms", by Jean Meeus.  
+The theory is essentially a Fourier-like expansion of the coordinates for 
+a planet as a function of time.  That is, for each planet, the Ecliptic 
+Longitude, Ecliptic Latitude, and Distance can each be approximated as a sum:
+
+  Long/Lat/Dist = s(0) + s(1)*T + s(2)*T^2 + s(3)*T^3 + s(4)*T^4 + s(5)*T^5
+
+where T is the number of Julian Centuries since J2000.  The s(N) parameters
+are each themselves a sum:
+
+  s(N) = SUM_i[ A(N)_i * Cos( B(N)_i + C(N)_i*T ) ]
+
+Again, T is the Julian Centuries since J2000.  The A(N)_i, B(N)_i and C(N)_i
+values are constants, and are unique for each planet.  An s(N) sum can
+have hundreds of terms, but typically, higher N sums have fewer terms.
+The A/B/C values are stored for each planet in the files
+<planetname>.<L/B/R><N>.vsop.  For example, the terms for the s(3) sum
+that describes the T^3 term for the Longitude of Mars are stored in
+"mars.L3.vsop".
+
+Pluto is a bit different.  In this case, the positional sums describe the
+Cartesian X, Y, Z coordinates of Pluto (where the Sun is at X,Y,Z=0,0,0).
+The structure of the sums is a bit different as well.  See KSPluto.cpp
+(or Astronomical Algorithms) for details.
+
+The Moon is also unique, but the general structure, where the coordinates
+are described by a sum of several sinusoidal series expansions, remains
+the same.
+
+
+2. The Implementation.
+
+The KSplanet class contains a static OrbitDataManager member.  The
+OrbitDataManager provides for loading and storing the A/B/C constants
+for each planet.  In KstarsData::slotInitialize(), we simply call
+loadData() for each planet.  KSPlanet::loadData() calls
+OrbitDataManager::loadData(QString n), where n is the name of the planet.
+
+The A/B/C constants are stored hierarchically:
+ + The A,B,C values for a single term in an s(N) sum are stored in an
+   OrbitData object.
+ + The list of OrbitData objects that compose a single s(N) sum is
+   stored in a QVector (recall, this can have up to hundreds of elements).
+ + The six s(N) sums (s(0) through s(5)) are collected as an array of
+   these QVectors ( typedef QVector<OrbitData> OBArray[6] ).
+ + The OBArrays for the Longitude, Latitude, and Distance are collected
+   in a class called OrbitDataColl.  Thus, OrbitDataColl stores all the
+   numbers needed to describe the position of any planet, given the
+   Julian Day.
+ + The OrbitDataColl objects for each planet are stored in a QDict object
+   called OrbitDataManager.  Since OrbitDataManager is static, each planet can
+   access this single storage location for their positional information.
+   (A QDict is basically a QArray indexed by a string instead of an integer.
+   In this case, the OrbitDataColl elements are indexed by the name of the
+   planets.)
+
+Tree view of this hierarchy:
+
+OrbitDataManager[QDict]: Stores 9 OrbitDataColl objects, one per planet.
+|
++--OrbitDataColl: Contains all three OBArrays (for 
+   Longitude/Latitude/Distance) for a single planet.
+   |
+   +--OBArray[array of 6 QVectors]: the collection of s(N) sums for 
+      the Latitude, Longitude, or Distance.
+      |
+      +--QVector: Each s(N) sum is a QVector of OrbitData objects
+         |
+         +--OrbitData: a single triplet of the constants A/B/C for 
+            one term in an s(N) sum.
+
+To determine the instantaneous position of a planet, the planet calls its
+findPosition() function.  This first calls calcEcliptic(double T), which
+does the calculation outlined above: it computes the s(N) sums to determine
+the Heliocentric Ecliptic Longitude, Ecliptic Latitude, and Distance to the
+planet.  findPosition() then transforms from heliocentric to geocentric
+coordinates, using a KSPlanet object passed as an argument representing the
+Earth.  Then the ecliptic coordinates are transformed to equatorial
+coordinates (RA,Dec).  Finally, the coordinates are corrected for the
+effects of nutation, aberration, and figure-of-the-Earth.  Figure-of-the-Earth 
+just means correcting for the fact that the observer is not at the center of 
+the Earth, rather they are on some point on the Earth's surface, some 6000 km
+from the center.  This results in a small parallactic displacement of the 
+planet's coordinates compared to its geocentric position.  In most cases, 
+the planets are far enough away that this correction is negligible; however, 
+it is particularly important for the Moon, which is only 385 Mm (i.e., 
+385,000 km) away.
+