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Package kepler (in kepler.i) -

Index of documented functions or symbols:

jpl_planets

kepler

kepler2

moon

### jpl_planets

```DOCUMENT jpl_planets
orbital elements from http://ssd.jpl.nasa.gov/elem_planets.html
"Mean orbit solutions from a 250 yr. least squares fit of the
DE200 planetarty ephemeris to a Keplerian orbit where each element
is allowed to vary linearly with time.  This solution fits the
terrestrial planets to 25" or better, but achieves only 600" for
Saturn.  Elements are referenced to mean ecliptic and equinox
of J2000 at the J2000 epoch (2451545.0 JD)."
J2000 = 2000 January 1.5

WARNING: these elements are 1.5 JD later than sch_planets

definitions:
argument of perihelion = longitude of perihelion -
longitude of ascending node
mean anomaly = mean longitude - longitude of perihelion
1 Julian century = 36525 days```

### kepler

```DOCUMENT xyz = kepler(orbit, time)
or xyz = kepler(orbit, time, ma, ta, norb)

return 3-dimsof(orbit(1,..))-by-dimsof(time) XYZ coordinates
corresponding to the orbit(s) ORBIT and time(s) TIME.  Optionally
return mean anomaly MA, true anomaly TA, and integer number of
orbits, each a dimsof(orbit(1,..))-by-dimsof(time) array.  The
MA and TA are in radians.  The x-axis is along the line of the
vernal equinox, the z-axis is ecliptic north.

ORBIT has leading dimension 12: [angle from perihelion, mean daily
motion, semi-major axis, d/dt(semi-major axis), eccentricity,
d/dt(eccentricity), longitude of ascending node, d/dt(ascending
node), angle from ascending node to perihelion, d/dt(perihelion),
inclination, d/dt(inclination)]
(Six pairs of a quantity and its time derivative.)
The angles are in degrees; d/dt units must match TIME units.

Mean anomaly is not an angle in real space; it is the quantity
proportional to time in Kepler's equation.  True anomaly is the
angle from perihelion to planet.

With a non-nil, non-zero full= keyword, return XYZUVW -- that is,
six coordinates including velocities as well as positions.
```

### kepler2

```DOCUMENT xyz = kepler2(orbit, xyz0)
or xyz = kepler2(orbit, xyz0, time, ma, ta)

return dimsof(xyz0) XYZ coordinates corresponding to the orbit(s)
ORBIT and direction(s) XYZ0.  The dimensions of ORBIT beyond the
first, if any, must match those of XYZ0, although XYZ0 may have
any number of trailing dimensions.

Optionally return TIME, mean anomaly MA, and true anomaly TA,
each a dimsof(orbit(1,..))-by-dimsof(time) array.  The MA and TA
are in radians.  The x-axis is along the line of the vernal
equinox, the z-axis is ecliptic north.  The XYZ0 direction is first
projected into the plane of the orbit; then XYZ will be proportional
to XYZ0.  The time derivatives of the ORBIT elements are ignored.

ORBIT has leading dimension 12: [angle from perihelion, mean daily
motion, semi-major axis, d/dt(semi-major axis), eccentricity,
d/dt(eccentricity), longitude of ascending node, d/dt(ascending
node), angle from ascending node to perihelion, d/dt(perihelion),
inclination, d/dt(inclination)]
(Six pairs of a quantity and its time derivative.)
The angles are in degrees; d/dt units must match TIME units.

Mean anomaly is not an angle in real space; it is the quantity
proportional to time in Kepler's equation.  True anomaly is the
angle from perihelion to planet.
```

### moon

```DOCUMENT xyz = moon(time)
return position XYZ of the moon relative to center of earth
at TIME; the XYZ has leading dimension 3; x is along the vernal
equinox, z is ecliptic north.  The corrections to the lunar orbit
are from Schlyter (see sch_moon).  Claimed accurate to 2 arc minutes
over some reasonable time.  TIME is in days since 0/Jan/00 (that is,
0000 UT 31/Dec/99).  This is 1.5 days earlier than the J2000 epoch.```

SEE: sch_planets

### sch_planets

```DOCUMENT sch_planets, sch_moon
from "How to compute planetary positions",
by Paul Schlyter of Stockholm, Sweden
http://hotel04.ausys.se/pausch
"Please note that the orbital elements of Uranus and Neptune as given
here are somewhat less accurate.  They include a long period perturbation
between Uranus and Neptune.  The period of the perturbation is about
4200 years."
After corrections in the case of the moon, jupiter, saturn, and uranus,
these are claimed to be accurate to under 1 arc minute for the inner
planets, about 1 arc minute for the outer planets, and 2 arc minutes
for the moon.```

### solar_system

```DOCUMENT xyz = moon(time)
return position XYZ of the moon relative to center of earth
at TIME; the XYZ has leading dimension 3; x is along the vernal
equinox, z is ecliptic north.  Corrections due to Schlyter (see
sch_planets) are applied.  Claimed accurate to under 1 arc minute
over some reasonable time.  TIME is in days since 0/Jan/00 (that is,
0000 UT 31/Dec/99).  This is 1.5 days earlier than the J2000 epoch.```