## functions in kepler.i - k

kepler
```
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.
Interpreted function, defined at i/kepler.i   line 6

```

kepler2
```
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.
Interpreted function, defined at i/kepler.i   line 89

```