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Package kepler (in kepler.i) -

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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

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.

SEE ALSO: sch_planets, jpl_planets, sch_moon, moon, solar_system

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.

SEE ALSO: sch_planets, jpl_planets, sch_moon, 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. 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 ALSO: solar_system, sch_moon, kepler

SEE: 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.

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.

SEE ALSO: solar_system, sch_moon, kepler