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**HELPFUL DESCRIPTIONS.**

**a : semimajor axis**

For elliptical orbits, the semimajor axis is half the length of the longest line segment that can be drawn inside the ellipse. For hyperbolic orbits, the semimajor axis is the distance from the vertex to the nearest point on either branch.

**e : eccentricity**

The orbit is a circle when e=0. The orbit is an ellipse when 0<e<1. The orbit is a parabola when e=1. The orbit is a hyperbola when e>1.

**i : inclination to ecliptic**

I prefer to use the principal value of the arc-cosine for my range of inclination [0 , pi radians]. I take the ecliptic to be the current plane of Earth's orbit. (This is the

*hillbilly*tutorial, remember?)

**L : longitude of ascending node**

The angle, subtended at the sun, measured in the ecliptic, from the Vernal Equinox to the ascending node. The ascending node is the point at which the orbit crosses the ecliptic having the Z component of its velocity in the direction of the North Ecliptic Pole. (Most people use a capital omega for this quantity.)

**w : argument of perihelion**

The angle, subtended at the sun, measured in the plane of the orbit in the direction of motion, from the ascending node to the orbit's perihelion. (Most people use a lower-case omega for this quantity.)

**T : time of perihelion passage**

The time (e.g. a decimal calendar or Julian date) at which the orbiting object passes through the perihelion of its orbit.

**Q : true anomaly**

The angle, subtended at the sun, measured in the plane of the orbit in the direction of motion, from the perihelion to the current position of the orbiting object. No Greek letters can be rendered here, sorry.

**M : mean anomaly**

The angle, subtended at the sun, measured in the plane of the orbit in the direction of motion, from the perihelion to the point at which the orbiting object would be found, if it moved constantly by its average angular velocity.

**u : eccentric anomaly**

The angle, subtended at the geometric center of the orbit, measured in the plane of the orbit in the direction of motion, from the perihelion to a point on the circle circumscribing the orbit, which point is found by extending a line perpendicular to the major axis through the current position of the orbiting object until it intersects the circumscribing circle. No pictures, sorry.

**WHERE TO FIND ORBITAL ELEMENTS.**

Planetary orbital elements (NASA/JPL):

http://ssd.jpl.nasa.gov/elem_planets.html

Except don't believe the values for Earth's inclination and longitude of ascending node. Set them both equal to zero. The other elements in that table are OK. Why they didn't just go ahead and give the times of perihelion passage (or a mean anomaly at epoch), I've no idea.

Planetary orbital elements (some other guy):

http://www.astro.uu.nl/~strous/AA/en/reken/hemelpositie.html

Don't believe

*his*value for Earth's longitude of ascending node, either. Set it to zero.

Asteroid orbital elements:

http://ssd.jpl.nasa.gov/sb_elem.html

Convert a calendar date to a Julian date:

http://wwwmacho.mcmaster.ca/JAVA/JD.html

Convert a Julian date to a calendar date:

http://wwwmacho.mcmaster.ca/JAVA/CD.html

Jerry Abbott

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