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# Figuring out orbital positions from orbital elements

Posted by Emily Lakdawalla

2012/02/16 05:03 CST

**Topics:**
explaining science

A few times a year I find myself confronting a table full of numbers describing the orbits of things in the solar system, and cursing at myself because I've forgotten, *again*, what all these numbers mean and how to manipulate them to get the particular numbers I want. In particular, despite the fact that determining perihelion and aphelion distances from semimajor axis length and eccentricity could hardly be easier, I still always draw a blank. So I'm sitting down now to write a blog entry that will tell me what these numbers mean and how to use them to get the numbers I want! I'm posting it because I figure it'll be useful for some of you, too. In the following post, I'll show you why I was interested in getting these numbers today.

Here we go. The shape of an elliptical orbit is described by two parameters:

- semi-major axis,
*a*: one half of the ellipse's long axis - eccentricity,
*e*: 0 for circular orbits; between 0 and 1 for ellipses

- Periapsis distance =
*a*(1-*e*) - Apoapsis distance =
*a*(1+*e*) - Orbital period = 2π√(
*a*^{3}/GM) - Orbital period (solar orbit, in years, with
*a*in AU) =*a*^{1.5}

(and recall that 1 AU = 149.60×10^{6}km)

- Go to http://ssd.jpl.nasa.gov/horizons.cgi
- Change the
**Target Body**to the one you're interested in (click "change" and search on the name or number or provisional designation) - Change
**Observer Location**to "@sun" - Go to
**Table Settings**and check "Helio eclip. lon & lat" (or set the list to "18,20" to get heliocentric lat/lon and range) - Click
**Generate Ephemeris**and look for "hEcl-Lon" and "hEcl-Lat," which are in degrees, and "delta," which is the range in AU.

HORIZONS can also be used to find the distance between Earth and any of these objects, too, obviously; and you can have it spit the results directly to a text file, which is very handy!

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