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Coordinate Transformations

Right Ascension and Declination

There are several different ways of specifying the position of an object against the background of stars and constellations, so every PyEphem “body”, whether a planet, comet, asteroid, or star, returns three sets of coordinates when you ask it to compute its position. Briefly, these are:

  • a_ra, a_decAstrometric Geocentric Position for the star atlas epoch you’ve specified
  • g_ra, g_decApparent Geocentric Position for the epoch-of-date
  • ra, decApparent Topocentric Position for the epoch-of-date

Actually, the third position, the“Apparent Topocentric” position, is only computed if you provide PyEphem with an Observer to work with. If you provide only a date for compute() instead, then ra and dec will have the same values as g_ra and g_dec. The Greek prefix topo- means place, and a topocentric position reveals where a body will appear in the sky when viewed from a particular place on the Earth’s surface.

The names ra and dec are short for right ascension and declination, which serve as longitude and latitude for the sky, telling us where admist the stars and constellations an object appears. See any introduction to astronomy if you need to learn how they are defined; the description below describes how the three versions of right ascension and declination returned by PyEphem differ.

How the three positions differ

The easiest way to define what each kind of coordinate means is to trace how PyEphem computes a body’s position, and show how it generates each of the values in turn. PyEphem performs its computations using routines from libastro, which contains the high-precision astronomy routines used in the XEphem graphical astronomy application.

  • To begin with, PyEphem figures out where both the body and the Earth are located for the exact date and time you have asked about, and then compares the two positions to work out both the body’s distance from the Earth and also the direction in which it lies.

  • For bodies in the Solar System, like planets, comets, and asteroids, PyEphem converts the distance from the Earth to the body into the light travel time that light from the body requires to reach us, and re-computes the object’s position for that many minutes earlier than the actual date and time you specified. For example, as I write this, Jupiter is about 3,100 light-seconds, or more than 51 light-minutes, from the earth:

    >>> import ephem
    >>> j = ephem.Jupiter('2007/12/6')
    >>> print j.earth_distance * ephem.meters_per_au / ephem.c, "seconds"
    3098.61793563 seconds

    This means that we on Earth are not actually seeing Jupiter as it really is at this moment; instead, we are seeing an image of where Jupiter was 51 minutes ago. So if I ask PyEphem for Jupiter’s position, it will begin by computing its location at this moment as a “first try”, will discover that Jupiter is currently 51 light-minutes away, and then will re-compute Jupiter’s position for 51 minutes ago since that is the position at which we will actually see Jupiter.

  • Having compensated for light-travel time, PyEphem now knows the “star-atlas position” of the body, and checks for which star-atlas epoch you want coordinates expressed in — which is supplied by the epoch attribute if you passed an Observer to compute() or by the epoch= keyword if you have merely passed a date. (Both default to the standard date 2000/1/1.5 if you do not specify your own value). PyEphem takes a copy of the body’s coordinates, performs precession to determine what those coordinates were called in the epoch you have chosen, and stores the result in:

    • a_ra and a_dec — the Astrometric Geocentric Position
  • Next, PyEphem adjusts the body’s position for relativistic deflection, which is the slight nudge that gravity gives to light that passes very close to the Sun. This only affects objects within about 10° of the Sun and which lie on the far side of it from the Earth.

  • Next, PyEphem adjusts the body’s position for nutation, which is really not an adjustment to the body’s apparent location at all, but a correction for the fact that the platform from which we observe — the Earth — wobbles over the span of months and years. If you want to point a very accurate telescope at an object, then you have to account for this wobble in the Earth’s pole. (Star atlas coordinates always ignore this, and pretend that the Earth’s pole doesn’t have this slight wobble, which is why the “Astrometric” coordinates above don’t have to include this correction.)

  • Next, PyEphem adjusts the body’s position for the aberration of light, the fact that the motion of the Earth through space causes a slight slant to the light reaching us from other objects, in the same way that driving through rain or snow will make the precipitation look like it is coming down diagonally, from in front of you, instead of looking like it is coming straight down from overhead. (PyEphem skips this step for the Moon, since the Moon travels with the Earth through space.)

  • Having made all of these adjustments, PyEphem is now confident that it knows the direction in which the object appears to lie from the Earth, so it stores the computed position in:

    • g_ra and g_dec — the Apparent Geocentric Position
  • If you provided an Observer to the body’s compute() method, then PyEphem has a few last steps to perform to determine where the objects appears from that specific location. Otherwise, if you only provided a date, then the computation stops here (and ra and dec are given the same values as g_ra and g_dec).

  • The first adjustment that PyEphem makes based on the location of the Observer is to correct for parallax. This is needed because all of the previous steps computed where the body lies when viewed from the location of the Earth itself in its orbit — that is, from the Earth’s exact center, which is why the previous coordinate sets were all named “Geocentric” (the Greek prefix geo- means Earth). But someone on the Earth’s surface is more than 6,300 kilometers away from the Earth’s center, which will shift, very slightly, the position of Solar System bodies against the background of stars (and will move nearby bodies like the Moon, or an artificial Earth satellite, even more). The parallax correction adjusts for this.

  • Finally, the very atmosphere through which we view the sky acts as a lens that displaces the positions of bodies when they get close to the horizon. PyEphem has to correct for this refraction both in order to give you a more accurate idea of where to point your telescope, and to be able to make correct predictions of rising and setting times. But doing this calculation accurately is difficult, because the atmosphere’s optical properties vary depending both on its temperature and on the amount of moisture the air is holding! PyEphem does its best to estimate the result, using the Observer attributes temp and pressure. These default to 25°C and 1010 millibar if you do not specify more specific values; set the pressure to zero if you want PyEphem to ignore the effects of atmospheric refraction.

  • PyEphem is now done, and produces its final set of coordinates:

    • ra and dec — the Apparent Topocentric Position
    • alt and az — the same position, measured from the horizon

Note that no precession was applied to either of the final two sets of coordinates, but only to the first. This means that only the “Astrometric” position will correspond to the lines in your star atlas. The other positions are what are called “epoch-of-date” coordinates, and are measured off of the orientation of the celestial pole and the celestial equator for the very day of the observation itself.