Accuracy of Guide's data and positions

The subject of the accuracy of any astronomy software is a very complex one. The accuracy of positions shown by Guide varies from about a thousandth of an arcsecond (for stars in the Hipparcos catalog) to being as poor as dozens of degrees (for some asteroids whose orbits have not been thoroughly studied). For moving objects, the accuracy is also a function of time; that of positions of planets within a century of the year 2000 is of the order of milliarcseconds, but probably no better than arcminutes for very distant dates.

There is also the issue of how accuracy claims can be verified. Where possible, this should be done by comparing data from the software to actual, observed data. Comparison to results from other software is simply not trustworthy, especially since most software authors use similar algorithms. It is very easy for us to generate identical, but incorrect, answers.

As you will see, when the accuracy claim is better than about a tenth of an arcsecond, verifying it becomes nearly impossible. In such cases, the precision claimed by the authors of the catalog or of the theory of motion is cited.

  • Accuracy of stellar positions and magnitudes
  • Accuracy of rise/set times and alt/az values
  • Accuracy of planetary positions
  • Accuracy of natural planetary satellites
  • Accuracy of artificial satellites
  • Accuracy of asteroid positions
  • Accuracy of comet positions and magnitudes
  • Accuracy of deep-sky data
  • Accuracy at very distant dates
  • Accuracy of Delta_T (TD-UT) values
  • Accuracy of stellar positions and magnitudes

    Guide displays stars using data from three different catalogs. In order of accuracy, these are the Hipparcos, Tycho-2, and UCAC-3 catalogs.

    The Hipparcos catalog is not only the most accurate catalog in Guide; it is the most accurate, period. Its positions are typically accurate to within a few milliarcseconds, for dates close to the present. The accuracy varies as a function of time and as a function of which star you are asking about. When you click on an Hipparcos star, and ask for "more info", you will see (among other things) data such as the following, for Capella in September 1998:

    J2000 position at current date (proper motion included):
    Right ascension: 05h16m41.3497s
    Declination: N45 59' 53.319"
    (Above is +/-5.8 milliarcseconds in RA, +/-3.8 milliarcseconds in dec)
    

    Those "sigma" (error) values are smallest for dates close to 1991, the year in the middle of the span during which the Hipparcos satellite collected data. As you ask for data at more distant dates in the past and future, the error values reported will get larger. For example, here is the data for Capella on 1 Jan 1 AD. The star is several arcminutes from its 1998 position (the effects of two millennia of proper motion), and the accuracy of that position is not nearly as good as it was in 1998:

    J2000 position at current date (proper motion included):
    Right ascension: 05h16m26.8097s
    Declination: N46 14' 06.520"
    (Above is 1532.5 milliarcseconds in RA, 995.1 milliarcseconds in dec)
    

    The sigma values are computed using fairly simple formulae supplied with the Hipparcos catalog. I have verified the formulae, but I have no means for assessing the accuracy of the input data. However, I have no reason to doubt that it is correct.

    The magnitudes in the Hipparcos dataset (and in Tycho-2 and UCAC) are given with error estimates. Those in the Hipparcos and Tycho-2 are probably good estimates of accuracy. Those in the UCAC-3 are usually pretty good, but shouldn't be used for photometry unless you have nothing better available. (Sadly, this is often the case.)

    Accuracy of rise/set times and alt/az values

    At the horizon, variations in refraction can be so extreme that there is little point in giving rise/set times to a precision greater than one minute, and this is exactly what Guide does.

    For computing altitude adjusted by refraction, Guide makes use of the data you provide in its Locations dialog for atmospheric pressure and humidity. This probably gives values to within an arcsecond, but the real atmosphere has been known to vary significantly from the "theoretical" one used in Guide.

    Accuracy of planetary and lunar positions in Guide

    Between the years 1800 to 2200, planetary and lunar positions in Guide are calculated using the JPL DE-406 ephemeris. One cannot get much better than this. The accuracy is stated to be of the order of milliarcseconds, and I've no good reason to doubt this.

    Outside that range, Guide defaults to use of analytic series solutions such as VSOP. These are good to within a fraction of an arcsecond within the years 1000 to 3000, and an arcsecond or two within -2000 to +6000. Outside that range, though, they start to diverge badly and are not to be trusted. (Actually, they might be good to within, say, a degree for many more millennia, sufficient for some uses; but I've no way of verifying that. They might be complete garbage at such a range.)

    There is one object for which the accuracy may be worse even a few millennia ago or hence: the Moon. That is because the moon's motion is somewhat irregular (the "delta-T" problem). We've a decent handle on it through historical records of ancient eclipses, but these were not measured using accurate clocks or with sophisticated instruments. And beyond a couple of millennia, there are no eclipse records available.

    Accuracy of natural planetary satellites

    General comments about planetary satellite accuracy:

    Perhaps the best way to verify the accuracy of planetary satellite positions is to examine "differential astrometry" results: data where the difference in positions, in RA and dec, between two satellites is given. This sort of data tends to give the most precise measurements possible, except for mutual eclipses of satellites and some data from probes such as Voyager and Galileo.

    The methods used to compute satellite positions vary considerably from planet to planet. There is no really standardized method of computing satellite positions, so the methods have to be discussed separately. (This is also why "more info" for each satellite -- and, for that matter, each planet -- will describe the method used to compute its position.)

    Small inner satellites: For the small inner satellites of the outer planets, I make use of precessing elliptical elements provided by JPL. These are a good fit to the actual motions of the objects. (This covers Phobos, Deimos, the inner four moons of Jupiter, some small inner moons of Saturn, and all inner moons of Uranus and Neptune except for Triton. For Triton, Guide uses methods from the Explanatory Supplement to the Astronomical Almanac.)

    Outer, irregular satellites: The gas giants all have distant, mostly very faint "irregular" satellites. These really can't be handled with an analytic theory. For each, I computed numerically-integrated ephemerides fitted to observations using Find_Orb. Guide then interpolates within these ephemerides.

    I've used a similar method with the faint moons of Pluto (Nix and Hydra). But here, I lacked observational data, so I downloaded ephemerides from JPL's Horizons system. Guide interpolates within these as it would within Find_Orb-generated ephemerides.

    Satellites of Saturn: For the eight main moons of Saturn, Guide uses the theory of Gerard Dourneau. This produces results considerably better than an arcsecond for the inner six moons. Hyperion has an RMS error of about an arcsecond; it is strongly perturbed by Titan, and the theory doesn't completely account for that. The outermost satellite, Japetus, is also not as precise as the inner satellites.

    Dourneau's methods are based over astrometry gathered from roughly 1900 to 1980. (The ranges vary from satellite to satellite.) However, the results match modern-day astrometry quite nicely, as you can see at the links given below.

    One can get differential data for satellites of Uranus and Saturn at the following links:

     Position of Uranian satellites (Veiga+, 1994) 
     Uranian satellites (Veiga+, 1995) 
     Astrometry of Satellites of Uranus (Jones+ 1998) 
     1990-1994 Saturn's satellites astrometry (Harper+ 1997) 
    

    For the above events, the test procedure is as follows. Set Guide's date and time to that given for a particular observation, and right-click on the two satellites measured. Then hit the Insert key. Guide will give the distance and position angle between the satellites, as well as the differences in RA and dec. These will agree with the observations to better than an arcsecond, for Uranus and Saturn.

    Observational data for satellite mutual events doesn't seem to be available, but some predictions can be found here:

     Mutual phenomena of the Galilean satellites (Arlot+ 1997) 
     Galilean satellites mutual events in 1997 (Arlot 1996) 
    

    Galileans: For the four largest satellites of Jupiter, Guide uses the "high accuracy" method described in Jean Meeus' Astronomical Algorithms. This, in turn, is based on J. Lieske's E5 theory..

    For Triton, Charon, and the satellites of Mars, astrometric test data is unavailable. The best I could do to test these was to compare results from the JPL Solar Systems Dynamics page. This indicates that the positions generated by Guide are indeed good to within better than an arcsecond. Exactly how much better, though, it is impossible to say.

    Accuracy of artificial satellites

    For artificial satellites, Guide uses the SGP4 (Simplified General Perturbations) theory for objects with an orbital period of less than 225 minutes, and the SDP4 (Simplified Deep-Space Perturbations) method for objects with a longer orbital period.

    The SGP4 is the best method currently available for low-earth objects, and does a pretty decent job over short time periods for higher objects. It is a rough approximation, for several reasons. At the time it was created, computers were not as powerful as they are today; had more subtle effects been included, the method would have not been very practical. It's been suggested, too, that the US Government was not very happy to have such theories distributed, and that we almost certainly do not get to see the really accurate satellite motion models.

    For practical purposes, though, the real limit to accuracy is that of the input data, the TLE (Two-Line Element) orbital data. To get good predictions, the data must be recent. For illustrative purposes, the Guide CD contains TLE data for some bright satellites and geostationary satellites; but you must get updated versions of these if you actually hope to find these objects! Fortunately, TLEs can be downloaded from a variety of sites dedicated to satellite observing; here are some links:

    Mike McCants' elements page
    Current NORAD Two-Line Element Sets
    Current TLEs from www.tle.info

    Also, one can use Guide 8's Settings... TLE= option, and then simply click on options to download fresh TLEs automatically from several sites (including the above.)

    Accuracy of asteroid positions

    For dates close to the present, one good method of verifying the accuracy of asteroid positions is to compare predictions for asteroid occultations to actual observations; some examples of this are available on this Web site. In general, they show that, for low-numbered objects close to the present, the precision is indeed somewhat better than an arcsecond. This has also been verified by people doing astrometry using the Charon astrometry software, which uses the same orbital data and computational methods to get a "predicted" asteroid position.

    For more poorly-observed objects, the accuracy naturally is lower. There is no easy way to determine, though, what that accuracy might be. One good clue comes from clicking on an asteroid in Guide and asking for "more info". The result includes text such as the following (the example is for the asteroid 1036 Ganymede):

    Orbital arc: 24852 days
    437 observations made to determine orbit
    Current ephemeris uncertainty (CEU) on 22 03 1998:
     1.0E-01 arcseconds, changing by 1.1E-03 arcseconds/day
    Next peak CEU: 2.4E-01 arcsec,  on 18 09 1998
    Maximum CEU in next ten years: 2.4E-01 arcsec,  on 18 09 1998
    

    This asteroid has had its position measured 437 times over a span of 24852 days (about 68 years), and can be considered "well-determined". (At the other extreme, in some cases, there may be only three or four observations gathered over the course of one or two nights. In such cases, the object is usually almost hopelessly lost; by the time a few years have passed, it could be virtually anywhere.)

    The good quality of the orbit shows up in the fact that its current ephemeris uncertainty is a mere .1 arcseconds, growing and expected to reach .24 arcseconds on 18 Sep 1998 (its maximum between 1998 and 2008). The CEUs should be taken with some caution (especially for very high and very low values), but do seem to match the results from astrometric observations tolerably well.

    For more distant dates, observations become more difficult to come by. One source has recently become available: the RealSky CDs. Each plate near the ecliptic contains images of dozens of asteroids, and the difference between their trails on the images and their positions as shown by Guide is a good indication of the amount of error in Guide. Also, the positions date back to the early 1950s, allowing one to see the effects of any possible perturbation errors in Guide.

    Here is an example of how this can be done. Start up Guide, and go to the star Theta Cancri. (In general, you would simply find a place near the ecliptic.) Set your latitude to N 33 21.6', W 116 51.8' (the location of Palomar). Go to level 5, select "Extras... Toggle user datasets", and turn the POSS plates on.

    Now click on the label for plate #426, and ask for "more info". Among other things, you will get the following data:

    Exposure start date: 1954 DEC 21
    Red plate exposure start time (PST): 02 11
    Blue plate exposure start time (PST): 01 54
    Red plate exposure duration: 45 minutes
    Blue plate exposure duration: 12 minutes
    

    So the plate was exposed on the "evening of 21 Dec", making the actual start of the exposure time and date 22 Dec 1954, 2:11 Pacific Time (10:11 UT). Set Guide's time and date accordingly. Go into the "Data Shown" menu, and turn asteroids on.

    As you will see, many asteroids were caught on this plate. I chose asteroids #5428 and #3002, zoomed in between them, and brought up a RealSky image large enough to cover both objects. The trails in the RealSky image matched the asteroids plotted by Guide. (#5428 is slightly off, but examination of its orbital arc length makes this a little less surprising.) Setting the time to 10:56 UT (the end of the exposure) moves the asteroids to the opposite end of the trails.

    In general, you can repeat this procedure for randomly chosen plates on the ecliptic, and for random asteroids in the image, and you will get similar results.

    Accuracy of comet positions and magnitudes

    Guide uses one set of orbital elements to cover the entire apparition of a comet. It does switch elements for each apparition; if it failed to do so, its accuracy would be horrible. But the perturbations during a particular apparition are neglected. The error resulting from this is usually a few arcseconds, at worst.

    There are exceptions, however. Comets that pass unusually close to Jupiter (or, as happened in 1994, crash into it) are obviously seriously perturbed, and the positional accuracy is less for such objects. Also, the positions for ancient events are obviously not based on exact astrometric measurements, and probably bear only a rough relationship to the real world.

    Guide uses standard formulae and data to compute magnitudes for comets. Unfortunately, comets tend to do rather random and unpredictable things in this regard (David Levy has commented that "comets are like cats; they both have tails, and they both pretty much do whatever they want to do".) The magnitudes computed by Guide should be considered a rough indication, rather than a certainty.

    Accuracy of deep-sky data

    Guide makes use of the best available catalogs for deep-sky data. Unfortunately, this does not always mean they are accurate. Things are much better than they were in 1993, when Guide 1.0 was released; the data errors in the RNGC (Revised New General Catalog) were frightening. But there is still much work to be done in this area. Guide's data for deep-sky objects is therefore about as good as one can currently get.

    In general, it is very rare to find errors in which objects are plotted erroneously. It is more common to find cases where an object is misidentified, or where there are disagreements as to how it should be identified. Many of these have been cleaned up, but the daunting size of the task has kept the astronomical data centers of the world busy for many years; and as the catalogs grow larger, so does the size of the job in question.

    Accuracy at very distant dates

    Most of the data used to generate the catalogs and theories used by Guide (and all software) were made using data collected in the last century or so. As a result, they provide impeccable accuracy during this period and for some time into the future and past. At more distant dates, as described above, they still provide fairly good data; the position given for Capella, for example, is still good to about an arcsecond at a distance in time of 2000 years.

    But one must be careful not to push this process too far. Many of the methods used in Guide deteriorate, gracefully or otherwise, outside their proper time span; the formulae fit observed values nicely over a particular range near the present, and are not really intended for use outside that range. The following examples should show what is meant by this.

    Between the years -8000 to +12000, Guide computes the earth's obliquity to within a fraction of an arcsecond. This is done using a standard formula expressing the obliquity as a tenth-degree polynomial. But as one gets outside this time range, the obliquity diverges badly.

    Set Guide's date to 30340 AD, for example, and Guide will inform you that the earth's obliquity is 90 degrees. On that distant date, our climate will be quite unusual, as our axis points through the sun twice a year, providing continuous sunlight in one hemisphere and continuous darkness in the other. A few dozen millennia after that, you reach a point where the obliquity reverses every few hundred years, and the earth basically tumbles like a defective top.

    If you set the date and time to about 74000 AD, you can learn that the Earth's orbit will pass through the Sun once or twice each year. In "Animation", you can watch the Sun slowly grow in Earth's sky, until it fills an entire Level 1 (180 degree) field of view. Again, the various planetary theories were not really intended for this sort of thing. No indication of the valid range of VSOP87 is given, but it apparently should not be extended this far.

    Siebren Klein has pointed out that, at still further dates, proper motion causes the Pleiades to leave their nebula behind.

    There are enough such cases that it is tempting to have Guide insist that dates must be between, say, -8000 and +12000. The only thing unfortunate about this is the loss of the ability to show proper motions, which does look interesting and does retain a high degree of accuracy, even at very distant dates. A more probable solution will be to have Guide post a warning message that accuracy will be poor at the distant date you have selected (this would be analogous to the "You are using the Gregorian calendar for a date before 1582" message.)

    Accuracy of Delta_T (TD-UT) values

    Delta_T reflects the difference between a smoothly increasing time scale, TD (Dynamical Time), and a time scale based on the erratic rotation of the earth, UT (Universal Time). It has an effect on any computation involving a topocentric observer, but is of particular importance in eclipse and occultation calculations.

    For the years 1620 to the present, Guide relies on actual measured values of Delta_T, which can be assumed to be accurate. For years outside this range, expressions due to Morrison and Stephenson are used. For years in the future, their expression gives a discontinuity with current data, so the constant term had to be adjusted. The result is:

    DeltaT( Year) = 69.3 + 123.5 * dt + 32.5 * dt * dt
    

    where dt = time, in centuries, from J2000. This gives a close match to recent behavior while retaining the quadratic term descriptive of behavior over the last few centuries. You can see the value used for Delta-T in the Quick Info section.