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 several 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
Guide displays stars using data from three different catalogs. In order of accuracy, these are the Hipparcos, ACT, and GSC 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 ñ1532.5 milliarcseconds in RA, ñ995.1 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 ACT and in GSC) are given with error estimates. Those in the Hipparcos and ACT are probably good estimates of accuracy. Those in the GSC are very questionable, and in my opinion, are excessively optimistic. Brian Skiff has expressed it thusly: "Don't use [GSC magnitudes] for anything. No, not anything." This may be a little harsh (they are certainly good enough for drawing star charts), but does indicate the lack of respect for GSC magnitude accuracy in the community.
The situation with ACT is similar to that with GSC, with the difference that the sigma values given are somewhat greater for both positions and magnitudes. Still, they are far better than were available with any previous catalog. Also, the accuracy of the sigma values has been verified for ACT, through observations of occultations of stars by asteroids . The errors in the predicted paths for these events matches the sigma values pretty well.
The accuracy of GSC positions is the worst of any of these catalogs. It is still usually better than an arcsecond, but not by much. A recent effort to improve GSC accuracy, by recalibrating the astrometry using the ACT, is described here. In general, ACT and GSC positions differ by about .7 arcsecond; this is essentially the same as saying that "GSC stars bright enough to show up in ACT are usually in error by about .7 arcsecond."
If GSC star positions are corrected using the GSC-ACT transformation, the positional error usually drops by about a factor of two. So it is still bad, but no longer appallingly bad.
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 positions in Guide
Planetary positions in Guide are calculated using three separate methods. In "low precision" mode, a truncated version of the VSOP87 (Variations Seculaires des Orbites Planetaires) theory is used. The accuracy of that method is discussed here. It was evaluated by comparing the difference between low precision and high precision, and assuming that the difference corresponds to the error in low precision (this is a pretty fair assumption).
In "full precision" mode, two different theories are used, depending on the date and time. For dates between 1900 and 2100, Guide uses the PS-1996 theory. (For Neptune, the time span is 1850 to 2100; for Pluto, 1700 to 2100.) This gives results that match the JPL DE403 ephemeris to within a few milliarcseconds over that time span.
Outside that date, the full (untruncated) VSOP87 theory is used for all planets except Pluto. This probably matches reality to within a fraction of an arcsecond, for dates running back several centuries. Beyond that point, errors in observations become significant. While VSOP87 will provide the best data currently possible anywhere, there are limits to our knowledge for such distant eras.
Computing positions for Pluto outside the 1700 to 2100 range is troublesome. Guide includes a series fit due to Jean Meeus' Astronomical Algorithms. This is also the method used in "low-precision" mode for all dates. The only problem is that, as the author notes, "...the method given here is not valid outside the period 1885-2099." The fact that Guide ignores this and extrapolates Pluto across millennia is unfortunate. Unfortunately, no other theory is presently available for the purpose.
Accuracy of 'low-precision' planetary positions in Guide
Planetary positions in Guide are completed in two modes: "full precision" and "normal precision". (The difference is specified through a checkbox in the Data Shown dialog.) In "full precision" mode, Guide gets planetary positions over the time span 1900-2100 using the PS-1996 theory. This theory gives results that match those from the JPL DE403 ephemeris to within a few milliarcseconds, during the time span 1900-2100. The JPL ephemeris is the best source we have right now, but it's quite doubtful that it matches the real universe to the milliarcsecond level! So a discussion of planetary accuracy in Guide during that time span begins and ends with the statement "as accurate as we can get".
Outside that time span, in full precision mode, Guide uses the VSOP theory (Variations Seculaires des Orbites Planetaires, or "secular variations in the orbits of the planets") of P. Bretagnon and G. Francou of the Bureau des Longitudes. The accuracy of this theory is essentially unknown. It's probably at about the .1 arcsecond level, except for extremely distant eras, but that is essentially a guess.
But in low-precision mode, the positions of the Sun and planets are computed using the methods described by Jean Meeus in Astronomical Algorithms, using the truncated series shown in that book. Astronomical Algorithms has become (deservedly) something of a bible for software developers, so much of the following discussion applies to other commercially-available software. (To my knowledge, the only such software that also implements the PS-1996 and full VSOP, and therefore can claim the same accuracy as Guide in this area, is Chris Marriott's SkyMap software.)
To test the accuracy of low-precision mode, I compared the results from the truncated series against results from the unabridged VSOP theory. I wrote software to generate dates at random over a specified time interval and compute planetary positions using both series. The difference in positions derived from both methods is a fair measurement of the amount of error in the truncated VSOP, and therefore, is a good measurement of the accuracy of Guide's planetary positions when running in low-precision mode.
The following table shows the root-mean square errors and maximum errors in heliocentric longitude and latitude for the period 1900 to 2100.
Table 1. Position errors for 1900-2100, in arcseconds: low-precision mode
Planet Longitude Latitude
RMS Max RMS Max
Mercury 0.52 2.11 0.39 1.94
Venus 0.42 1.19 0.25 0.99
Earth 0.16 0.52 0.08 0.26
Mars 0.59 2.36 0.41 1.81
Jupiter 0.49 1.77 0.25 0.83
Saturn 0.66 2.02 0.40 1.71
Uranus 0.53 1.20 0.26 0.86
Neptune 0.50 1.25 0.20 0.54
As you can see, the RMS errors are all under an arcsecond. The maximum errors during this period are somewhat worse, but still quite reasonable. The next test was of the period 0-1000 AD. The VSOP theory involves polynomials in time, and its accuracy degrades as one gets farther from the year 2000. However, as Table 2 shows, the accuracy in the 0-1000 AD era is only slightly poorer than that of the 1900-2100 era.
Table 2. Position errors for 0-1000 AD, in arcseconds: low-precision mode
Planet Longitude Latitude
RMS Max RMS Max
Mercury 0.52 2.48 0.39 1.87
Venus 0.43 1.27 0.25 1.03
Earth 0.16 0.52 0.08 0.28
Mars 0.63 2.46 0.38 1.29
Jupiter 0.61 2.45 0.33 0.98
Saturn 0.72 2.55 0.42 2.03
Uranus 0.63 1.97 0.29 0.82
Neptune 0.41 1.13 0.25 0.64
The next test, of the -2000 to -1000 era, shows some serious deterioration in accuracy. In particular, the outer planets are much worse than they were in previous tests.
Table 3. Position errors for -2000 to -1000 AD, in arcseconds: low-precision mode
Planet Longitude Latitude
RMS Max RMS Max
Mercury 0.65 2.45 0.45 1.89
Venus 0.57 1.69 0.40 1.42
Earth 0.32 1.16 0.09 0.30
Mars 1.12 5.17 0.61 2.32
Jupiter 1.58 4.85 0.81 2.75
Saturn 2.01 6.84 1.83 6.02
Uranus 1.71 5.31 0.53 1.75
Neptune 0.95 2.08 0.38 1.07
I tell people that the planetary positions in Guide are utterly untrustworthy for dates before -2000 and after +6000 (i.e, for dates more than four millennia away from 2000). To demonstrate this, I ran a final test for dates between -4000 and -3000. As you can see, the accuracy deteriorates very rapidly outside the valid range, becoming as poor as an arcminute for Saturn during this period.
Table 4. Position errors for -4000 to -3000 AD, in arcseconds: low-precision mode
Planet Longitude Latitude
RMS Max RMS Max
Mercury 2.25 7.33 1.67 5.48
Venus 2.31 5.39 2.25 5.63
Earth 2.18 5.88 0.12 0.35
Mars 6.79 24.33 3.72 9.43
Jupiter 11.62 35.76 5.78 21.07
Saturn 15.42 55.83 15.52 45.78
Uranus 9.90 16.15 1.13 2.98
Neptune 9.76 16.28 0.75 2.17
The accuracy of the high-precision modes in Guide is presumably at the level of a few milliarcseconds; but at present, I have no "higher standard" to compare the results to.
The above comparison provides some hard data to support claims of arcsecond-level accuracy in planetary positions in Guide, when in "low-precision" mode. Table 4 shows that my assumption that the theory is not really intended for the very distant past and future appears to be correct. I'd assume that, even in high-precision modes, the accuracy deteriorates at distant eras.
The accuracy of the Moon is a separate problem. For this, Guide can use a truncated version of the ELP-2000 theory of Michelle Chapront-Touze and Jean Chapront, of the BDL (Bureau des Longitudes) in France. The accuracy looks to be in the neighborhood of a hundred meters or so, but I'm still investigating that question. (Such accuracy may appear to be "more than anyone would ever need", but in truth, greater accuracy wouldn't hurt when doing lunar graze work. One can never be too rich, too thin, or have too much accuracy in one's astronomy software.)
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.
For Mars and Uranus, I was unable to find an accurate theory for some time. I eventually did locate astrometry for these objects, and used it to generate circular orbits for them, using a least-squares fit to the data; these orbits proved to be surprisingly accurate, to within about 0.2 arcseconds (root-mean square).
Unfortunately, this was based only on recent observations (over 1993 to 1997). I'm sure the accuracy holds over the next few years, but beyond that, it's nearly certain that errors will slowly accumulate.
Since then, it's been pointed out that I overlooked algorithms in the Explanatory Supplement to the Astronomical Almanac for these objects. I intend to switch to these; I would have done so already, were it not that the accuracy of the circular orbits was quite good and I had other projects to complete.
For the eight 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)
For satellites of Jupiter, Guide uses the "high accuracy" method described in Jean Meeus' Astronomical Algorithms. This, in turn, is based on the theory E2 due to Lieske, with improvements known as E2x3.
For Triton and Charon, Guide uses methods from the Explanatory Supplement to the Astronomical Almanac.
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. It can use the SDP4 (Simplified Deep-Space Perturbations) method, which has advantages for objects with an orbital period greater than 225 minutes, with this add-on to Guide 8.
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
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 1998, 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.