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9.1 Ephemeris Accuracy

The orbital elements used by Scientific Astronomer are fairly accurate. Planet positions are accurate to about one arc-minute during this and the next century (i.e., the years 1900 to 2100), and you should be able to go several thousand years into the past or future with very little error. The orbital elements used to calculate the Moon's position are also accurate to one arc-minute, and are sufficient to predict precise times for lunar and solar eclipses. Terms like evection, variation, annual-equation, reduction, and many more are all included in the equations for the Moon's position. Perturbations due to Venus are incorporated as well.

One thing that is not computed with high accuracy is the rising/setting time reported by Ephemeris. A difference of several minutes may exist between the true rising and setting times and those reported, since the full calculations with astmospheric corrections are not done. Another consideration is that right ascension and declination are relative to the time of observation epoch, not a fixed epoch year of, say, 2000. If you have a printed star chart for epoch 1950.0 or epoch 2000.0, you can expect a few arc-minutes discrepency due to the precession of the Earth's tilt, which Ephemeris correctly takes into account. The option Epoch is available in most functions to choose a specific epoch, other than the current one.

Scientific Astronomer correctly adjusts for light travel time when the option ViewPoint is set to an object other than the Earth. When you view a planet, you are actually seeing it as it was when the light first left it, not as it is now. The correction is very small, but sometimes it can make a difference. For example, it makes a difference in PlanetPlot3D[Jupiter, {1993,11,17,3,20,0}, ViewPoint -> Mars], where the positions of the Galilean moons and the Great Red Spot would be slightly wrong if the light travel time were not taken into account.

A final note about the time system used: Scientific Astronomer correctly uses Terrestrial Dynamic Time (TDT) for internal ephemeris calculations, and only converts to Universal Time (UT) when showing the date and time on input or output. Universal Time is the time you effectively use in the everyday world; that is, your watch is set to UT plus a time zone correction in hours. The problem with UT, however, is that it is related to the rotation of the Earth, which is now known to be irregular and slowly running down. For midnight to remain in the middle of the night it is necessary to add leap seconds to UT every now and then. Such jumps in UT are determined only by observation of the unpredictable rotation of the Earth. A more satisfactory time measure is TDT, which is completely regular (without leap seconds, for instance) and is governed by atomic clocks. In about the year 1900, TDT and UT corresponded almost exactly, but by the year 2000 the TDT-UT difference will amount to about 67 seconds. The TDT-UT difference increases at roughly a quadratic rate, assuming the Earth is uniformly slowing down. Thus, by the year 2100, this difference will probably be over 4 minutes.

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