A Brief Summary of Computations

Earth

Computations involving the earth are:

  1. Latitude and longitude computations. These are restricted to WGS-84 system current version.
  2. Julian day and sidereal time computations, along with Delta T corrections.
  3. Values of the Obliquity of the Ecliptic, Precession and Nutation.

Moon

  1. Compute location relative to Geocentric Ecliptic coordinates.
  2. Parallax correction (Diurnal).
  3. Atmospheric refraction correction.

Solar System, including the Sun

  1. Compute locations relative to Geocentric Equatorial coordinates using VSOP87C. Light time corrections are considered.
  2. Precession and Nutation corrections.
  3. Parallax correction (Diurnal).
  4. Atmospheric refraction correction.

Stars

The raw star location data is taken from the Hipparcus catalogue and corrected to J2000 Epoch The raw data from the Hipparcus catalogue is as viewed from the Barycentre of the Solar System. This data is used on the main Star Map.

Corrections are then applied for, in the order shown

  1. Proper motion.
  2. Annual Aberration.
  3. Precession and nutation.
  4. Annual Parallax
  5. Atmospheric refraction.

In the listings, the data shown under “ICRS 2000” have proper motion correction applied, while the data shown under “ICRS Corrected” have after additional aberration, precession, nutation and parallax corrections. The data shown under “Apparent” have additional atmospheric refraction corrections applied.

Diurnal aberration and diurnal parallax corrections are not computed for stars, as these are extremely small.

The zoomed in Star Chart plot has Proper Motion and Precessions corrected applied. These two corrections are the more significant long term corrections and are the only two that can be noticed on the scale of that plot. If you focus in on a nearby star such as Sirius and scan across several 100’s of years, then the effect of Proper Motion can be observed by noting that Sirius will move off the constellation lines which are only corrected for Precession effects.

For a more insight into the vales of the stellar corrections, go to the main menu and click on “View->Proper Motion, Aberration and Parallax Plots for a Selected Star”.

 

Obliquity, Nutation, Precession and Stellar Corrections Plots.

 Select either View->Stellar Corrections or View->Obliquity-Nutation to show these plots.

 

Right Ascension and Parallax

The only location that the stated value of parallax of a star will be equal to the apparent variation in RA over the year, is when that object is on the celestial equator. As the declination of the object increases the variation in RA will be greater than the parallax of the object. This occurs since the RA lines all converge together at the poles. For example, Rigel Centaurus has a parallax of 0.7548 arcsec, but its variation in RA over a 6 month period is 1.5 arcsec.

This phenomenon exists for all the corrections applied, and an extreme examples occurs for Polaris at around the year 2100, when it is closest to the north celestial pole.

 

 

Accuracies and Validation

The computations are validated by comparison to worked examples in Meeus, and comparison to other software such as CalSky, TheSkyX and Occult4. Some minor differences observed can be attributed to using algorithms of different accuracy, differing databases of starting parameters and different definitions. It’s noted that even the different software give different values from each other. Further follow up and understanding on these issues is ongoing.

  1. Earth computations. Good.
  2. Moon. As mentioned in Astronomical Algorithms by Meeus on page 337, the accuracy of the position of the Moon is approximately 10” in longitude and 4” in latitude.
  3. The Sun and Planets. Good. Using VSOP87C.
  4. Stars. When the Proper Motion, Aberration, Precession, Nutation and Parallax corrections are applied, the accuracy of the Right Ascension and Declination should be much better than 1 second of an arc.
  5. Rise, Set and Meridian Transit Times. The meridian transit time should be accurate to within several seconds of time. The Rise and Set times are much less accurate and this is due to the unpredictability of atmospheric refraction near the horizon. As such they should be accurate to within about a minute when at low to moderate values of observer latitude. Accuracy decreases at very high observer latitudes where the sun and moon never rise very high and rise/set at a very low angles relative to the horizon. At these high latitude observer locations, objects spend a longer period of time in the disturbed atmosphere near the horizon while rising/setting, hence the lower accuracy.

The “Sky Map” plots. The stars on these plots have no corrections applied and are shown at J2000 Epoch.

The “Star Chart” plot. This objects on this plot are corrected for Proper Motion and Precession.