# Computational method and precision

This page give some information about the computation method used by Cartes du Ciel - Skychart and the precision you can expect for the displayed values.

You must be careful this description is valid with the standard configuration setting of the program, using the default catalog data. You have many option available to alter the results, principally in the Chart,Coordinate setting page. Use this settings only if you really know what you do!

## Stellar equatorial positions

The basic precision depend on the star catalog used, for the precision of the position but also for the proper motion. The default catalog is the Extended Hipparcos Compilation (XHIP, V/137). The advantage of this catalog is the availability of the full space proper motion parameters for almost every stars.

After it get the catalog data the program compute the position corrected for the star proper motion at the current chart date using the pmRA and pmDEC values, and full space motion if the parallax and radial velocity are available (u_projection.pas, ProperMotion). This give the equatorial astrometric J2000 position.

Then the precession is computed for the chart date using the method given by J. Vondrak, N. Capitaine, P. Wallace in ”New precession expressions, valid for long time intervals A&A 2011” (u_projection.pas, PrecessionV). This give the equatorial mean of date position.

To find the apparent position we compute the nutation using the value given by the JPL ephemeris, then the annual aberration and the light deflection by the Sun (u_projection.pas, apparent_equatorialV). This give equatorial apparent position.

For the current epoch the precision is expected to be better than 0.1 arcsec.
The precision of the proper motion calculation over a long time period depend of the availability of the parallax and the radial velocity, but also of the standard error on the values. An error of about 1 arcsecond by millennium is to be expect.
The precession computation is valid for a +/- 200'000 years period. The precision is better than one milli arcsec at the current epoch, it reach a few arcseconds throughout the historical period, and a few tenths of a degree at the end of the period.

## DSO equatorial positions

The main problem about the position of deep sky objects is the difficulty to precisely define the center of the object. Because of this difficulty the position differ when using different source catalog. Also many historical catalog still in use give the position with one arcminute precision only.

After it get the catalog data the program compute the precession and the apparent position as describe above for the stars.

## Planets equatorial positions

The position of the planets are computed using the JPL ephemeris or if no file are found for the current date, the library plan404 by Steve Moshier that allows for computation from -3000 to +3000 with a precision better than one arc second.
By default an extract of DE405 valid between 2000 and 2050 is supplied with the program. So the first thing to do if you want long term high precision planet position is to install a full DExxx file.
DE431 is recommended if you can afford the 2.5GB download. With this file you can compute precise planet position and nutation between -13000 and +17000.

The computation function return the J2000 planet position corrected for light time, so the program use the same function as for the stars to compute the precession for the current date. This is the geocentric mean of date position.

Then we correct the position for the parallax for the observer location on Earth (u_projection.pas, Paralaxe). This give the topocentric mean of date position.

Then the apparent position is computed by applying the nutation and annual aberration (not for the Moon). This is the topocentric apparent position.

For the current epoch the precision is expected to be better than 0.1 arcsec.
For a date far in the past or the future the major source of error is the uncertainty in the difference between the universal time and the terrestrial time deltaT. You can see and change the value of deltaT in the Time setting window.
The precision of the computation itself depend on the individual ephemeris, but it is always far better than every expectation for a terrestrial observer. Refer to the JPL documentation.
The error on precession is the same as discussed for the stars.

## Comets and asteroids equatorial positions

Comets and asteroids computation are based on elements in MPCORB format. You need to download the required elements first.
The elements are then loaded in a database that allow for many set valid at different epoch. The program always use the element set the nearest to the current date.
For the asteroids it also compute a monthly value of the magnitude that is used to exclude the objects that are currently way to faint to be visible. This help to speed up the other computation.
When the current day change, the program compute a position for each object. This position is then used to know if a precise position need to be computed for the current chart FOV. The NEO are exclude from this process because the position change too rapidly. All of this processing is require to avoid to compute too much position every time the chart is refreshed.

After the elements for an object are selected, the program compute the heliocentric rectangular coordinates and then the J2000 geocentric position corrected for light time.

Then precession, parallax and apparent position is computed the same as for the planets.

When using current element data the precision is expected to be about 0.1 arcsec.
You can reliably compute the asteroids and comets position only for a few month around the date of the elements. So it make no sens to compute this position for a date far in the past or future.

## Alt/Az positions

This is how the program convert the apparent equatorial position of any object to the azimuth/altitude at a given location.

We first get the geometric azimuth/altitude by a rotation of the coordinate system using the equatorial coordinates, the sidereal time and the observer latitude.
If you give the current Earth pole coordinates in the Observatory settings the position is corrected for this small offset.

Then the position is corrected for the diurnal aberration and refraction.

The refraction is computed using two different method, one for the display on the map, the other to display a more precise value in the detailed information window.
The first method need to be fully reversible without too much computation. It is currently based on Bennett formula.
The second is based on the method in SLALIB (REFCO,REFZ,REFRO) and take account for more atmospheric parameters. To fully benefit of this increased precision you need to carefully indicate the atmospheric pressure, the temperature, the relative humidity and if possible the tropospheric rate (from a nearby sounding or a meteorological model). The wavelength used for the computation is 550nm.

If all the observatory parameters are given with the maximum precision, the precision of the azimuth and the geometric altitude must be better than 0.5 arcsec. The precision on the refracted altitude depend on the difference between the model and the real atmosphere.
But remember that 0.1 arcsec represent 3 meters on the soil and a star on the celestial equator move by this distance in 0.007 second. You need to set your observatory location and measure the time with this precision if you want it make some sens.