FIVE/2 Coordinate Systems
OUR PLACE IN THE GALAXY:
Our galaxy is a giant "pinwheel" of stars, with a close-to
spherical core (the "bulge") and a flat disc containing the spiral arms.
This disc is about
It is useful to be able to provide a defined location for star systems in the form of coordinates (X, Y, Z). The coordinates are often based upon Earth's sky, but as Earth's equator isn't the same as the galactic equator the resulting coordinates don't tell how stars are placed relative to the galactic plane and center. Thus, it may be wise to utilise galactic coordinates. The easiest way to generate galactic coordinates is to take the "normal" coordinates based upon right ascension, declination and parallax and convert them.
RIGHT ASCENSION, DECLINATION AND PARALLAX:
These three things (optionally, distance instead of parallax) are necessary to provide coordinates. Right ascension (ra) is the celestial version of longitude, declination (dec) the latitude equivalent and parallax the displacement angle the object shows due to the annual motion of the Earth. Parallax translates into distance as
calculating in radians. Distance is in light years, parallax in milli-arc-seconds (mas). The coordinates of an object, when distance, right ascansion and declination are known, are as follows:
Use trigonometry in radians, distance in light years and dec/ra in decimal degrees.
However, the right ascension and declination of an object is subject to change. One reason is that the object actually moves fast enough to make a difference, but the main reason is that Earth itself undergo changes in orbital elements. The rotational axis slowly undergo precession and thus the pole do not face the exact same spot over time. Thus, the astronomical measurements are accompanied by an "epoch", a sort of time-tag. Some star data you may find (Gliese, for instance) are 1950, while Hipparcos (another big data source) is 1991. Depending on how painstakingly precise you decide to place stars (decimal fractions of light years?) this may be more or less important.
For 1991-data (Hipparcos), you can transform the X, Y and Z coordinates above to galactic coordinates (centered on Earth, but with X-Y-Z axis oriented according to the galaxy) by using
Xg = - (0.0571 x X) - (0.8733 x Y) - (0.4838 x Z)
Stars move relative to each other. Over a short enough time,
say 500 years, this will be of little importance (
To measure distances between star systems is simple.
distance = ( (X1 - X2)2 + (Y1 - Y2)2 + (Z1 - Z2)2)0.5
where the two sets (1 & 2) of coordinates are those of the two involved stars.