Milky Way Galaxy Solar motion calculations from space motionsastronomy

For nearby well-observed stars, it is possible to determine complete space motions and to use these for calculating the solar motion. One must have six quantities: α (the right ascension of the star); δ (the declination of the star); μ_α (the proper motion in right ascension); μ_δ (the proper motion in declination); ρ (the radial velocity as reduced to the Sun); and r (the distance of the star). To find the solar motion, one calculates the velocity components of each star of the sample and the averages of all of these.

Solar motion solutions give values for the Sun’s motion in terms of velocity components, which are normally reduced to a single velocity and a direction. The direction in which the Sun is apparently moving with respect to the reference frame is called the apex of solar motion. In addition, the calculation of the solar motion provides dispersion in velocity. Such dispersions are as intrinsically interesting as the solar motions themselves because a dispersion is an indication of the integrity of the selection of stars used as a reference frame and of its uniformity of kinematic properties. It is found, for example, that dispersions are very small for certain kinds of stars (e.g., A-type stars, all of which apparently have nearly similar, almost circular orbits in the Galaxy) and are very large for some other kinds of objects (e.g., the RR Lyrae variables, which show a dispersion of almost 100 km/sec due to the wide variation in the shapes and orientations of orbits for these stars).