Summary of Stellar Motions
The stars exhibit a number of motions, over various time scales. The simplest and fastest of these motions is their daily motion to the west, as a result of the Earth's rotation around its axis to the east. This is the only motion that an ordinary observer will notice, during their entire lifetime. But there are other motions, most caused by the rotational and orbital motions of the Earth, and one caused by an actual motion of the stars relative to our solar system, which can be observed with specialized equipment, over a period of time. These other motions are:
(1) Precession -- A gradual drift relative to the Vernal Equinox, parallel to the Ecliptic, caused by the precession of the Earth's axis of rotation. As will be discussed in detail on another page, the Earth's axis gradually swings around the pole of our orbit, once every 26,000 years, as a result of tidal torques exerted on the equatorial bulge of the Earth by the Moon and, to a lesser extent, the Sun. If the Earth were not rotating, the Earth's axis would gradually swing toward the pole of our orbit, so the equatorial bulge ended up in the average orbital plane of the Moon around the Earth, and the Earth around the Sun. But because the Earth is rotating, the axis of rotation of the Earth maintains a nearly constant angle of 23 1/2 degrees relative to the pole of our orbit, but swings westward around the orbital pole at a rate of about 1/70th of a degree per year, or one degree every 70 years. This causes the Celestial Equator and the Vernal Equinox to also move westward, at the same rate. Since the Vernal Equinox is used as the starting point for measurements of the positions of the stars, this causes the celestial longitude of the stars to increase by one degree every 70 years, while keeping their celestial latitudes constant. This phenomenon was first noted by Hipparchus, around 2000 years ago, in comparing what he would have considered "ancient" Greek observations of the stars to his own observations. He found that on the average, the distance north or south of the Ecliptic remained the same from the ancient to what he considered "modern" observations, but the position of the stars relative to the Vernal Equinox had shifted nearly 10 degrees to the east (since the Vernal Equinox had moved nearly 10 degrees to the west, during the time involved). As a result, it was known, even in ancient times, that the stars seemed to have two motions -- the daily motion to the west, parallel to the Celestial Equator, and a twenty-some-thousand year motion to the East, parallel to the Ecliptic. The fact that the stars could have two simultaneous, apparently uniform circular motions at the same time, helped lend credence to the idea that the motions of the other celestial bodies -- the planets -- could consist of a number of uniform circular motions, of which the daily westward motion was only the fastest and simplest. (Note: the motion of the stars to the east relative to the Vernal Equinox, and of the Vernal Equinox to the west relative to the stars, causes the Sun to reach the Vernal Equinox twenty minutes earlier each year than the year before, compared to moving once around the sky. The time required for the Sun to go once around the sky relative to the stars is our orbital period, or sidereal period of revolution. The time required for the Sun to go once around the sky relative to the Vernal Equinox is the year of the seasons, the basis of our year, and is called a tropical year. The term precession of the Equinoxes is applied to the motion of the stars relative to the Vernal Equinox, because the Sun reaches the Equinox each year at a time preceding the time it would have, if the Vernal Equinox had not moved. The difference in time is small -- only the time required for the Sun to make up the 1/70th of a degree that the Vernal Equinox shifted during the year, or about 1/70th of a day, which is about 20 minutes. Thus, the year that we use for our calendar is about 20 minutes shorter than our actual orbital period.)
(1a) Nutation -- If only the Sun were responsible for precession, the swing of our rotational axis around our orbital axis would maintain a constant angle of 23 1/2 degrees. However, the Moon actually produces twice the effect of the Sun, and its orbit is tilted by 5 degrees relative to our orbit. The direction of this tilt gradually changes over an 18 year period, so on the average, the effect of the Moon is in the same direction and plane as that of the Sun; but when the Moon's orbit is tilted one way, our tilt slightly increases, and when the Moon's orbit is tilted the other way (when the direction of the tilt has swung halfway around our orbit to the west), our tilt slightly decreases. This small 'wobble' in the angle of our tilt is referred to as nutation, and produces small changes in the right ascensions and declinations of the stars, in addition to the long-term changes in those coordinates due to the average precession of the Equinoxes. However, this does not affect the motion relative to the Ecliptic, discussed in point (1).
(2) Proper Motion -- As the Sun and stars move around our Galaxy, their positions gradually change, relative to each other. On the average, it takes a thousand or more years for any star to noticeably change its position in this way, and for most of them, the time required is tens of thousands of years (see The Changeable Constellations; so in a human lifetime, the stars appear to remain fixed relative to each other. But careful telescopic observations can reveal motions of the stars against the fixed background of far more distant stars (which being further away, have to move further in order for us to notice their motion) in periods as short as a few decades. There is also a change in the distance of the stars as a result of their changing position relative to us, but we cannot see that as an actual change in their position. Instead, that is measured by looking at their spectra, and measuring their radial velocities.
(3) Stellar Aberration -- As the Earth moves around the Sun, stars which are in the direction we are moving appear to shift their positions relative to us by as much as 20 seconds of arc, so that they appear to be more in front of us than if we were not moving. This effect was discovered by Bradley, and is discussed in more detail in the link at the start of this paragraph.
(4) Parallax -- As the Earth goes around the Sun, someone on a distant star ought to be able to see our motion around the Sun as some kind of ellipse. If viewed from above or below our orbit (that is, from the direction of the north or south Ecliptic poles), our motion would appear to be practically circular. If viewed from the plane of our orbit, we would seem to swing back and forth in a straight line. If viewd from any other angle, we would seem to follow an elliptical path around the Sun. (Note that this is exactly analogous to the creation of different elliptical shapes by rotating a circle, as discussed in Ellipses and Other Conic Sections.) The circular/linear/elliptical path followed by the Earth, as seen from a distant star, would appear to us as a mirror-image of our motion in every way, but as a motion of the star around a circular/linear/elliptical path of the same shape and size (the size being measured by the semi-major axis of the path). The apparent motion of the star caused by our orbital motion is called its parallactic ellipse, and its apparent semi-major axis (usually measured in seconds of arc) is the parallax of the star. If a star were about two hundred thousand AUs away, its parallactic ellipse would be one second of arc. As a result, that distance is referred to as one parsec, and is used as a yardstick for distance measurements, whether accomplished through parallax observations, or some other method. As it happens, very few stars are close enough to have measurable parallaxes. Less than a thousand stars can have their parallaxes measured with any accuracy from the surface of the Earth. And even with telescopes in space, which are spared the effects of our atmosphere, less than one star in a million can have its parallax measured, even in our own galaxy.
As noted at the start, this page is mostly a placeholder. More detailed discussions can be found at the pages linked from the above summaries, and as time permits, additional pages will be added, to discuss all the topics on this page in more detail. When that happens, the discussion here will actually be simplified, as it will merely serve as an introduction to the other pages (e.g., as shown above for Proper Motion and Stellar Aberration).