The order and regularity of the planetary motions provided the key to the structure of the Solar System and the discovery of the law of gravitational attraction. Likewise, the study of galactic dynamics has been, and is, essential to a determination of the structure of the Galaxy. Careful observations of stellar radial velocities (motion of the star along our line of sight) and proper motions (motion across the celestial sphere), revealed a certain amount of orderliness. These velocities are due to the simultaneous effect of two causes. Firstly, since no star is attached to the others, every one has a certain RANDOM VELOCITY with respect to the LOCAL STANDARD OF REST (that is the centre of mass of the Sun and its nearest neighbours). Secondly, all stars move in their orbits around the galactic centre. The random velocity of the Sun causes the proper motion vectors of the other stars to point systematically away from a certain point in the sky (the apex) towards a point diametrically opposite (the antapex): the apparent trajectories seem to be radiating from a point in the direction of motion of the observer (the same effect that causes the ‘radiant’ of a meteor swarm). The orbital motions of the neighbours are best understood by making the simplification that all the mass within the solar orbit is concentrated in the galactic centre and that all stars have the same orbital energy. Then, classical mechanics tells us that all orbits have the same length of semi-major axis, and the magnitudes of all orbital velocities near the Sun are the same.

The solar apex lies at right ascension 18h and declination 30°, towards which point the Sun moves with a velocity of 20kms~1 with respect to the local standard of rest. The two streams, caused by the presence of non-circular orbits, appear in the motion of the HIGH-VELOCITY STARS, that is, those stars which have velocities in excess of 63kms-1. These stars all belong to the galactic halo; it follows, then, from these dynamical data, that the younger Population I stars move in the plane in approximately circular orbits around the galactic centre, whereas the older Population II stars follow non-circular orbits in the halo.

Once these large-scale motions have been determined, astronomers can study the more subtle dynamical effects. The object of this effort is to determine the distribution of the mass in the Galaxy, and to find the total mass of the Galaxy. Clearly, such knowledge is of enormous importance for the understanding of the structure, and ultimately the history, of our Milky Way system.

The most obvious difference between galactic and planetary motion is that the latter is almost entirely governed by the central gravitational attraction of the Sun, whereas the Galaxy is held together by the gravitational attraction of its widely-distributed stars, gas and other constituents. This difference is reflected in the way in which the systems rotate. In the Solar System, rotation is described by Kepler’s third law. In the Galaxy, as we shall see, the situation is vastly more complicated. Consider firstly the motion of the Sun in its galactic orbit: it is in equilibrium between its centrifugal acceleration and the attraction of all the mass in the Galaxy enclosed by the solar orbit . A star with a galactic orbit greater than that of the Sun will experience the attraction of a greater mans, because the larger orbit encompass more matter . Conversely, a star within the solar orbit is effectively attracted by a smaller mass. This effect of the variation of attractive force with position in the Galaxy causes the galactic law of rotation to differ markedly From Kepler’s third law . This difference shows up in the motion of the stare.

Stellar orbits are not restricted to a plane: the path which a typical halo star traces is rather reminiscent of a three-dimensional known as a LISSAJOUS PATTERN . Even if a star moves exactly in the galactic plane its path is not an ellipse, but is a ROSETTE ORBIT as in . It has been already mentioned that the distance between stars is very large, and that interstellar matter is extremely tenuous. Therefore, a star can move on an orbit as in without noticeable hindrance from stellar collision or slowing down by friction with the gas or dust. Hence the mass distribution as it is observed today is essentially the same as it was when the Galaxy formed-. The presence of a halo therefore indicates that the protogalaxy (the gaseous cloud from which the Galaxy formed by gravitational contraction in the early phases of the Universe) was originally roughly spherical. The presence of a disc shows that somehow the matter which did not turn into stars early on, has collapsed to a very flattened sub-system. Subsequently, later generations of stars have formed, and are still doing so, from the gas in the disc. This course of events is also indicated by the fact that halo stars are poor in heavy elements compared with disc stars. Nuclear fusion processes associated with stars constantly increase the amount of heavy elements in the inter¬stellar medium, because some stars disintegrate at the end of their evolution. Hence the halo stars were apparently the first to form, before this nuclear enrichment had really got under way.

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