2.5.2 Milky Way Galaxy
The nearest stars to the Sun are those of the Alpha Centuri trio, at a distance of about 1.2 parsecs. Next is Barnard's Star at 1.8 parsecs. The nearest twenty stars are all within 3.6 parsecs of the Sun. Assuming that the mass of these stars is comparable to that of the sun, their gravitational zones are not encompassed by that of the Sun, hence they are not in orbit around it.
The gravitational situation in the Milky Way Galaxy is difficult to estimate since the center of the Galaxy is obscured, but appears to consist of a very massive object surrounded by many stars clustered in a bar shape. This central mass is estimated to be about \(4\ 10^6\) times greater than the Sun. A mass of this magnitude would have a gravitational boundary at a radius from the Galactic center of about 14,500 parsecs. This is consistent with the steep fall-off in star density at a radius of 12,000 parsecs, and the estimate of about 30,000 parsecs for the diameter of the whole galaxy.
The nearest galaxy to the Milky Way is Andromeda, which is approximately the same size as Milky Way. The distance between the two is about 750,000 parsecs. This is well beyond the radius of either galaxy and hence they do not attract each other.
The attenuation of gravity by Hubble expansion means that the gravitational force exerted by the galactic center on the stars in the outer arms falls off more rapidly than an inverse square law. Hence their own gravitational limits are not encompassed by that of the galactic center, and they do not take up Newtonian orbits. Furthermore, the gravitational attraction between stars in the outer arms is stronger than that of the central mass, so that their motion is governed as much by star-to-star gravitational linkages as by attraction towards the center.
While gravitational limits explain why the stars in the spiral arms do not orbit in the conventional Newtonian manner, it does not explain the shape of the spiral arms nor the velocities of individual stars within them. Though the velocities of stars within a particular arm are too high for Newtonian orbits, neither are they compatible with an assumption that the whole spiral arm moves as one rigid structure.
A plausible theory is that the stars in each spiral arm which are closest to the center have Newtonian orbits, and those in the outer arms are 'towed' by the inner ones like barges on a river. It is likely that the shape of the spiral arms change as they rotate, unwinding as time progresses. This explanation is consistent with the shapes of other galaxies, in which the spiral arms show greater or lesser degrees of tightness.
It is unlikely that a single mathematical expression can be found which will explain the motion of stars within a galaxy. The overlap of gravitational zones is considerable and there is no star with sufficient mass to dominate all the others. However, the tendency to form spiral arms suggests that there is some kind of self-organizing process at work.
On the larger scale of the whole universe, gravitational boundaries explain why galaxies have not coalesced into one huge galaxy, and show no signs of doing so. It also justifies the approximation that gravity dominates motion within galaxies, while Hubble expansion dominates expansion of the space between them.
This analysis has shown that gravitational attraction does not extend to infinity, and that there is a definite limit to the attractive forces between masses. The consequences of this limit is that galaxies may be considered to be isolated systems, their relative motion being governed more by Hubble expansion than by gravity. The motion of stars within galaxies is governed more by gravity than by Hubble expansion, however, the attenuation of inverse square law does not allow them them to take up Newtonian orbits. The diameter of the Milky Way galaxy is consistent with this finding.
The theory presented here shows that the limits of gravitational attraction probably eliminate the need for the mysterious substance known as 'cold dark matter', which is supposed to exist in a halo around galaxies to prevent them collapsing under their own gravity.
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