On the motions of the Sun, the Galaxy and the Andromeda nebula

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Abstract
The sum of the velocity of the Galaxy, G, and the velocity of the Sun may be determined from their reflection in the radial velocities of the members of the Local Group of galaxies excluding Andromeda. Since Andromeda and the Galaxy are much more massive than all other members combined their momenta must be equal and opposite. Thus the observed velocity of Andromeda is a reflection of the already determined sum, plus the mass ratio times a reflection of the Galaxy's velocity. The knowledge of the observed radial velocity of Andromeda and the mass ratio allows us to determine both the velocity of the Galaxy and the circular velocity of its rotation at the Sun, Vc. The method gives Vc = 294 ± 42 km/s G = (−34, +7, −16) ± 23 km/s where G is with respect to the centre of mass of the Local Group. Uncertainty in the mass ratio gives little change and may be removed by using Tully & Fishers' observed law |$M\propto(V_\text {max})^{5/2}$|⁠. The uncertainties in the above determination of Vc may be considerably lowered if we make the further assumptions: (1) The Galaxy does not have an exceptionally large maximum circular velocity for a spiral. This gives us the limit Vc < 300 km/s. (2) The Galaxy and Andromeda obey the Tully & Fisher relationship and move in a bound ellipse about one another. (3) The mass of Andromeda is < 4 × 1011M⊙. We then obtain |$V_\text c=290^{+10}_{-15}\enspace \text {km/s}$|⁠. The new values are discussed in terms of known Galactic parameters and other determinations. Finally we draw conclusions concerning the binding of the Local Group, and the epoch of galaxy formation.

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