6.2 The effect of the motion of the Earth
6.2.1 The need for a reference frame for describing the Universe
The speed of the Earth in its orbit round the Sun is 29.8 km s−1, in a heliocentric frame. But to specify the velocity vector, it is not sufficient to specify the Sun as the origin of the coordinate system; fixed directions must also be identified.
Here are two possible rules for fixing an x1-direction:
(i) The x1-axis is taken as the line from the Sun to the nearest star (Proxima Centauri);
(ii) The x1-axis is taken as pointing in the direction from the centre of the Galaxy to the nearest large galaxy (the Andromeda galaxy).
Are these two methods equally acceptable? If not, which is preferable, and is it completely satisfactory?
Proxima Centauri is the nearest star, and so is undoubtedly in our Galaxy. Our Galaxy is rotating, as is suggested independently of all frames of reference by its disc-like shape. So the line to Proxima Centauri is not a good x1-axis, because of the relative motion of the Sun and Proxima Centauri within the Galaxy.
The Andromeda galaxy is the nearest galaxy to ours (apart from satellite galaxies and the Magellanic Clouds). It is gravitationally bound to our Galaxy and moving relative to us. The period of the mutual ‘orbit’ of our Galaxy and the Andromeda galaxy is certainly longer than the period of the Sun (or Proxima Centauri) round our Galaxy, because the distance from our Galaxy to the Andromeda galaxy is about a hundred times bigger than the distance of the Sun (or Proxima Centauri) from the centre of our Galaxy. Nevertheless, the line connecting our Galaxy to the Andromeda galaxy cannot be taken as fixed because of their motions within the Local Group.
Thus methods (i) and (ii) are not equally acceptable; (ii) is preferable to (i), but is still not fully satisfactory.
The considerations of Question 13 force one to look at bigger and bigger aggregates of matter in the search for reference bodies with respect to which a system of coordinates can be defined independently of the motion caused by the gravitational effects of nearby matter in our local region of the Universe. We assume that the clusters of galaxies fulfil this role. But clusters may be loosely associated (though not bound) in superclusters.
For this reason, we would like to have an alternative way of establishing a reference frame. The 3 K radiation provides such a means.
If the 3 K radiation filled the Universe at early times and has not interacted appreciably with matter since decoupling, then this radiation defines a system in which matter and energy in the early Universe are assumed to have been distributed homogeneously. So if we were to find that the 3 K radiation is completely isotropic when observed on Earth, we could conclude that we are at rest with respect to the average distribution of matter and energy in the Universe. In that sense, the radiation can be said to define a ‘rest frame’ of the Universe. But if we find that the radiation is not isotropic, and moreover, that it varies in a characteristically systematic fashion according to direction, then we can conclude that we are moving in a particular direction with respect to the frame in which the radiation is isotropic.
It is a matter of great interest to know the velocities of the Earth, the Sun, our Galaxy and our Local Group with respect to the system defined by the 3 K radiation. It might, for example, provide support for the idea that gravitational effects within a supercluster must be taken into account in mapping out the Universe.