Hubbles law can be stated in vector form as . Outside the

Chapter 46, Problem 57

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Hubbles law can be stated in vector form as . Outside the local group of galaxies, all objects are moving away from us with velocities proportional to their positions relative to us. In this form, it sounds as if our location in the Universe is specially privileged. Prove that Hubbles law is equally true for an observer elsewhere in the Universe. Proceed as follows. Assume we are at the origin of coordinates, one galaxy cluster is at location and has velocity relative to us, and another galaxy cluster has position vector and velocity Suppose the speeds are nonrelativistic. Consider the frame of reference of an observer in the first of these galaxy clusters. (a) Show that our velocity relative to her, together with the posi tion vector of our galaxy cluster from hers, satisfies Hubbles law. (b) Show that the position and velocity of cluster 2 relative to cluster 1 satisfy Hubbles law.

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