under the condition that the two bodies are isolated. This analysis leads to low OMEGA. A more proper treatment of the problem uses a non-linear approximation which works for higher values of delta rho/rho .
For OMEGA = 1 non-linear approximatation recovers delta rho/rho ~ 4.5 for delta v/v = -1 for OMEGA = 1. The previous equation recovers this with delta rho/rho = 3 and that's incorrect. ( delta rho/rho = 4.5 can be derived analytically for the OMEGA = 1 case)
Last time we considered this cartoon:
To recover the observed CBR Dipole Anisotropy requires that there is more than just Virgo which is gravitationally accelerating the Local Group. The nearest other region of mass over density is the Hydra-Centaurus Supercluster. This is shown below:
The spatial distribution of catalog galaxies. The diagonal band containing lots of points is called the Supergalactic Plane and it may be a very large structure.
The simplest approximation to assume that HC is at rest and is perturbing both our motion as well as the entire Local Supercluster.
But, in 1986 it was announced that HC itself was moving. This was the beginning of the quest for the Great Attractor.
Searching for the Great Attractor
Astrophysical Journal Paper
Another indicator that the flow declines to zero at v ~ 6000 km/s (from Giovanelli \etal 1996)
Ultimately the aim is to infer the large scale gravitational field from the large scale density field. This method is known as POTENT and is illustrated below: