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We live in the Laniakea supercluster. Galaxies including the Milky Way are being pulled toward the "Great Attractor" in its center.

Two questions (note that the answer to one can be used to derive the answer to the other):

  1. How fast are we moving toward the Great Attractor?
  2. What is the escape velocity of the Laniakea supercluster? That is, assume it is the only supercluster in the universe.

As in this question I understand that the answer depends on uncertain data. A reasonable guess is perfectly fine for me.

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Finding the escape velocity seems simpler than to find the $\Delta v$, for the reason that our movement relative to the centre of the cluster is in best case close to pure guesswork.

A starting point is to use the estimated distance ($250×10^6$ ly) and the estimated mass ($10^{17}$ M☉), and plug that into the escape velocity equation:

$$v_e=\sqrt{\frac{2\mu}{r}}$$

That gives $3.35×10^6$ m/s.

Of course, the shell theorem does not exactly fit, as the shape of the structure is highly irregular, and the fact that we are actually inside the cluster, so you can perhaps assume that the actual escape velocity is a little bit lower.

Back to velocity estimation, we can use the stated Hubble constant. At $h^{−1}_{0.6780 ± 0.077}$ for 159 Mpc, we can calculate a relative velocity of $1.08×10^5$ m/s, a much smaller number than the escape velocity.

In conclusion, the escape velocity and $\Delta v$ are both around $0.01 c$.

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