# Gravitationally bound and Hubble time

• BearY
In summary, by estimating the time it would take for a galaxy in the Coma cluster to travel from one side to the other using its radial velocity dispersion, it can be concluded that the time is approximately 0.4 times the Hubble time. This suggests that the galaxies in the Coma cluster are gravitationally bound, as the timescale is much smaller than the Hubble time. This can also be confirmed by using the virial theorem and estimating the mass enclosed in the cluster. Therefore, it can be inferred that the motion of a galaxy in a gravitationally bound system is much smaller than the Hubble time.
BearY

## Homework Statement

Estimate how long a galaxy in the Coma cluster would take to travel from one side of the cluster to the other. Assume that the galaxy moves with a constant speed equal to the cluster’s radial velocity dispersion. How does this compare with the Hubble time, t H ? What can you conclude about whether the galaxies in the Coma cluster are gravitationally bound?

Carroll, Bradley W.; Ostlie, Dale A.. Introduction to Modern Astrophysics, An: Pearson New International Edition (Page 1184)

## The Attempt at a Solution

The first 2 questions are simple, with values(from some very not reliable encyclopedia)
diameter is 6 mpc
hubble time = 13.8 billion years
I reached a conclusion of the time needed is about 0.4 Hubble time.

But I have no clue how does it imply anything about gravitational bound.

How does the motion of a galaxy look like if the timescale is much smaller than the Hubble time?
How does it look like if it is much larger?
In which case do you get something that looks as expected for a gravitationally bound object?

mfb said:
How does the motion of a galaxy look like if the timescale is much smaller than the Hubble time?
How does it look like if it is much larger?
In which case do you get something that looks as expected for a gravitationally bound object?
If the radial dispersion velocity is too large then the system is probably no gravitational bounded, because then the kinetic energy of most of the galaxies in the cluster would be enough to escape?
If it is very slow too slow I can't think of anything else except that it can be bounded?
Yesterday I had an idea about if it has anything to do with the virial theorem. We can assume the cluster is bounded and estimate the mass enclosed using Faber–Jackson relation, then with mass enclosed we can estimate the average Ek and average Ep, and see if it violate the virial theorem by too much?
But to be honest I don't know how does it relate to Hubble time and still pretty clueless in general.

Now you are overthinking this. The timescale you found is all you need.

As an example, for Earth the timescale is 1 year. It has been done billions of orbits. It is clearly gravitationally bound.
If you take two galaxy clusters far away you get a timescale of hundreds of billions of years: They cannot orbit each other. There was not even enough time in the universe for that.

## What is the concept of gravitationally bound?

Gravitationally bound refers to the state in which objects are held together by the force of gravity. This can occur on various scales, from the planets in our solar system to entire galaxies.

## How does gravitationally bound relate to the formation of celestial bodies?

In the early universe, the force of gravity caused matter to clump together, forming clumps that eventually grew into galaxies, stars, and planets. Without the force of gravity, these objects would not have formed and the universe as we know it would not exist.

## What is the Hubble time and how is it calculated?

The Hubble time is the estimated age of the universe based on the current expansion rate and the assumption that the expansion has been constant throughout time. It is calculated by dividing the speed of light by the Hubble constant, which is a measure of the rate of expansion of the universe.

## Why is the Hubble time important in understanding the evolution of the universe?

The Hubble time gives us a framework for understanding the age of the universe and the rate at which it has been expanding. This information is crucial in studying the evolution of the universe, as well as the fate of the universe in the future.

## How does the concept of gravitationally bound relate to the Hubble time?

The concept of gravitationally bound objects is closely tied to the Hubble time, as the force of gravity is what holds these objects together. The Hubble time also gives us insight into how long these objects have been bound together and how long they will continue to be bound in the future.

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