# If a galaxy forms from a spherical stationary cloud, how much of the gas will escape?

Let's ignore the dark matter legend and stay with Keplerian physics.

Assuming that there is a cloud with $$N$$ stationary particles with the same size uniformly distributed in a sphere and they condense to form a galaxy.

$$N>>10^{\text{many}}$$

Some particles come to the center. Some will escape. Is there any estimation that how much percentage of particles remain in the galaxy and how much will escape to the infinite space?

So the fraction remaining is $$2/N$$. This assumes random motions, which is fairly plausible.
The time to evaporation is on the order of $$t_{evap}\approx \frac{14 N}{\log(N)}t_{crossing}$$ where $$t_{crossing}$$ is the typical time to cross the cloud of particles, $$\langle r\rangle /\langle v\rangle$$.