# Practical Exercise 7: BALLOON MODEL OF EXPANDING UNIVERSE

Expanding Universe is hard to imagine. We will try limit ourselves to its basic features. The expansion effect applies only in the big distances and among the objects whose mutual gravitational interaction can be ignored, typically among the galaxies in the distances of tens million ly or more. On the contrary, within the Solar System, Milky Way or the Local Group of Galaxies, this effect is not observed and needs not to be taken into account. The decisive role is played by the gravity (e.g. M31 Galaxy from our Local Group is not moving away from the Milky Way, on the contrary, it will collide with it in approximately one billion of years).

Fig. 8: Model of expanding Universe (source: NASA,
(zdroj: NASA, https://map.gsfc.nasa.gov/universe/bb_tests_exp.html)

## Objective of Practical Exercise:

The objective of this activity and the activity sheet is to visualize the mutual distancing of galaxies. The situation can be compared to the raisins in the dough (see Fig.8). A rubber inflatable balloon, used in this activity, is an easily available tool, but whilst our Universe is three-dimensional, the balloon surface has only two dimensions. As we can see in the model, from the point of view of balloon surface, there is no need to consider any centre of expansion. This expansion centre is not situated up on the surface (we would search for it „inside“ the balloon, but there is no „inside“ in the Universe, as it would not be visible for an ant on the balloon surface). In place of marks, drawn by a felt-pen or a marker, we can use tiny stickers (e.g. price labels or Christmas stickers with stars; then we should point out that the expansion concerns the distances among galaxies, not among the stars within the galaxy). Determination of distances in three successive steps should show that the further away are the galaxies (marks on the balloon) from our Galaxy, the more the distance after each blowing up increases (and thus the speed of recession).

If we would like to go deeper in the topic, we could determine the distance relative to a mark different from G, the found relation – more remote marks are moving farther and faster away from the observed mark – would be confirmed as well. In this sense, our Galaxy is no „centre of the Universe“, the expansion looks the same from any other galaxy.

For more curious students we can add quite simple Hubble's law for the speed of recession of galaxies

where d stands for the galaxy distance and H is so-called Hubble parameter whose value changes in time. The actual value is labelled as Hubble constant H0 and its value is about 70 (km/s)/Mpc. We can see the typical units – velocity in km/s and distance in Mpc within the unit of the constant. The speed of recession can be determined from the electromagnetic spectrum. Since not the intrinsic movement of galaxies in the space is concerned, but the expansion of the space itself, the speed can even exceed the speed of light (for the very remote galaxies). Right by the means of recession speed and Hubble constant we are able to estimate the greatest distances in the Universe when no other method is available.