TITLE:
The Balloon Model and the Mass of the Universe
AUTHORS:
Masoud Asadi-Zeydabadi, Alberto Sadun, Clyde Zaidins
KEYWORDS:
Balloon Model, Red Shift, Doppler Effect, Hubble Distance, Mass of Universe
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.4,
April
27,
2026
ABSTRACT: A good example of the use of a model to describe a complex entity is the Balloon Model of the Universe. This model has long been a valuable teaching tool for explaining the observed expansion of the cosmos. By adding quantitative values to the model, we have been able to consider the red shift,
z
, that would be observed for a distant galaxy using two different techniques. The first way is by using the Doppler effect, which results in the Hubble distance/velocity relation. The second is the red shift predicted by Einstein’s Theory of General Relativity. As the light travels from the past to the present it is also climbing from a lower gravitational potential to a higher one, i.e. going “uphill”. The resulting values for
z
must be equal. However, there is an unknown value of the mass,
M
, needed to calculate the gravitational potentials.
M
becomes a free parameter that we can determine and although it is dependent on this simple model, it turns out to be quite reasonable.