Newtonian cosmology

From Universe in Problems
Revision as of 16:38, 13 October 2012 by Igor (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Problem 1: the first equation

Obtain the first Friedman equation basing only on Newtonian mechanics.


Problem 2: the second equation

Derive the analogue of the second Friedman equation in the Newtonian mechanics.


Problem 3: conservation law

Obtain the conservation equation for non-relativistic matter from the continuity equation for the ideal fluid.


Problem 4: no static Universe in nonrelativistic theory

Show that equations of Newtonian hydrodynamics and gravity prohibit the existence of a uniform, isotropic and static cosmological model, i.e. a Universe constant in time, uniformly filled by ideal fluid.


Problem 5: cosmic energy and the Layzer-Irvine equation

Find the generalization of the Newtonian energy conservation equation to an expanding cosmological background$^*$.

$^*$P.J.E. Peebles, Principles of Physical Cosmology, Princeton University Press, 1993.


Problem 6: the virial theorem

Using the Layzer-Irvene equation, discussed in the previous problem, recover the Newtonian virial theorem.