Galaxies form by the gravitational collapse of regions that are denser than average. Noting that the present-day average mass density of the universe is ρ = 3 × 10-30 g/cm-3, estimate how long it takes for a galaxy to collapse. Hint: You only need to
General relativity says that the total orbital energy of a binary system consisting of
two neutron stars will decrease over time through the emission of gravitational waves.
If this happens slowly enough that the orbit stays circular, answer the following (and explain your answers)
(a) Will the distance between the two stars increase, decrease, or stay the same?
(b) Will the kinetic energy of the two stars increase, decrease, or stay the same?
(c) Will the gravitational potential energy increase, decrease, or stay the same?assume a density for the region before collapse, although your estimate will be uncertain by a factor of order unity. Does your answer make sense compared to the age of the universe? If there is a conflict, what assumptions could you improve in order to reconcile it?