First of all, remind yourself of the basic relationship between velocity, distance and time:
If we know the distance between M100 and the Milky Way, and their relative velocity, we can calculate how long it took them to travel their distance of separation.
In other words,
so the age of the universe is
That seems simple enough. There's only one little hitch... We used units of (km/sec/Mpc) for Ho in the previous section. Inverting these gives units of (sec Mpc / km) for the age of the universe. How long is a (sec Mpc / km)?!! We'll have to use some conversion factors to transform these units into a comprehensible age.
Using the relationships
1 sec Mpc (3.09 x 1019 km) (1 year) Age of universe = ---- ------- ----------------- ---------------- Ho km 1 Mpc (3.15 x 107 sec)Note that the units of sec, Mpc and km all cancel, leaving an age in years.
Calculate the age of the universe, using the numerical value for Ho from Section III. Enter your result in Section IV, Part A of your lab sheet:
Age of universe = ________________ years. (Constant expansion.)
Does your answer seem reasonable? How does this compare to the presumed ages of the oldest globular clusters? Write your answer on your lab sheet in the space provided.
The rate at which the expansion has slowed over time depends on the average density of the universe. The higher the density, the greater the deceleration. If the density is lower than some critical value we call c, the universe will continue to expand forever. It will get cold and dark. If the density is higher than c the gravitational attraction will eventually halt the expansion, then begin a contraction toward what has been dubbed the "Big Crunch." If is just equal to c the expansion will slow to a stop, but only after an infinite amount of time has passed.
Cosmologists often speak in terms of the density parameter o, defined as
Calculating the density of the universe is no simple task. The universe contains perhaps ten times more matter than the luminous matter we can directly detect. We know the "dark matter" is there because we can see its gravitational effects. Most cosmologists believe that baryons ("normal matter") comprise at most 10% of all matter (i.e. b 0.1). The other 90% is thought to be composed of "exotic" particles we cannot easily detect.
The age of the universe you calculated above corresponds to the case when o = 0. Suppose the average density of the universe is equal to the critical density, so that o = 1. In that case, it can be shown that the age of the universe is given by
2 Age of universe = ----. (o = 1) 3 HoMultiply your previous result for the age of the universe by 2/3 to calculate the revised age of the universe for the case when o = 1. Write your answer on your lab sheet in Part IV, Section B:
Age of universe = ________________ years. (o = 1)How does this compare to the presumed ages of the oldest globular clusters? What can you infer about the actual value of o by comparing the two ages you have calculated? How does your evaluation of o compare to what you learned in class? Write your answers on your lab sheet in the spaces provided.
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