The Density Parameter

In previous posts, I've discussed the density of the universe in terms of all the matter and energy the universe contains. I've also mentioned how the universe has a critical density, i.e. the matter and energy density required to make the universe flat (expanding forever while reaching a finite distance asymptotically.


Let's remember what we mean by open, closed, and flat universes.

• An open universe is a universe that has a smaller density than the critical density. An open universe will expand forever and never reach a finite size.
• A closed universe is a universe with a larger density than the critical density. A closed universe will reach a maximum size then gravity will take over and cause the universe to collapse.
• A flat universe is a universe with a density equal to the critical density.

What we can measure is something called the density parameter, Ω. It is the ratio between the actual density of the universe and the critical density. If Ω is less than one, we live in an open universe. If it is greater than one, our universe is closed. What is the value of Ω?


We know right now that Ω is close to one. We know this from all the observations and measurements we make. The amazing thing is the majority of the mass and energy in the universe can only be inferred by the measurements. Only 4% of the mass and energy is found in stars, gas, and dust that can be directly observed. Dark matter takes up 22% of the mass and energy. And the dark energy is a whopping 74% of the overall density of the universe.


We know that Ω is close to one because of the measurements we make. We also know that the density has to be close to the critical density because if it wasn't, we wouldn't be here.


If Ω was 0.95, the expansion would have been too much for gravity to counteract, gas clouds would not have collapsed, stars and galaxies wouldn't have formed, planets would not have condensed out of the stellar clouds, and life would never have a chance to even exist.


If Ω was 1.05, gravity would have overwhelmed expansion before it even had a chance to start. Without enough time for gas clouds to collapse, again, no stars, galaxies, planet, and yes, life could have formed.


We still don't know if we are in an open, a closed, or a flat universe. Right now, all evidence points to an open universe (with Ω slightly less than 1), but that is what is awesome about science. The search for knowledge means we could learn new things and change our perception of the universe.

Your Nighttime Sky

Say you want to go out into your backyard and look at the night sky. How do you know what you will be able to see when you look up? It all depends on two things: your location on Earth and the time of year.


First, let's define the position of celestial objects in the sky. Anything that is not a solar system body has a position determined by its location on the celestial sphere. They are the right ascension and the declination.

• Right Ascension (RA) is similar to longitudes on Earth, but are measure in hours from 0 to 24. 0h RA is defined as the line that contains the vernal equinox and RA increases as you go east along the celestial equator
• Declination (Dec) is similar to latitudes on Earth and are measured in the same way. 0° Dec is at the celestial equator and increases as you go north or south along a RA to 90°. In astronomy, +90° is the north celestial pole and -90° is the south celestial pole.

Your zenith is the point directly above your head on the celestial sphere. The zenith will always depend on your location on Earth. So a zenith for someone in Pittsburgh will be different from someone in Kuala Lumpur. The declination of your zenith will always be the same as your latitude. If you draw a semicircle north-south that includes your zenith, you get an imaginary arcs that can be used to define a local coordinate plane.

• The north-south line is called your local meridian. Any object that lies on your meridian will have the same RA at that time. However, at different times, due to the rotation of the Earth, the meridian's RA will change. What we use is something called the hour angle to describe an objects position in the sky relative to meridian's RA. The hour angle is defined as how far east or west of the meridian an object is in the sky. It's the local sidereal time minus the right ascension of the object you are observing. If the hour angle is negative, the object is to the east of the meridian. If the hour angle is positive, it is to the west.

Your latitude is also important. By definition, if any object is more than 90° from your zenith, it should be visible, assuming no obstructions lie on the horizon. For example, Pittsburgh is at 40°N. By definition any object that is north of -50° declination should appear in the sky sometime during the year. (In reality, because the horizon is obscured in most locations, the declination is closer to -40° for objects to appear.) There is also a unique feature of any objects that are within 40° of the north celestial pole. These objects are called circumpolar because they never rise nor set in the sky (you can't see them during the day, but if you took a time lapsed image of stars that are circumpolar, they would make an arc around the north celestial pole).

Another way you can describe an object's position in your local sky, is by using the altitude and azimuth of the object. The altitude is just how far above the horizon an object is and is measured in degrees (the altitude of the zenith is 90°). The azimuth is how far east or west of due north or due south an object is (also measured in degrees). Most astronomers use the angle from due north so an object can have an azimuth of greater than 90°. There is a caveat to using altitude and azimuth, however. These are only good for your location. If you are trying to coordinate with another observer elsewhere, you should always use an object's RA and Declination.