### Assignments:

Unfinished Assignment Study Questions for Lesson 54

### Lesson Objectives:

- Measuring the distance to galaxies
- Standard candles
- Hubble's Law
- The age of the universe Since the distances between galaxies is so great, there is no one-step method that allows us to calculate distance.

The greater the distance, the more steps we need to use to calculate how far away a galaxy is.

As we have discussed, stellar parallax can be used to measure the distance to nearby stars. Since parallax is the shift in a star's apparent position as Earth orbits the Sun, we first need to know the exact Sun-Earth distance, or Astronomical Unit (AU).

That brings us to the first step in distance measurement -- radar ranging. Radar ranging is where we bounce radio waves off of Venus to find its distance. That distance is then used to calculate the exact distance to the Sun, which can then be used in parallax calculations. Standard Candles are objects whose luminosity we know. For example, a G2 main-sequence star similar to our Sun would be expected to have the same luminosity as the Sun.

If we know a star's luminosity, then we can use that and its apparent brightness in the inverse square law for light formula to calculate its distance.

For measuring distances beyond the Milky Way galaxy, we use extremely luminous stars known as Cepheid variable stars, or Cepheids for short. Cepheids can be used as standard candles because they follow a period-luminosity relation. In other words, when we measure the apparent brightness of cepheids over time, they alternate between getting dimmer and brighter. Measuring the time between the brightness peaks allows us to estimate its luminosity, which can then be used with the inverse square law for light to determine its distance. Using Cepheids as standard candles allow us to measure distances up to 100 million light-years away, but for distances greater than that, astronomers need an even brighter standard candle. The solution is to use white dwarf supernovae. As you have learned, white dwarf stars have a limit of about 1.4 times the mass of the Sun. When they exceed that mass, they explode as a white dwarf supernova.

Since these supernovae all come from stars of similar mass that died in a similar way, they all have essentially the same luminosity. White dwarf supernovae have allowed scientists to calculate distances for galaxies billions of light years away. One of the limitations of using white dwarf supernovae as standard candles is that there are many galaxies in which a white dwarf supernova has not been observed.

That is where Hubble's Law comes in.

Edwin Hubble discovered that galaxies that are farther away are moving away from us at greater speeds, indicating that the universe is expanding.

This concept is expressed as a formula called Hubble's Law: "V" equals H-naught times "D". "V" is the galaxy's recession speed, or the speed it is moving away from us. "D" is the galaxy's distance, and H-naught is a number called Hubble's constant.

A galaxy's recession speed is estimated by analyzing its spectrum. The more red-shifted a galaxy's spectrum is, the faster it is moving. H-naught, or Hubble's Constant, is estimated by looking at far-away galaxies that have white dwarf supernovae. Since we know their distance and velocity, we can solve for Hubble's Constant and then use that in the Hubble's Law equation when calculating distances to other galaxies. Hubble's Law allows us to do a simple calculation of the age of the universe by taking the inverse of Hubble's Constant. That is because the inverse of Hubble's Constant tells us how long it took the universe to expand to its current size. This calculation results in an age of about 14 billion years.

The limitation with this method is that it depends on a constant rate of expansion. If expansion is slowing down with time, then that means expansion used to be faster and the universe is actually younger than 14 billion years. And on the contrary, if expansion has actually accelerated with time, then the universe is even older than we had thought.

We know that light from a supernova that is 1 billion light-years away happened a billion years ago. Since the universe is expanding, that supernova was a lot closer one billion years ago. That is why astronomers prefer to use lookback time when describing a galaxy's distance. A galaxy that is one-billion light years away actually has a *lookback time* of 1 billion light-years.

The cosmological horizon refers to the limits of our observable universe. Since a lookback time of 14 billion light-years would exceed the age of the universe, our cosmological horizon is 14 billion light years. Light from sources beyond that would not have had time to reach us yet.