Wednesday, November 28, 2012

Measuring the Universe

In a lot of previous posts you have read about redshift and the distance between the Milky Way and other galaxies. In this post, we step back a little bit and explore the size scales in the Universe and how distances can be measured.

First off, let's start in our Solar System, on planet Earth. Assume the size of the Earth is represented by a peppercorn (a size of about 0.08 inch). Using the same size scaling, the Sun can be represented by blowing up a balloon until it is 8 inches in diameter. In reality the Earth's diameter is about 8000 miles wide, the Sun's diameter is 800 thousand miles. This means that in the peppercorn model we assumed a single inch stands for 100 thousand miles. A yard (or 36 inches) then represent 3.6 million miles. If we rank all other planets in the solar system accordingly, Venus, our sister planet, is also a peppercorn. Both Mars and Mercury are smaller than Earth and Venus. They can be represented by the head of a pin (about 0.03 inches wide). For the size of Jupiter, the first gas planet we would encounter when travelling out of the solar system, we can use a walnut (about 0.9 inches wide). Saturn is a little smaller, about the size of an acorn (0.7 inches). Uranus and Neptune are even smaller still, so a peanut for each is adequate (0.3 inches). If you still count Pluto as a planet, than you would want to represent it by another pin head. 

Size comparisons between Solar System planets and other stars. Image source here and here.

So now, that we have established the sizes of the planets using peppercorns and nuts and so on, what about the distance between them? Well, if you take a huge step that is about 1 yard wide, you travel those 3.6 million miles described above. If you take 10 steps away from the Sun, you reached your pinhead Mercury (it's about 36 million miles away from the Sun). After another 9 steps you'll find Venus, one of the peppercorns. Take another 7 steps and you finally reached your Earth peppercorn. So the distance between the Sun and the Earth is 93 million miles (also called 1 Astronomical Unit) means taking 26 steps from the balloon Sun and your Earth peppercorn. From Earth you have to take another 14 steps to reach Mars. From there now, it is a much larger distance to reach Jupiter. You have to walk 95 steps. Remember, each step has to be the size of about 1 yard! In comparison to this distance, look at the size of Jupiter, which we represented by a walnut. From now on you have to take more and more steps between the planets to reach the next one. Saturn takes another 112 steps. From there Uranus is another 249 steps away. And to get to Neptune from Uranus, walk another 281 steps. That is nearly 3 football fields! And if you still care about Pluto, then walk another 242 steps to reach it.

Now you have walked more than 1000 yards, or across about 10 football fields and the planets have merely the size of nuts or smaller! There is a lot of space between them! 

To reach the next star, Proxima Centauri, from the Sun, a travel of 4.21 light years is required (or 1.20 parsecs). A light year is the distance light travels in a year, which is 5,878,625 million miles or 63,241 times the distance between the Earth and the Sun. In the scale we assumed for the solar system above this is about 16443 football fields or the distance between Tucson and Houston. So to reach the next star in that scale you have to travel this distance more than 4 times. You could reach Oslo in Norway from Washington D.C. and that would still be not quite far enough to go.

Our Solar System is located in the Milky Way, our home galaxy. But the Sun is only one star among 100 billion in it. And there are hundreds of billions of galaxies in the Universe. 

The cosmological distance ladder

So how do astronomers measure distances to so many far away objects, may it be other stars or other galaxies? Well, we use what is called the cosmological distance ladder. In order to reach the next step on the ladder you have to be sure about the step you are standing on. The principle of the ladder is based on the fact that each method to measure distances overlaps with another method, so that the next can be calibrated with the previous. 
Measuring distances to other stars via the Parallax and the distance R between the Earth and the Sun.

The distance ladder starts in our Solar System (or even on Earth if you want). In this previous post about the Venus transit we explained how some 100 years ago astronomers measured the distance between the Earth and the Sun and the size of the planets. Nowadays distances in our Solar System can be determined using radar, the same technique with which ships try to find the location of other ships on the ocean. Once we know the distance between the Earth and the Sun, we can determine the distance to other nearby stars using the Parallax method (see figure above). The Parallax method works out to distances of about 100 light years. The Milky Way has a diameter of about 100,000 light years. So with the Parallax we can measure only our more local neighbourhood.

For the next step on the ladder, the so-called Main Sequence Fitting, is used. With this method the distance to star clusters can be determined by exploiting the relation between brightness and colour of the cluster stars, i.e. their position in the Hertzsprung-Russell Diagram. Stars like our Sun line up on the Main Sequence in this diagram and by measuring the properties of stars, their absolute brightness can be estimated and used as distance indicator. Main Sequence Fitting can be applied across the Milky Way.

Beyond the Milky Way out to other close-by galaxies (within 10 million light years) a relation between the period of variability of Cepheid stars and their luminosity serves to measure the distance to these stars. Cepheid stars are so-called standard candles. This means that their brightness is very well known. From the difference between the observed and the known brightness, the distance can then be measured. The calibration for this method can be achieved using stars in the Small Magellanic Cloud for which main sequence fitting is still possible.

Similarly to the Cepheids, certain types of Supernovae, can also be used as standard candles. Supernovae are exploding dying stars and we already told you a lot about them here. For the calibration of this method one looks for a Supernovae in a galaxy for which the distance could be determined with Cepheid stars. Again the comparison between the absolute and the observed brightness of the Supernova allows us to calculate the distance. With Supernovae distances out to about 10 billion light years (or a redshift of about 1) can be measured.

Beyond Supernovae, Hubble's law and redshifts are used for distance measurements. Hubble's law relates the distance of an object to the speed with which it moves away from us due to the expansion of the Universe. In modern astronomy most distances beyond our local galaxy group system are given in terms of redshift. 

Having reached for out in the Universe at the end of this blog post, we have long outgrown the simple scaling that we used at the beginning to describe the distances and sizes of planets in the Solar System. And even my astronomer mind is regularly boggled by the truly astronomical scales I am confronted with every day.

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