# What can be measured in kilometers

### Cosmic distances

(Student internship project by Björn-Eric Reitz from 2007)

Space is full of great distances as well as small ones. But especially the big ones hold secrets that we would love to elicit from him. The dimensions are so huge that you even had to determine your own units so that the numbers don't get too big. Much is so far away that one can only guess. Just imagine that Voyager 1 which was launched in 1977, and is much faster than any car, has only recently reached the edge of the solar system. But between the solar system and the nearest star there will be a much longer journey that would last for many millennia. But the distances pose another danger. Since radio signals propagate at a finite speed, a signal arrives much later than it was sent over greater distances. For example, the signals to the Voyager spacecraft take more than 14 hours. The light from the stars also takes time to reach us. So the image of a star that is 2.4 billion light years away is also 2.4 billion years old !!!

#### Units of distance in the universe

There are different units to measure the large as well as the small distances that occur in our galaxy.

• The meter Although it is the most common unit for measuring everyday distances, it is much too small for the unimaginably large distances in our universe. For measuring small objects, the parts of a meter, such as the nanometer, are best.
• Even with multiples of a meter, for example the kilometer, you are quickly confronted with huge numbers.
• The unit Light yearwhich is not a unit of time, is better suited for measuring large distances. You don't get huge numbers all too quickly. One light year is about 9.5 trillion !! Kilometre.
• The Parsec is the more popular unit for measuring long distances among astronomers. One parsec is roughly 3.3 light years.
• Furthermore, one often uses the Exponential representation, because it allows the numbers to be shortened and determined more quickly.

#### A journey through the dimensions

Template: Ten High by Philip and Phylis Morrison

We begin our journey through the various size dimensions in the middle of Microcosm and Macrocosm: In humans.

We first move away into the world of the microcosm:

• With our first step we are about 10 centimeters. This world is nothing special to us as we encounter it often in our everyday life. It is the dimension of, for example, a flower or a hand and much more.
• Even if we go one step further and have reached one centimeter, we can still see this world with the naked eye.
• After the next step, and about one millimeter away, we can no longer see anything with our naked eye. Now only one thing can help us microscope further.
• At about 0.1 millimeter, an unknown world opens up to us. We see hair as thick as trees and the rough surface of the skin.
• Inside a blood vessel, red blood cells become visible when you get closer to about 10 micrometers. After that, our normal microscope slowly gives up and we can only see the world with the help of one Scanning electron microscope consider.
• One step further, with a micrometer, we are already in the dimension of an individual Cell nucleus penetrated.
• At around 0.1 micron (or 1000 Ångström) we are in the proportion of several Strands of DNA.
• With the next step at about a nanometer, we see a single strand of DNA. You can see the individual Molecules recognize what DNA is made of.
• At about 0.1 angstroms, or 10 picometers, we are inside one Atom penetrated.
• When you get to a picometer, you can already see the atomic nucleus in the "distance".
• After the next steps, at 10 Fermi, you get so close to the atomic nucleus that it fills the entire field of vision.
• In the vicinity of about a Fermi one can even look at the internal structure of a neutron and determine that it is made up of other Elementary particles, the quarks exist. Which goes even deeper into the Quarks one can only guess.

Our journey into the microcosm ends here.

But what is possible in the direction of the microcosm is also possible in the direction of the macrocosm.

• If we slowly zoom out, again starting from the human being, we can still reach familiar dimensions at a height of 100 meters, for example from a football stadium.
• At one kilometer we are the size of a small village.
• At a distance of 100 kilometers we reach the order of magnitude of the catchment area of ​​a large metropolis such as New York.
• After a further step at 1000 kilometers, there is not much to see of the metropolis. You are above the cloud cover so that you can still grasp the dimension.
• The earth fills the field of vision when you zoom out to 10,000 kilometers from the people in New York.
• If we take a step back and have reached 100,000 kilometers, the earth will slowly get smaller.
• At 1 million kilometers we see the earth and theirs Satellites: the moon.
Enlarge image
(Source: NASA Astronomy Picture of the Day)
(Source: NASA Astronomy Picture of the Day)
• After another 9 million kilometers, we can no longer see the earth. However, if you imagine a part of the earth's orbit, it is just as big that the earth can traverse it in just under 4 days.
• If we go to 1 billion kilometers or about 7 Astronomical units we see all inner planets and the orbit of Jupiter fills the edge of our field of vision.
• At 10 billion kilometers we can already see the orbits of all planets.
• During the next steps the sun and our system get smaller and smaller. From 10 light years or about 3 parsecs we can no longer distinguish the sun from the other stars. It disappears in a tangle of bright spots.
• At a distance of about 1000 light years, the cloud of stars becomes more and more dense.
• From 10,000 light years onwards, one can clearly see the star clusters that form the pattern of the galaxy arms.
• At a distance of about 100,000 light years, the Milky Way can be viewed in its full size. You can see that she rotates clockwise around a point in the middle so that her arms spiral.
Enlarge image
(Source: ESO press release 14/98)
(Source: ESO press release 14/98)
• If you take a step further and have reached 1 million light years, you can see both of our Milky Way, which has now become smaller, as well Magellanic clouds see.
• After moving a few steps away, and at about 100 million light years, you can see a large collection of galaxies Virgo cluster.
• At a distance of 1 billion light years, the Virgo cluster also becomes increasingly smaller. You can see other galaxies that are many millions or even billions of light years away from us.

It is difficult to imagine that in these vast expanses of many light years no life has yet been found or perhaps does not even exist. The answer will be a long time coming, as the distances are far too great for today's telescopes.

The offers a journey through cosmic dimensions, during which one can zoom through from the direct surroundings of our sun with the closest neighboring stars to the "edge" of the universe Atlas of the Universe by Richard Powell.

#### Distance examples in the universe

Now that many have said about distances, here are some examples from our solar system and the rest of the universe:

• As already mentioned, the distance between the earth and the moon is approximately 1.3 light seconds, which is approximately 390,000 kilometers.
• The distance between earth and sun is approx. 8.3 light minutes, that is around 150,000,000 km.
• It takes about 5.7 hours for light to reach the dwarf planet Pluto. That's about 6 billion kilometers.
• The entire solar system has a diameter of approx. 150 hours of light, which corresponds to approx. 160,000,000,000 kilometers.
• Alpha Centauri, the star closest to our Sun, is a full 4.2 light years away. This means that at the current speed (1.6 million km per day), it still took Voyager 1 approximately 70,000 years to reach this star.
• The diameter of our entire galaxy, the Milky Way, is about 100,000 light years. Even if we could fly at close to the speed of light, a single human would never be able to cover this distance. At the Effelsberg radio telescope become the dimensions of the Milky Way through one Milky Way Path clarifies, on which one on a scale of 1 to 1017 (100 quadrillion) objects of the Milky Way can "wander" over 40,000 light years over a distance of 4 km (from the outside area past the sun to the galactic center).
• The next galaxy, the Andromeda Nebula, is an unimaginable 2.5 million light years away from us.
• The Virgo cluster has a diameter of almost 10 million light years and is about 60 million light years away.
• The diameter of the universe is estimated to be a few billion light years (age of the universe approx. 14 billion years.)

#### Measurement method

There are many different methods that can be used to measure distances in our universe.

Optical interferometry

Optical interferometry is best for measuring short lengths, ranging from kilometers to a few attometers (10-18 m) !! pass.

There are two different procedures:

1) phase shift method
Be there coherent Waves that are thrown back by an object, shifted at least twice by a known value, spatially or temporally, while the intensity is measured at one point. You can then use a suitable formula to determine the difference and thus the distance.

2) white light interferometry
Here is the interference exploited broadband light. Since broadband light has a short coherence length, interference phenomena are only visible if the two path lengths in the arms of the interferometer are the same apart from the coherence length. The Coherence length in white light is equal to the wavelength. The fact that interference only occurs when the object and reference arm are aligned is used to measure the distance with appropriate devices.

The runtime measurement

The transit time measurement is used for distances from 0.01 meters up to billions of kilometers. When measuring the transit time, electromagnetic or acoustic waves are directed at a target object. You then measure the time it takes for the signal to be reflected and to get back to the starting point. Since you know how fast the waves are moving, you can use a suitable formula to calculate the distance. It can be used, for example, to determine the distance from the moon.

The formula is:

The triangulation

Triangulation is the oldest measuring method and was already used by the ancient Greeks for land surveying.

The principle is quite simple: if you want to measure a point P at some distance, you aim at this point P from 2 points (station 1 and 2). Measure the angles at these two points. If you now calculate the angle difference, you can use the angle sets to calculate the missing lengths, in this case the distance. This method requires only simple mathematical knowledge and can thus be used for lengths of a few micrometers up to distances of a few hundred light years in our Milky Way (parallax).

The parallax

The principle of parallax is the same as with triangulation, only that here the diameter of the earth's orbit is used as the basis. This allows you to calculate much greater distances. But since the distances are so gigantic, the angle difference is extremely small (less than one Arcsecond!!!), so the measurements must be very accurate. Measurements with the satellite HIPPARCOS are again by a factor of 4 more accurate than measurements from the ground.

Distance measurement with the help of Cepheids

Cepheids are a class of variable stars in which the luminosity changes periodically. With the help of Period-luminosity relationship one can deduce the absolute brightness. The ratio of distance and luminosity obtained in this way is then used, as in the case of supernovae 1a, to determine the distance of other objects, for example a galaxy, in the vicinity of the Cepheid.

Distance measurement using type 1a supernovae

Since the radiation of a type 1a supernova is fed by radioactive decay, from nickel to cobalt and finally to iron, the shape is the Light curve always the same. They are observed in distant galaxies and the supernovae are used as Standard candlesto pinpoint distant galaxies in the universe with relative accuracy. You know which ones absolute brightness the supernova must have and can derive the distance by comparing it with the measured brightness.

The redshift

Our universe is expanding. As a result, like a yeast dough with raisins, the galaxies move away from each other. Because of this, the light waves that are emitted by the stars or galaxies are pulled apart and the light spectrum is shifted into the red. The redshift of a distant star or an entire galaxy is greater the further away the object is. Since different distance determinations can now be used for many galaxies (supernovae type 1a or Cepheids), the respective redshift can be ascribed to a certain distance. The conversion factor is saved as Hubble constant designated.

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Wikipedia
"Physics" by Karl Kolde
"Powers of Ten"(German book title:" Ten High ") by: Philip and Phylis Morrison and the studio of Charles and Ray Eames
"The construction of the universe" by: Peter von der Osten-Sacken
"The Milky Way" by: Nigel Henbest and Heather Couper

(Created by Björn-Eric Reitz, Rheingymnasium Sinzig, under the supervision of Dr. Norbert Junkes)

ur 4/2013