Rupert Genseberger

"EAAE Summerschools" Working Group

OSB-Amsterdam, Utrecht University (The Netherlands)

#### Abstract

An intriguing question for a lot of people is how it is possible that astronomers can know the unimaginable distances in the universe. Gaining that knowledge about distances in space was a step by step process, starting nearby and moving further out. In fact it was hard and long work, based on methods that were sometimes ingenious, sometimes simple.

In this workshop the participants will get an insight in how it is possible to determine successively the distances from earth to moon, sun, planets, stars and galaxies. They will work on some of those steps themselves, using simple but historical methods and data gained by observation. A method will also be proposed to make those distances more imaginable.

The materials and teaching methods that are used in the workshop are also applicable for students of about 15 years and older. In fact they are used in a course on astronomy that has been designed by the leader of the workshop as part of a new curriculum in General Science in Holland.

#### Determining distances in the universe

In this workshop we learn and practise determining distances in the universe without leaving the earth. In the first part we stay in our solar system, using mostly methods that were invented in ancient Greece. In the second part we show how distances are determined outside our solar system, from the most nearby stars until the farthest galaxies.

The determining of distances is a gradual process: the next step always builds upon the step before. You are guided along those steps, beginning at the circumference of the earth until the borders of the universe. Calculation is essential to get insight in this topic: it belongs to the method. We don't use complicated calculations, in fact everything is very simple, but we should be aware that knowing distances in universe means always a combination of measurement and cleverly designed calculation.

#### Far: our solar system

The steps we use to determine distances in our solar system are the following:

1. Circumference of the earth

We determine this according to the famous method invented by Erathostenes of Cyrene (275-194 B.C). If there is sunshine during the workshop we may measure a part by ourselves.

2. Diameter of the moon

If we know the circumference of the earth, we may determine the diameter of the moon when there is an eclipse of the moon. In the workshop we use photographs of a lunar eclipse.

3. Distance earth - moon

If we know the diameter of the moon, we may measure and calculate the distance of the moon on a full moon night in a very simple way.

4. Distance earth - sun

We make a rough estimate of the distance earth - sun by first estimating the proportion distance earth - moon and distance earth - sun. We use a method invented by Aristarchos from Samos (310-250 B.C.) This is in fact the most inaccurate step in the chain, but useful to show that, in principle, it is possible to determine the distance earth - sun.

5. Diameter sun

We use for this the diameter of the moon and the distances earth - moon and earth - sun and a simple calculation.

6. Distance planets

Kepler invented an easy method to determine the distance sun - planets, we need only the distance earth - sun and the time the planets need for one revolution. In the workshop we calculate the minimum and maximum distance of earth - planet.

#### More far, farthest… stars and galaxies

Before you will be able to understand about measuring distances outside our solar system, you have to realize that what looks like very similar stars are in reality very different objects. What seems a star maybe for instance a group of stars or a galaxy.

Until now we have given a description of how to determine the distance to an object in space and how to use a different method for each object. In the next part we will see that there is no uniform way of determining distances to stars or galaxies, it depends again on the distance which method should be used. Therefore here we focus more on the methods.

7. Distance to nearby stars: Parallax method

In 1838 for the first time the distance to a star was determined. It was done by measuring its parallax. The measured angles were very small, because of that it was not possible before, the instruments were not accurate enough. The greater the distance is between the star and the earth, the smaller the angle of the parallax. So when the stars are very far away, also with our most accurate telescopes it's not possible anymore to measure the parallax and calculate distances. Then we need another method.

In this part we learn to use two techniques to measure the parallax: directly by telescope and by photographic method.

8. Distance to distant stars and nearby galaxies: Cepheïd method

It is not possible to determine by way of the parallax method the distance of stars further than 300 light-years. In the beginning of the 20th century Henriette Leavitt discovered how to determine the distance to some of those far-away stars. The method is named after the kind of stars she could use: the Cepheïds. It was not necessary to measure the parallax. This method used the measured light intensities of similar stars. It was known they were similar because they became more and less bright with the same period. To discover the special stars with this properties it was necessary to know the distances of a vast amount of stars by the parallax method.

9. Distance to the farthest galaxies: Hubbles idea

In 1923 Edwin Hubble determined the distance to a nearby galaxy (the Andromeda nebula) by distinguishing some Cepheids in that galaxy and determining their distance, so he knew also the distance to that galaxy. After that he continued to look for galaxies with Cepheids. When he couldn't find some Cepheids in the galaxy, he supposed that galaxy had the same brightness as the other galaxies. If it appeared less bright, surely it was caused by a greater distance. With the help of that he estimated a lot of distances of far-away galaxies, up to 500 million light-years. It became clear that all the stars are clustered in galaxies.

In the workshop we will have the materials to make calculations concerning all those methods.

References

Rupert Genseberger, Robert Wielinga (1996) Ontwikkeling van ideeën over het heelal.

Rosa M.Ros, Eder Viñuales (1999) Aristarchos' Proportions. Proceedings 3rd EAAE International Summer School Barcelona: Universitat Polytècnica de Caraluny.