Seeing is Believing !

How to show that Copernicus was right - 2004 Exercise

Mogens Winther

Level : From primary school K6 up to K12 .

Objectives : To show how a simple laboratory experiment in possible combination with easy observations, will repeat Galileos first 1610 proof that our Sun, and not the Earth, is placed in center of our planetary system.

Background: The students need to know:

Mathematical content of the first part : 1 full circle is equal to 360 Degrees, students should be able to draw angles of e.g. 50 Degrees.

If you do choose to enter the second extended part of this exercise, knowledge of trigonometry (tangent) is needed.

Materials needed : Pocket calculator, candlelight - table tennis balls- if you have an astronomical telescope, that will be fine - but neither a telescope nor other expensive equipment is needed.

Introduction:

This occasion may allow our students to estimate the distance towards the Sun and planet Venus.

In order to do so, we however first have to investigate the orbit of our neighbour planet Venus.

This chapter will give a description how this investigation can be done - by means of simple math and easy methods.

Originally, this idea goes back to Galileo 1610 - the method below was the first scientific proof that the Sun, and not the planet Earth - was center of our solar system.

What is Venus ?

Venus is a well known planet, similar to our Earth. It's slightly closer to the Sun then we are. Around 1900, several researchers including the famous Swedish Arrhenius even believed this planet could support life. Simple calculations showed that a planet like our own would only have a slightly higher temperature, around 35 C, if placed that close to the Sun. Arrhenius imagined the planet atmosphere having a composition similar to our planet during the Carbon period, where primitive life was believed to flourish all over.

However, in the 1970's, Russian spaceprobes showed that our sister planet has extreme, killing temperatures, hot lava flows (NASA - Magellan Radar Image - notice the structure moving left to right), conditions 500 C above what was expected. These high temperatures are the result of a powerful greenhouse effect. Venus has a thick cloud cover with an atmosphere more than 100 times as massive as ours. This thick acidraining atmosphere acts as a huge quilt, reflecting practically all infrared heat back to the surface of Venus.

Looking at Venus with an ordinary astronomical telescope, you will observe how the surface is totally covered by these thick clouds.

However, one interesting detail will appear. You may see there is both a sunlit part and a dark shadow part. Astronomers say, this planet shows "phases". The same word is often applied in relation to our Moon. If the Moon is full, the phase is 100%, if the Moon is half, it's phase is 50%. Similar to the Moon, the phases of Venus change all the time, depending on where the planet is placed. These phases have played a most important role in astronomy history.

Is the Sun or the Earth placed in the centre of our Solar System ?

Unfortunately, the Catholic Church later supported this idea. The Earth with all its wonders of Nature was created by God, and thus should be placed in the centre.

However, in 1543 the Polish monk Nicholas Copernicus published a book, suggesting the Catholic Church was wrong. Not the Earth, but the Sun had to be placed in the centre.

The Catholic Church reacted furiously and placed the book at the Index Librorum Prohibitorum, the list of forbidden books. Here the work of Copernicus stayed until 1835... (source - Patrick Moore, "Atlas of the Universe",1976).

Which world system was the correct one, first had to be proven. One of the very first proofs came due to the Italian scientist Galileo Galilei. He had constructed a telescope and was the first person to point such an instrument to the night sky. An early, cold December morning in 1610, Galileo had observed the phases of Venus, and the first real proof that Copernicus was right appeared.

The Catholic Church reacted on this and other discoveries by taking Galileo to court on June 21, 1633, were he was "vehemently suspected of heresy." Eventually Pope Urban VIII allowed Galileo to return to his home in Florence, where he remained under strict house arrest until his death in 1642. Fortunately he was able to collect his thoughts and write them down in those last years.

Galileo's support for the Copernicus' theory had nearly implied his sentence to death by fire. A similar dreadful fate had previously been provided to another Copernican supporter, Bruno Giordani.

Recently, in 1979 and in 1983, Pope John Paul II officially excused these acts by the earlier Catholic Church.

Student Exercise - measuring the Distance

Try this yourself: - Find a good telescope, an astronomical telescope with 25-50 times enlargement is well suited for this task. When Earth is very close to Venus, an ordinary home-binocular will even be sufficient.
The picture below gives an indication of the phases you may observe.

Click to see a most detailed image - taken at the TGS observatory.

Please notice, the nearly "half-moon" like phase at the end of March 2004.

- Ask your students to bring a piece of paper and a pencil. Before the observations start, they have to draw a nice circle on their paper.

- Now, observe the phases of Venus. One student from each group has to make a detailed drawing. Tell them they have to watch the planet at least for half a minute, in order to enjoy the short moments of calm, steady air.

- Then, let them draw the phases in detail. Let the different groups compare their results, in order to see who is most accurate.

Finding the Distance of Venus.

In the following, we take an example based on the computer drawing above of Mar 31 2004.

Now comes the trick. The Earth, the Sun and our sister planet Venus together join in a gigantic triangle.

We call the corresponding angles for Earth, Sun and Venus: "E", "S", and "V".

The angle E is very easy to estimate. The method below is not 100% accurate, but there is no need to introduce high math on these simple measurements.

We all know our planet Earth performs one rotation (360 degrees) in 24 hours.

This corresponds to 15 degrees per hour. Let your students check this themselves.

On Mar 31 2004 - the Sun will be placed directly South at 12h 04m.

The time difference : 14h 59m - 12h 04m corresponds to 2 hour 55 minutes = 2 + (55/60) hour = 2,92 hour.

Exercise - show the latter result is correct. (1 hour = 60 min)

As you know - our planet Earth rotates 360 degrees in 24 hours - corresponding to 15 degrees per hour.

Please show - the time difference of 2.92 hour corresponds to an angle of approximately E = 44 degrees.

(If you have a measuring device like the sextant, this angle E may be measured directly in a more precise way, but do not forget the solar filter.)

Now we are very close to the solution. Go into your laboratory, and place a torch light, slide projector, or similar powerful light source on the floor. We will now try to make a scaled down version of our solar system:

- Take a piece of chalk, and draw a line, 1 meter long, going from the light source to where you stand.

Astronomers define this distance betweek Sun and Earth as "1 Astronomical Unit" = 1 AU.

Modern measurements have shown that this distance is equal to 149.6 million km.

- You now only have to draw the angle E, in our case above: 44 degrees.

- Extend the left leg of this 44 degree angle, so it runs out in the laboratory for say 2 meters.

- Find a circular object (Galileo took an apple, but an orange is even better). Place it along this angle-leg. Let the light from the our light source fall on the orange. Now observe how the phases vary according to increasing distance.

- Vary the distance, until the phases correspond to our Mar 13 2004 image. Now you have a correct model of the solar system. Your students may directly measure the Earth-Venus distance, and the Sun-Venus distance.

- Calculate the angle E for the date of your observations, or for the drawing Feb 09 2004 or drawing apr 09, 2004.

Detailed data may be found below - you should make a plot of these values versus time - in order to estimate the data needed on your day of observation

In the laboratory : - Again, move the orange until its shadows are comparable with the December drawing of Venus.

Now measure the Sun-Venus distance, and the Earth-Venus distance.

Please observe; the Earth-Venus distance has increased dramatically, but the Sun-Venus distance has remained constant.

If Venus keeps a constant distance to the sun, it has to perform a circular orbit. This means, Copernicus, Bruno Giordani, and Galileo were correct and Ptolemy and the Catholic Church were wrong.

As you may see, these observational arguments are simple, and they convinced Galileo that Copernicus was right. Even though Galileo was forced to deny all his results, his daring work opened the Age of Enlightenment, and actually changed the world.

Detailed Venus Data -

---

Concerning angular size - 1 arcsecond = 1/3600 degree

Click to compare with the official orbit values

Additional work - second Part - requires trigonometry (tangent).

Above you may find the angular diameter of Venus. Calculate the planet diameter applying the formula ;

Physical diameter = 2 x Distance x Tangent ( ½ angular diameter).

Please derive this formula.

Please compare the physical diameter to our Earth's diameter, and the diameter of Mars. Why is Venus often called a "sister-planet"?

Note to the teacher.

As one may imagine, Galileo did not KNOW that 1 AU is equal to 149,6 mio Km.
Actually - finding the exact value for 1 AU was a big astronomical problem, which astronomers tried to solve during a Venus transit, observed during one of the adventurous voyages by Captain Cook.

More details in dr. David Sterns homepages. However - in our case - the basic mathematical principle still work - on a relative scale.

The method above might be refined in several ways. A lot of more mathematics might be introduced, including sine relation, great-circle distances, etc...

However, these simple hands on arguments and student performed drawings/discussions actually give equally as good results as many much more complicated derivations.

Suggested software - this JAVA Applet on Venus, written by Juergen Giesen

Galileo Virtual Museum

Suggested readings, J. M. Rogers, "Physics for the Inquiring Mind", p. 248, Princeton 1960.

Have a nice Hunt ! M. W.

Mogens Winther teaches in the Amtgymnasiet, Grundtvigsalle 86, 6400 Sonderborg (Denmark).

Here is a more advanced Astronomy On Line 1996 Student project based on the same ideas - Measuring the distance and size of Saturn - written as a general ready-to-use science exercise.

Teachers notice - the data above were calculated for 0 Deg Longitude (Greenwich) - and subsequently differ from location to location - however the difference does not matter. Local data may be found in most sky simulations software.

Suggestions for improvement : We have estimated E applying a method based on the Earth rotation. Our simple calculations strictly assume that both our Sun and Venus have astronomical declination equal to zero.

This will give a value for E being slightly too high - again giving a Sun-Venus distance a bit too high too. So far, students results however fit within 10% from the official values.

Applying high level math - or sky simulation software - a more correct value for E may be estimated.

However, this first order method still works reasonably well.
Please send your results, drawings etc. to the EAAE network .

2D EAAE transit method.

Official Venus Transit Page

Mogens Winther

Amtsgymnasiet in Sonderborg, Denmark.