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Transit of Venus

with a Do-It-Yourself Telescope

Dennis Engel

 

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There will be a transit of the planet Venus across the face of the sun on Tuesday, 8 June 2004. Viewed from Durban it will begin at 07:17 and end at 13:28, which means that the full six hours of the transit will be visible as the sun is already up at 06:47.

Venus is the brilliant evening "star" that has been visible in the west after sunset for several months and has been moving lower and closer to the sun over the last few weeks.

A Venus transit is very rare - the last one was in 1882 - and so the small amount of initiative needed to get to view this daytime astronomical occurrence will be well worth it.

What is a transit

The planet Venus is closer to the sun than the earth is. This means that at certain times, Venus will be exactly on an imaginary line between the sun and the earth. At such a time Venus will be seen to "transit" as a small disc travelling across the face of the sun, about 1/30 of the diameter of the sun.

Transits and occultations

A transit happens when there is an alignment of three astronomical bodies, the viewing body being the earth. Transit implies that the body in front appears smaller than the body behind and covers only a part of it. Other examples of transits in the solar system are transits of the four biggest moons of Jupiter across the face of that planet. They are happening all the time only days apart.

An occultation is an alignment of three bodies where the body in front appears larger than the one behind and completely covers it. The moon is continually occulting stars and planets on its passage through the heavens each month. Less often the planets and even asteroids occult stars. A total solar eclipse is another example of an occultation.

Frequency of transits

As Venus is closer to the sun than the earth it travels round the sun in a shorter time. It actually travels at a greater speed and has a shorter distance to go. It takes about 19 months to catch up with the slower-moving earth and so transits could occur every 19 months. However, the orbit of Venus is slightly tilted (about 3º) relative to the earth's orbit round the sun. This means that most times when Venus catches up with the earth, the two planets are not closely enough in line for a transit to occur, and so transits occur much less often. Calculations show that Venus transits come in pairs 8 years apart, but more than 100 years elapse from one pair to the next. The last transit was in 1882. The next transit will be in 8 year's time, but will unfortunately not be visible from southern Africa. And the next after that is again more than a century away.

The other planet that is closer to the sun and can therefore transit the sun is Mercury. These transits occur much more frequently than those of Venus, about 13 in a century as opposed to about 2 per century for Venus. There was a transit of Mercury on 7 May 2003. (This transit was seen by 800 learners at five schools in Durban, with the help of members of the local branch of the Astronomical Society of SA.) The next one will be in 2006. However, during a transit of Mercury that planet appears five times smaller than Venus, and so the phenomenon is not as clearly visible.

All in all, Venus transits are rare, and the more frequent Mercury transits are less impressive. The June 8 Venus transit is at a convenient time of day, especially for schools, and there is the whole morning to fit in a time slot. So this transit is definitely the one to go for!

Viewing methods

Looking directly at the sun will very quickly damage the eyes. So attempting to view the transit is dangerous and great care must be taken. The following options are available.

Eclipse glasses
Many people will have eclipse glasses left over from viewing a partial eclipse of the sun from Durban, or a total eclipse from Musina or Lusaka. Viewing the sun through these glasses is safe but it is important to place the glasses over the eyes before turning to look at the sun. The little disc of Venus should be just visible this way.

Optical instruments - binoculars or telescope
The same principles apply for both binoculars and telescope.
There are two methods to use.
1) Filter viewing: The transit can be viewed directly through the instrument if a suitable filter material (the same as in eclipse glasses) is placed in front to reduce the sun's radiation before it enters the instrument. The filter must be very firmly stuck onto the instrument (both lenses in the case of binoculars). If the filter were to come off, the amount of direct sunlight and heat entering the eye would be enormous and blindness could occur immediately. Also, if inappropriate filter material is used this can damage the eye. (A spare pair of eclipse glasses would be a source of suitable filter material, but the filter must be well mounted and firmly stuck to the binoculars. The material would have to be mounted on a piece of cardboard big enough to cover the whole of each objective lens with no gaps to let direct sunlight through.)
2) Projection viewing: The light coming through the instrument can be projected onto a screen. When using this method no filter is needed. A problem here is that the eyepiece of the instrument can become very hot as the sun's rays are concentrated towards it. This can damage expensive equipment. In the case of the telescope one option is to replace the eyepiece with a cheap lens mounted temporarily.
The instrument needs to be firmly supported. A telescope comes with its own support. Binoculars would have to be clamped onto some kind of stand. The instrument needs to be defocused a little from the normal adjustment in order to focus an image of the sun on the screen. One can experiment with screen distances and defocusing to give a sharp image of a suitable size. The light that has passed through the instrument can be reflected onto a screen off to one side using a mirror placed at an angle of about 45º. This avoids having to shield the screen from sunlight passing along the side of the instrument.

Making your own telescope

A very accessible solution is to make your own telescope and use the method of projection onto a screen. This avoids the dangers of damage to your expensive binoculars or telescope, or to your priceless eyes. It could be a good project for school classes.

The principle of a telescope
A telescope consists of two lenses. The first, the objective, forms a small image of the sun, and the second, the eyepiece, acts as a magnifying glass with which the observer views this image. The larger the focal length (f1) of the objective the larger the image, the smaller the focal length (f2) of the eyepiece, the greater is its magnification. So the total magnification of the instrument is m = f1/f2. This formula is correct for direct viewing through the instrument. When using the method of projection onto a screen, a further factor influencing the size of the projected image is the distance to the screen. This leads to a different formula (formula 7 in the appendix), but the principle still holds that for a large final image the focal length of the objective should be large. The formulae for the projection method are explained in more detail in the appendix.

 

Recipe for a sun telescope

Apparatus:
two lenses, objective - 50 cm focal length, eyepiece - 20 cm. (other values also OK)
small piece of mirror glass
strip of wood 1 m long
Assorted materials

Construction
1.Construct some sort of holders for the two lenses and for the mirror. The mirror needs to be supported at an angle of about 45º in order to reflect the light sideways.
2.Attach the three items to the strip of wood in such a way that they can be moved along the strip - for example using clothes pegs.
3.Set the two lenses to be a distance apart that is a little bigger than the sum of the focal lengths. For the values given, 71 cm would be suitable. Set the 45º mirror to be a short distance behind the eyepiece.

 

(click on the image for a larger version)

4.Set up this telescope in line with the Sun's rays. It is sufficient simply to rest the front upper end on some adjustable support like a retort stand, and to stop the bottom end from slipping using a science textbook. Adjust the alignment so that you can see the light from the objective falling onto the centre of the eyepiece. Little specks of dust on the eyepiece should make the light area visible. Look for the image of the Sun out to the side using a sheet of paper stuck onto some supporting stand. Adjust the angle of the mirror to move the image around. Adjust the position of the eyepiece and the distance of the screen to focus the image and change its size.

Some comments
1.Make the telescope well before 8 June in order to test it and fine-tune it.
2.The mirror should be small enough so that stray light that goes past the lens and its housing is not reflected onto the screen.
3.Try out different lens combinations. A longer focal length objective gives a larger final image. A shorter focal length eyepiece gives a larger final image at the same screen distance. (Two lenses mounted together make an eyepiece with a shorter focal length.) A larger screen distance gives a larger image. But a wide range of focal lengths should all work reasonably well.
4.With simple lenses the edge of the Sun will not be completely sharp and will show some colours. This is because the different colours (wavelengths) that make up the white Sunlight are focussed (refracted) differently by the lenses. (This effect can only be avoided by using expensive compound lenses which could be damaged by the Sun's heat.) During the transit the little disc of Venus should still be visible even with these simple lenses. However, the disc will not be completely dark but coloured like the edge of the Sun.
5.Put the telescope and the screen on tables so that the image is at a convenient height for viewing. The telescope table needs to be stable to avoid vibration of the image. Put the screen on a separate table so that you can experiment with long distances of a few metres.
6.Shield the screen from the general daylight as far as possible. The screen material could be stuck inside a deep open box for example.
7.Try out different screen materials. Ordinary typing paper lets some light through and so the surface has a slightly mottled grey-white appearance which can be disturbing. Try thicker card or some other white material.
8.The telescope and screen need to be moved continually as the Sun travels across the sky. Check a few days before the transit that the support you have designed and the location you have chosen are convenient for viewing the moving Sun during the full time of the transit from about 07:30 to 13:30.
9.The distance from the eyepiece to the focussed image on the screen is the distance from the eyepiece to the mirror plus the distance from the mirror to the screen.

 

Appendix -  Optical formulae for the projection method

For a single lens:

Distance formula:
     1/f = 1/u + 1/v     (Eq.1)
f  - focal length of the lens, u - object distance (from the lens), v - image distance.

Magnification rule:
     angular size of image = angular size of object      (Eq.2)
Call this angular size (angle) alpha.

Diameter of image:
     d(image) = v tan(alpha)     (Eq.3)
(Equivalent formula for the object: d(object) = u tan(alpha) )

Magnification formula:
     m = v/u.  (Eq.4)
This means that the further away the image is formed, the bigger it is. (Formula 4 comes directly from 2 and 3.) These formulae need to be applied to the objective and the eyepiece in turn.

Application to the objective

As the object, the Sun, is at a very large distance (u approx. infinity), the distance formula becomes:
     v_1 = f_1.
i.e. the image is at the focal point, a distance f_1 from the lens [the notation "_1" should be read as "subscript 1" and is used for the objective lens].
The angular size of the Sun is known to be a = 0.5º (approximately). The diameter of the image formed by the objective is therefore:
     d1 = v_1 tan(0.5º) = 0.009 f_1    (Eq.5)
This image now becomes the object that is magnified by the eyepiece.

Application to the eyepiece

Formula 1 can be modified to be written:
     (m =) v/u = f/(u-f)
For the eyepiece
     (m_2 =) v_2 / u_2 = f_2 / (u_2 - f_2)     (Eq.6)
(u_2 is the distance that the eyepiece is placed away from the image formed by the objective, and v_2 is the distance from the eyepiece to the screen.) This magnification of the eyepiece is applied to the image formed by the objective.

The diameter of the final image projected onto the screen is therefore:
     d = d_1 . m_2 = 0.009 f_1 . f_2 / (u_2 - f_2)     (Eq.7)
We see that in order to produce a large image on the screen, 1) the focal length of the objective should be large and 2) the eyepiece should be positioned so as to make u_2 only a little larger than f_2.

Some suitable numbers for lenses available in school laboratories are:
f_1 = 50 cm
This gives
d_1 = 0.009 . f_1 = 0.009 . 50 cm = 0.45 cm = 4.5 mm
f_2 = 20 cm
u_2 = 21 cm
u_2 - f_2 = 21 cm - 20 cm = 1 cm
m_2 = f_2 / (u_2 - f_2) = 20 cm/1 cm = 20
d = d_1 . m_2 = 4.5 mm . 20 = 90 mm = 9 cm.

 

 

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(c) ASSA 2003, 2004  • updated 2004 september 20