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During a Venus transit, the planet Venus passes between the Sun and Earth in such a way that we can see it as a black dot in the sky in front of the solar disc.
The distance to the Sun (called the astronomical unit, AU) or the distance of the planet Earth from the Sun scales the entire solar system using Kepler’s third law.
These two images are based on real photos: André Müller took the transit in Jena in 2004 with the Philips ToYou webcam and calculated this path with Giotto software (artificially supplemented to a full circle). Arndt Latußeck took one thousand three hundred and forty-eight photos with a Canon 600 D in Krasnoyarsk in 2012. I combined these photos with Giotto to create this path (enhanced and colour-corrected with TheGimp).
The contact times are measured, i.e. the time at which the edge of Venus touches the edge of the sun at exactly one point.
The 1st and 4th contacts are naturally extremely difficult to observe. During the first contact in particular, Venus must first be found at the edge of the sun.
However, observing the 2nd and 3rd contacts well is completely sufficient to measure the distance of the sun from the earth and therefore to find the absolute scales in the solar system.
Before the Venus transits of 1761 and 1769 were analysed using this method, the relationship between the distances of the planets was only known from Kepler’s 3rd law. Only relative distances were known and there was no absolute scale.
1716 Philosophical Transactions: Sir Edmond Halley proposes for the first time to use Venus transit observations to determine the distance to the sun. His method is based on observations at locations at different latitudes, so that observers A and B see Venus travelling on a different path across the sun:
These paths are of different lengths (see Fig.), which is why the duration of the transit at locations A and B is compared here. You must therefore measure the time difference between the 2nd and 3rd contact and compare this for the two locations.
DISADVANTAGE of this method: The sun must be visible at second and third contact, i.e. it must be above the horizon and the sky must be clear.
That is why Joseph Delisle came up with a different method half a century later – for the next transit of Venus. He compared two observation sites with different longitudes.
(Of course, all drawings here are not to scale, but exaggerated).
The two observers measure the entry of Venus onto the solar disc at different times. The image above is a snapshot taken at a specific point in time. At this moment, the western observer sees Venus just at the edge of the sun (mentally walk along the ‘visual ray’ to see this), while the eastern observer already sees Venus clearly in front of the solar disc.
Now we ‘only’ need two observations of a Venus transit to apply these methods. The problem is that transits of Venus are rare and the next once occur in more than a century. Therefore, we recorded the last one; so please watch the videos to “observe”/ measure.
Take a look at this film by a Berlin amateur astronomer of the 2004 transit: Observe which optical phenomena will complicate the exact timing of the contacts: The Lomonossov ring outwards, but above all the black-drop effect, i.e. the phenomenon that looks like a dark bridge between the edge of the sun and the edge of Venus. With a smaller or worse telescope, it would still or already look like contact when there is no contact at all.
What effects do you observe? Can you determine contact time yourself here? (if yes, write it down – if no, write down why not)
Now follow our expedition: We have sent three expeditions:
Of course, some people at home in Germany also observed and gave us their data.
Recordings from Krasnoyarsk (10 min):
Here we present our recording from Krasnoyarsk in Siberia. Determine the contact time yourself in the historical way (by listening to the time signal – note: when the seconds are counted, it is 6:04 in the Krasnoyarsk time zone, i.e. UTC+8h. The minutes are announced out loud and the seconds are counted in between):
Making of: during the transit, a photo was taken every 20 seconds. The duration of the transit of approx. 7 hours was condensed here into 10 minutes, so that the image frequency is sufficient to show the human eye a continuous film. Around the time of the contacts – i.e. when a sound is audible here – real film recordings are inserted between the individual images. All recordings (video and photo) were taken with a Canon 600D in Krasnoyarsk (Russia). [Raw material edited with IrfanView and VideoPad from NCHsoft]
Nowadays, we no longer need to measure contact times, but can even read the parallax angle directly from two pairs of images. We can directly compare the positions of Venus with photos of the sun during its transit. Look for two images that were taken at different locations at the same time, e.g. an image from Tromsö and an image from Krasnoyarsk from 6 June at 3:25 CEST.
Then we just have to compare the images. I suggest three methods for this in workshops:
There are two pairs of images to choose from. It is best to carry out the method with both and then calculate the astronomical unit with both. Afterwards you can see which image pair is more suitable.
Sun at 03:25 (PDF)
Sun on 05:01
Now we follow simple geometry to estimate the A.E. The calculation method contains numerous approximations and you have probably noticed that the accuracy often leaves a lot to be desired. For this reason, this estimate is really only for orientation and is nowhere near as accurate as the historical calculation methods according to Halley or Delisle:
First we have to convert our measured pixels or millimetres into an angle. We use the fact that the sun had an apparent diameter of 1891 arc seconds on 6 June 2012. Using a rule of three, you can now convert your measured value into an angle in arc seconds:
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If the parallax (angle) of the triangle on the left is known, the required distance to the sun can be calculated, as the azimuth angles of Venus are the same. Since the distance Sun-Venus is known as 0.72 AU, the length of the other side is also known, namely (1-0.72) AU = 0.28 AU
Now we only need to apply an angle function. We can safely work with the approximation that for small angles the tangent and the sine are equal to the angle itself.
You can determine the distance between the two locations on Earth using Google Earth or luftlinie.org, for example, or you can simply calculate it assuming that the Earth is (approximately) a sphere and has a radius of 6370 km. This distance gives your triangle the absolute scale.
Think about which angle function you want to use and rearrange it according to the cathetus you are looking for so that the AU comes out!
1. Of course, the astronomical unit would be highly variable if it were really only described exactly as the distance to the sun. Since the earth moves in an elliptical orbit, it is sometimes further and sometimes closer to the sun.
Strictly speaking, of course, we use our method here to determine the distance of the Earth to the Sun on a particular day and not the ‘average distance to the Sun’. We would now have to deduce the mean A.E. from the ephemeris, because we know that on 6 June the Earth is almost at aphelion, i.e. not even close to a mean distance position.
However, the shape of the orbit has basically been known since antiquity. Even in ancient times, the exact orbital shape of the Earth (albeit in the geocentric reference system) had been fairly well determined using shadow stick measurements.
2. In the meantime (21st century), the astronomical unit is of course defined as a multiple of S.I. units. This Système International d' Unité has defined seven basic dimensions in physics.
Today, the unit ‘metre’ is defined by the second, linked to the speed of light, i.e. the metre is no longer defined - as in the 18th century - by an ‘original metre’, which is located in an institute in Paris and is subject to temperature fluctuations and evaporation processes even with the best materials in the world.
Instead, a metre is defined as the distance travelled by light in a finite time and the astronomical unit as a multiple of this metre.
We estimated the following at our first workshop on the subject:
142 million km if we apply Delisle's contact time method,
131 million km if we apply our own image overlay method
and if we (improperly) averaged these two values, we would end up with 137 million km.
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