Photographing the Sun and measuring exact position of Venus
The following advices of 2004 corresponded to analogously photographing (the usual method in 2004!). We have actualized them to digitally photographing by highlightening those hints valid for analoguous imaging only and by a newly added section.
Additional annotations about building solar filters, mounting the camera, ... can be found on Tim Cole's noteworthy page Solar imaging with a digital camera and in an article of "Sky and Telescope".
In order to be able to determine the position angle of Venus with respect to the direction to east we propose to photograph the Sun twice on each picture with fixed camera. Precondition of this procedure is, of course, that the size of the picture is large enough for more than one image of the Sun. The smaller the Sun's face is compared with the size of the picture the longer can the time intervall be chosen and the more exactly can the orientation of the picture be determined.
In 2004 we used daylight slides (36mm*24mm) together with an optic of 800mm focal length. In this case, both exposures can be seperated by up to 6 minutes (see below).
Pictures of the Sun, taken with equivalent focal lengths of 250mm, 400mm, 1000mm and 1500mm
As our 2004 transit experiences show there are several crucial points to be regarded:
Tips for photographing
Use a little sensitive film (50 ASA, for instance).
The focus must be as exact as possible because a bad focus causes uncertainties in determining the Sun's radius and errors in measuring the position of Venus. But this position has to be measured with greatest precision! But: The visual impression of a good focus when looking through the viewfinder is no guarantee for a well focussed picture!
The edge of the Sun, possible sunspots and, perhaps, Venus itself will offer the best opportunity for focussing. Using a magnifier for the viewfinder (today a feature of many digital cameras) may facilitate the focussing but because of its own focus it must be tested in advance: The pictures below have been taken using a new (and not properly adjusted) magnifying glass!
The exposure time must be suitably chosen so that the picture is neither too bright nor too dark. Some hints may be useful:
If the camera can exposure automatically it should be tested if shortening the time by one or two steps yields better results (see the examples below).
|90 seconds time difference
||Automatic exposure -1 step
||Automatic exposure -2 steps
Most often the brightness of the picture is measured in the center of the picture. Therefore, by automatic exposure, the Sun will be taken with different brightness depending on its position on the picture (see the left picture below).
Perhaps it will be better to choose a fixed exposure time. With our optics, 1/1000 second has proved to be suitable. Of course, it depends not only on the aperture of the optic but also on on the Sun's elevation above the horizont and on the state of the atmosphere!
The time difference between both pictures should be adjusted to a fixed value and maintained carefully:
If you will have found the suitable time difference you will be sure to catch as much of "both" Suns as possible - and that is a precondition of precise measuring their positions.
Choose the time difference as large as possible, if possible so that both pictures don't overlap (150s, at least). In this way you can minimize the probality of Venus to be positioned in the overlapping region of both images.
If you know the time difference you also know the exposure moments of both pictures and the position of Venus on both pictures can be evaluated.
If you know the time difference and the declination δS of the Sun you will be able to determine the angular radius ρS of the Sun. Position measurements with the program "evaltransitpicts" provides ρS as an additional result. For primary methods of measuring it see the additional project "Measuring the angular radius of the Sun".
Example: The pictures above and below have been taken on March 8th, 2004 (δS=-4.7°). Because of the rotation of the sky (or of the Earth, if you prefer this viewpoint) in each minute the Sun will move by 15'*cos(δS)=14.95' and, therefore, by 89.70' in 6 minutes. In this way, we found ρS=16.2' (The correct value was ρS=16.11'.)
- Multiple exposuring must be exercised!
Does your camera offer the possibility of double exposuring the same picture? That means: Are you able to wind up the camera without transporting the film?
Are you able to keep the position of the camera unaltered during winding it up? A very stable tripod is necessary for this reason.
In the pictures above we found the direction of displacement to be constant within +-0.5°, approximately.
|90 seconds time difference
|Fixed exposure 1/250s
Does the counter count a new picture when you wind up without transporting the film?
Is the film be transported between the twice exposured pictures by the same amount as usual (with our camera it is transported less!). For savety, you should always insert one additional frame.
Additional hints for digital imaging
Digital photographing is much easier!
- The results can be inspected (and eventally corrected) immediately.
- The pictures can be manupulated afterwards.
- Multiple exposuring is very easy: Simply take the pictures one after another. They can be combined when the transit is over!
Of course, a stable tripod is again important and the use of a timer or remote activator is very advisable in order to avoid shocks.
For processing digital images we recommend the public domain program ImageJ. But there are many other programs offering appropriate manipulating possibilities.
The following advices refer to "ImageJ".
The combination of successive photos can be done by the following steps (sequence of menu items to be followed in red):
- Open the images simultaneously with the program: File → Open
- Stack the pictures: Image → Stacks → Images to Stack
- Combine the pictures laying one "upon" the other (in the z-direction): Image → Stacks → Z Project.
Following kinds of ZProjection should be tested:
- Average Intensity
- Max Intensity
- Sum Images
In most cases averaging (middle) seems to yield the best results. (The pictures have been taken with little experience with a new camera and at difficult weather conditions.)
- Improve brightness and contrast of the combined picture: Image → Adjust → Brightness/Contrast
Probably, Auto will lead to a satisfying result. But there ar some other possibilities for manipulation.
GOOD LUCK !!
In a picture with two solar discs which have been taken with fixed camera, the line connecting both discs represents the direction from (celestial) east to west. The position angle θ' of Venus is measured counterclockwise with respect to the direction to west. The position of Venus can be specified in the following two manners:
by the position angle θ' and the relative distance r'=r/rS to the Suns's center or
by the rectangular coordinates x'=r'cosθ' and y'=r'sinθ'.
Mercury, photographed from Namibia, May 7th, 2003 at 9.45 UT
Position measurement with "evaltransitpicts"
We offer the little program evaltransitpicts which allows to fit circles to the solar discs and to the discs of Venus. Resulting, it calculates both positions of Venus. Following the above outlined procedure it additionally calculates the angular radius of the Sun if its declination angle and the time difference between both exposures are known.
In the case of a single exposured picture the program determines the position angle with respect to the direction to the right edge of the picture unless the orientation of the picture is known.
If several pictures have been taken from the same site time and position are saved in a text file in a format which can easily be imported to an Excel worksheet. Excel than determines the line fit to the rectangular coordinates:
x' = x'0+a*t
y' = y'0+b*t
This fit makes it possible to interpolate or to extrapolate the positions to a common moment for different sites. The distance between two of those positions gives the parallactic shift β of Venus from which the solar parallax πS can be deduced following the procedure described in our basic paper.
The procedure is described in more details in our Mercury project and in the corresponding evaluation page of the measurements of 2004.
Typical results of our Transit of Venus 2004 Project can be found here.
|| last update: 01.06.2012