Measure the distance to the Sun

Method B: Drawing Venus' path across the solar disc

Venus will be seen to cross the Sun at different angles, if observed from different parts of the world. Drawings of the path from at least to widely spaced observing sites will make it possible to calculate the distance from the Earth to the Sun.

In this activity you have to register and find a school to cooperate with.


Full size. Ill. by Trond Erik Hillestad

Equipment

The drawings must be performed using an astronomical telescope, preferably a refractor (a lens telescope) with an equatorial mount.

  • If the refractor's aperture (free diameter of the front lens) is larger than approximately 80 mm (3,2 inches), the lens should be stopped down as explained below. Otherwise, the telescope may be harmed by the heat. You can block parts of the sunlight by cutting a circular hole in a piece of cardboard, and attach it in front of the telescope. The diameter of the whole could be about 30 to 50 mm (1,2 to 2 inches).


  • Catadioptric telescopes, i.e. telescopes that contain both lenses and mirrors, should in no circumstance be used for solar projection.

  • Reflecting telescopes (Newtonians and Dobsonians) may also be used, but with a much greater chance of harming the telescope itself. If you use a reflector, make sure it is stopped down considerably, and only allow it to point at the Sun for shorter periods of time. Reflecting telescopes may be stopped down by making an off-axis hole. This avoids the quality loss that normally arises due to the use of the secondary mirror (the black disc in the center).


You will also need:

  • A white and stiff piece of cardboard or a similar material. Draw a circle on the paper. Attach the plate to the telescope, in an appropriate distance so that the image of the Sun is focused. The circle should be as large as practically possible, preferably 30-40 cm (about 12-16 inches).

  • A stiff piece of cardboard or a similar material, that provides the rear piece with a dark shade (see illustration below).

Schematic illustration of the eyepiece projection method. It is important to obtain a large image of the solar disc. Too large an image will however give a (too) dark image of the Sun, so find a suitable compromize.

The drawing

The image of the Sun should fit exactly into the circle you have drawn prior to the observation. If not, make a sketch of the solar limb. .

Draw the position of Venus on the solar disc at a number of occasions. As the hours pass by, this will show Venus' path across the solar disc.

The distance of the Sun is huge. The distance between the two lines of the drawing thus becomes rather small, even if the observing sites are widely spaced geographically. Though, it is very important that you draw Venus' path as accurate as possible, and use a large image of the Sun.

To achieve the best accuracy:

  • Use a telescope with a sturdy tripod and mount. The mounting should preferably have motors, or at least some means for manual fine adjustment of the telescope's position.
  • Position the telescope on a basement or sturdy soil. The telescope should not be moved during the observation. Therefore, you must in advance check (preferably several days before) that the Sun does not disappear behind trees or buildings during the transit, as seen from your observing site.
  • The cardboard that you draw on should be mounted so firmly to the telescope that it cannot be displaced during the observation. If it does, the observation will probably be spoiled.
  • Magnify the Sun a lot when drawing Venus' path across it. The image should be at least 20 cm, preferably up to 40 cm (8 to 16 inches). However, using too large an image will result in a dark picture of the Sun, making it difficult to see Venus. You should, several days in advance, find out how large an image that can be practically used. Once you have found a usable magnification, sketch the entire solar limb on a piece of paper. On June 6th, it will then be easy to match the circumference of the Sun exactly within the pre-drawn circle.
  • Practice on several occasions in the weeks and days prior to the transit. Practice by drawing the Sun's circumference, and its sunspots, if any.
  • The observation must be carried out using an equatorial mount. The reason for this is that the Sun will rotate as it slowly traverses your local skies. A properly aligned equatorial mount will compensate for this rotation, so that the Sun's "up" and "down" will always match the "up" and "down" on you drawing. If you try to use an alt-azimuth type mounting, the Sun will rotate during the transit, and any drawing of Venus' path will be close to useless.
  • The equatorial mount should be positioned accurately. An equatorial mount is a mount where one of its two axis point toward the celestial pole. The best alignment with the celestial pole is achieved pointing the telescopes at stars near the pole.

Estimating the distance to the Sun

By comparing your drawings and observations taken from other parts of the world, the distance from the Earth to the Sun can be calculated.

Obtain a similar observation from a site that is situated as far away from you as possible. You should especially strive after a big difference in latitude. Draw both paths on a sheet of paper, and in the same scale.




Measure:

  1. The distance between the two paths, in centimeters
  2. The Sun's diameter on the drawing, in centimeters
  3. The distance between the two observing sites, measured along the Earth's surface, in kilometers. You can find this distance on this webpage.


Estimate the Sun's distance in kilometer using the formula:




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