Simultaneously Photographing of the Moon
and Determing its Distance

First Challenge: Proper motion of the moon

Second Challenge: First Parallax Effect

Meanwhile, you may try to combine pictures from Bulgaria and Tenerife. The moon's parallactic displacement has become more obvious: Going from East (Bulgaria) to West (Tenerife) we see the moon moving towards Jupiter that means, in eastern direction!

Here are some of my solutions:

Bulgaria and Tenerife, 21.00 UT	Bulgaria and Koblenz, 21.00 UT	Koblenz and Namibia, 21.00 UT	Süderdeich and Namibia, 22.30 UT

I've got them by the following procedure:

• Scaling both of the pictures so that Jupiter and Saturn have the same linear distance.
• Rotating one of the pictures so that the angle between the bottom line and the straight line from Jupiter to Saturn is the same in both pictures.
• Linear translation of one of the pictures so that Jupiter has the same pixel coordinates in both pictures.
• Finally, adding both of the pictures.

You can comprehend this procedure using any image processing software or, respectively, by using a photocopier and putting the pictures on top of each other so that Jupiter and Saturn coincide on both pictures.

Stereo picture of the moon as seen from Süderdeich and Namibia, December 9th, 2000, 22.30 UT
(You can see the sterographic effect by 'parallel locking', most easily donne with the help of stereo glasses.)
(I hope I can combine a better stereo picture, soon!)

Detailed Problems (under construction!)

1. Find the exact geocentric positions (i.e. rectascension and declination) of Jupiter and Saturn due to our observation times.
   1. Look for daily ephemerides in an astronomical almanach and interpolate!
   2. Alternatively, use an astronomical computer program!
   Due to the large distance to the planets, their topocentric positions are the same, with sufficient precision.
2. Determine the related angular distances of the planets!
   1. You can measure these distances with the original slides of your own by measuring the linear distance of the planets on the slide and taking into account the focal length of your camera.
   2. Alternatively, you can derive these distances from the positions determined above.
      1. Try to use the theorem of Pythagoras.
      2. For correct calculation, you will need some spherical trigonometry.
3. With the known angular distance of Jupiter and Saturn, determine the scale (in angle per pixel, for instance) of the pictures.
4. Now you can measure the angular distance between the moon and the planets.
5. Determine the angular distance of the moon's positions as observed from different locations.
   There are different possibilities to do that:
   1. Construct scaled drawings with ruler and compasses. (For instance, you may project the slides at the wall. The following pictures may give you an impression of what we did in Koblenz.)
   2. Print different pictures to the same scale and put them together so that the planets cover on both pictures.
   3. Calculate from the angular distances determined above and the planets's coordinates the topocentric coordinates of the moon. Then, the parallactic displacement of the moon can be calculated in the same way as above.
6. Determine the distance between different observers as muliples of the radius of the earth. There are, again, three possibilities:
   1. Use the pictures of the earth contained in the main document.
   2. Measure the distance with the help of a globe and a piece of a string.
   3. Calculate the distance from the geographic coordinates of the locations.
   The measures got by the different procedures will not correspond exactly. Only the first procedure will give you the distance as seen by the moon at that moment!
7. From the parallactic displacement of the moon and the the distance between the related locations calculate now the distance of the moon as a multiple of the earth's radius!

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last update: January 10th, 2020