The Magazine About Learning and Teaching Astronomy


Here is a link to an article on the Lunar Parallax experiment done on the June 2011 eclipse, in The Classroom Astronomer magazine, Issue 9, Fall 2011.



The Parallax technique has to be done with two observers sufficiently far apart (we estimate at least 2000 miles (3200 kilometers).  It must be recorded with photography and the photographs have to be taken at the exact same time, with a field of view wide enough (4-8 degrees) such that the neighboring stars can be recorded at the same time on both photographs.  A comparison of photographs through overlay procedures will show the shift of the stars (or Moon) as seen from one side of earth to the other.  The larger the shift, the closer the Moon.  

A summary of what to do to measure the Moon using the Lunar Parallax technique:

  1. 1. Take photographs of the eclipsed Moon, showing stars.
  2. 2. Find another observer who has taken a photo at the exact same moment but from some place 1000s of miles (kilometers) from you.
    3. Overlay the photos, matching up lunar surface features.
    4. Measure the shift of one star between the two places using the Moon’s average 30’ diameter as your ruler.
    5. Use the Geobytes website to find out how many miles or kilometers apart you and the other observer are.
    6. Use the three equations (or our online calculator or the Table provided) to find out the real distance between the places through the Earth (also called the Chord), the distance to the Earth’s center, and the Moon’s distance.


Before The Eclipse

You need to find a partner (preferably, more than one partner, in case someone gets clouded out!) and communicate before the eclipse date.  For the parallax to work, you and your partner should be either at the approximate same latitude (or the opposite latitude, i.e. if you are at North 35 degrees, your partner should be near North OR South 35 degrees), AND you should both be as equally distant as possible from the mid-eclipse longitude. 

If you are more near the center of the eclipse viewing area, you will not be able to get a parallax.  You would have to use the Shadow method.


During The Eclipse

     Take photographs of the totally eclipsed moon (start about 15-20 minutes before totality begins, and end 15-20 minutes after it ends).  These photographs must be exposed long enough to show round images of nearby bright stars, within around 5 degrees in any direction, and yet short enough that you can see the lunar seas and the edge of the shadow clearly.  Generally, exposure times of about 0.5 to 1.5 seconds seem to work best.  Always try a range of exposures and note that the darker the Moon, the longer the exposure may have to be.   See the three eclipse photographers' remarks on the photography page.  

     RECORD THE TIME TO THE MINUTE FOR EACH EXPOSURE.  We recommend that you take photographs on any minute that ends with the number "5"--:05. :15, :25, etc.--or exactly on every five minutes on the clock, e.g. :05, :10, :15, :20, etc.

  

Here are two photographs, from China (left) and Turkey (right, contrasted adjusted, the star is not well seen here but is on the original), taken at the exact same instant of time.  The circles are around the same star, 51 Ophiuchi, during the June 2011 total luncar eclipse.  Notice that in China the star is to the Moon's eastward (left) side but it is to the west (right) from Turkey.


After The Eclipse


1. Examine your photographs for those that are the best ones--no blurring of the moon or stars (stars should be as close to tiny dots as possible), clear shadow edges, ample stars to find one in common with someone else.  

2. Find  out if your partner(s) were also successful and use their photographs that were taken AT THE SAME MINUTE!  This experiment will not work if the times are more than a minute different.

3. Find a star that shows up in both photos and mark it.  You must  be very sure of your star identification--use a planetarium computer program like Starry Night or Stellarium to identify the field stars.  


4. You will need to adjust the rotation of the images, and the sizes of the images so that the Moon is the same size and angle on each photograph, or on the same page of  a graphics or desktop publishing program.

5. Measure the diameter of the moon using a millimeter scaled ruler, or some other device (even your computer program may be able to do that!).  Divide that number of millimeters into 30 minutes of arc, the average angular size of the Moon, which equals one-half degree.  This is the scale of your photograph.  



The Turkish and Chinese Moon images overlaying on each other and rotated so that the maria (seas) are on top of each other, as well as the shadow edge.  Contrast has been adjusted and the stars show well on the original photographs.

6. On your combined, overlaying photographs, adjust the transparency of the photographs so you can see the marked star on BOTH photographs.  Measure in millimeters how far apart they are, and multiply by the scale of the photograph.  THIS IS THE LUNAR PARALLAX VALUE!

7. Go to the Geobytes Website and, using the names and countries of your location and your partner's, find out how many surface miles apart are your locations.  This is along the surface of the Earth; you need the distance THROUGH the Earth, which our 
Table 2LP will find for you.  The through-the-Earth distance (the Chord) will always be less than the surface distance!  

8. Input the Lunar Parallax value in minutes of arc, and the surface miles apart you and your collaborator are into our Table 1LP and get the Moon's Distance!

9. To find the Moon's Diameter, divide the Moon's angular size (30', thirty minutes of arc) by the lunar parallax in minutes of arc (should be between 30 and 70 minutes of arc).  Then multiply that number by the number of miles
you and your partners area apart measured THROUGH the Earth .  This should give you the Moon's diameter!