Physics Photo of the Week

October 12, 2012

Lunar Libration



Aside from the color, these images of the Moon look identical.  They were taken about 7 hours apart on the same night between October 4 and 5, 2012.  The left image was taken about 11:30 at night and the right image was taken at about 6:50 the following morning before sunrise.  The difference in color is due to different atmospheric properties - different elevations.  The night image (on the left) was taken when the Moon was quite low on the eastern horizon, but left image was taken while the Moon was still quite high in the sky.  A more subtle difference in the two images shows the terminator (the edge of the sunlit portion) has shifted very slightly to the left due to the progression of the Moon in its orbit.  In the 7 hours between the images, the angle between the Moon, Sun, and Earth has become slightly smaller.

The most striking difference between these images can only be noticed if the images are "blinked" in the animation below.  The Moon seems to be saying "No" - wobbling its head back and forth - even though the Moon generally keeps the same face toward the Earth due to tidal locking.  This back and forth motion is predominantly due to the geometry of our angle to the Moon.  In the 7 hours between the images, the Earth has rotated slightly more than 1/4 revolution.  This causes our perspective to be shifted slightly.  This is similar to the change in appearance of buildings or mountains viewed from different angles.  The same effect would be seen if two photos were made simultaneously from two widely separated parts of the Earth.

Earth Moon Distance.  We can use the data from these images to estimate the distance from the Earth to the Moon by measuring the apparent angular change in the Moon's apparent orientation between the two images.  I obtained the distance from Earth to Moon to be about 120 times the Earth's radius.  (The accepted value is about 60 times the Earth's radius).  These results would be much more accurate if we measured on a night of a full Moon.  I have also neglected the change in Lunar position in its orbit.  Finally simultaneous measurements should improve the results dramatically.  If any observers in different parts of the world can make their own telephoto images of the Moon during the next full Moon please write to me and receive instructions.  You will need a digital camera with greater than a 250 mm focal length lens (or a telescope) and a tripod.  This experiment had been suggested to me by former student Tom Overman (WWC class of 1984) a few years ago, but I did not believe we would see a significant shift.
 



Physics Photo of the Week is published weekly during the academic year on Fridays by the Warren Wilson College Physics Department. These photos feature interesting phenomena in the world around us.  Students, faculty, and others are invited to submit digital (or film) photographs for publication and explanation. Atmospheric phenomena are especially welcome. Please send any photos to dcollins@warren-wilson.edu.

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