Determining Lunar Heights
Grade: 7 to adult
Object: to calculate the heights of various lunar objects by
measuring shadow lengths
Methods: One of the most rewarding pursuits for the amateur engaged in lunar observing is the determination of the heights of lunar features. Once characterized by tedious mathematical calculations, this noble pursuit is now made infinitely more simple and enjoyable by Harry Jamieson's collection of software programs the Lunar Observer's Tool Kit. When using the Tool Kit one need only furnish certain basic information and let the program do all of the number crunching. The data required are as follows:
Location of the observer in degrees and minutes, and elevation in meters. The best source for this information is a geodetic map published by the U.S. Geological Survey. These are often available in sporting goods stores and/or public libraries.
Universal date and time to the nearest minute. Location of the lunar feature being measured in degrees and minutes of latitude and longitude. The better the lunar atlas used, the more accurate the results.
Length of the shadow being cast by the feature. This information may be in kilometers, fraction of the lunar radii, or seconds of arc. Obviously, accuracy is critical here. Several methods of shadow measurement are available to the amateur, the most common being:
ESTIMATING BY EYE: This method is the least accurate and is performed by visually comparing the length of the shadow to a feature of known size. If the shadow length appears to be half the size of a 30 km crater, the value is entered as 15 km.
DRIFT METHOD: Here the shadow is allowed to drift across the reticle of a high power eyepiece, with the clock drive running, while timing its passage with a stop watch. That time is then compared to the time it takes for a feature of known size to drift across the same reticule. As a rule of thumb, the Moon will drift from west to east at the rate of slightly less than 1 kps.
BIFILAR MICROMETER: Probably the most precise method of shadow measurement is achieved with the aid of a bifilar micrometer. Measurements can be made by comparing the length of the shadow to the size of a known feature, or by calibrating the micrometer on a double star of known separation and measuring the shadow in seconds of arc.
GRADUATED RETICLE: Eyepieces with graduated reticles such as Celestron's Micro Guide may be used in the same manner as a bifilar micrometer. Although not as precise, they are less expensive and easier to use.
PHOTOGRAPHIC: Measuring shadow lengths on a photograph is similar in procedure to that of using a graduated reticle eyepiece. Results are comparable but a photograph has the advantage of containing many shadows which can be measured under more controlled conditions, and the measurements are infinitely repeatable.
PS: For a more extensive article on lunar height calculations using the shadow method, see the Lunar Heights Article in the Article Section.
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