Calculator Details
Author: Bill Kramer
Last update: Saturday, 18-Apr-2015 09:57:22 EDT

Calculator Details

Understanding the Results: Results from pressing the Do the Calculation button are displayed both on the map and web page for the four primary contacts. First contact (C1) is when the partial eclipse starts. Second contact (C2) is the beginning of totality. Third contact (C3) is the end of totality. Fourth contact (C4) is when the partial eclipse ends. The results show the time of each major contact to the tenth of a second. The altitude above the horizon for the sun is provided with each contact in degrees. Zero degrees is right on the horizon. Ninety degrees is directly overhead.

Directly below the map you can see the current location of the cursor/pointer as it is moved around the map. After calculating an initial result, click on another location and the distance from the "C" marker to the new marker point is shown in kilometers and miles.

The graphic below the map depicts the lunar limb (exaggerated 10x) at the time of eclipse. This is useful for determining limb corrections as well as where the diamond ring and Baily's beads will appear.

All computations assume a stationary observer. Relative speed (such as in aircraft and ships) are not accounted for when computing circumstances.

Refraction: Astronomical refraction of light occurs when a ray of light enters the atmosphere and bends. The atmosphere of the Earth is layered with increasingly dense air causing the ray of light to continue to refract. This calculator automatically accounts for refraction using averaged temperatures and barometric pressures (from an aeronautical engineering handbook) for various elevations and approximations from the Astronomical Almanac for refraction. Refraction can be as much as half a degree right on the horizon. The calculator will display "-" for Not Visible when the refracted eclipse contact is more than five degrees below the horizon. Note that the results will vary slightly between this calculator and those not including astronomical refraction.

The following equation (an approximation based on is used to compute the refraction correction for objects 15 to 25 degrees above the horizon.
   R = 0.00452 P / ((273 + T) tan a)
and for object below 15 degrees:
   R = P (0.1594 + 0.0196a + 0.00002a²) / [(273+T)(1 + 0.505a + 0.0845a²)]

Where P is the barometric pressure in millibars, T is the temperature in degrees C, a is the altitude measured in degrees. The result, R, is the amount of refraction measured in degrees. Refraction calculator Standard temperatures and pressures were obtained from Standard atmosphere tables.

Alt.: The altitude represents the height above (or below) the astronomical horizon in degrees. The astronomical horizon is defined as being 90 degrees off of the zenith (directly overhead). Your actual horizon will vary depending on surrounding terrain and your elevation. The higher up in elevation, the more the horizon will dip below the astronomical horizon. In the case of a commercial jet operating at 10,000 meters the drop will be over three degrees. The results shown in the table are relative to the astronomical horizon. Look in the paragragh below for the dip in the horizon when elevations are input over 100 meters. The dip in the horizon is added to the calculated altitude to estimate the height of the eclipse above the apparent horizon. This value is an estimation as refraction values cannot be known in advance.

Time information: The calculations use UTC (Coordinated Universal Time). If you are using a GPS please note that time data may be in GPS time and not UTC when the GPS is first turned on. Leap second updates are sent to the GPS network about every quarter hour and if your GPS is set up to work with the data then the clock will be updated. GPS time is over ten seconds ahead of UTC. To learn the current GPS offset as well as other time systems click here.

Calculation Method: Elements used in the calculations are based on the lunar center of mass as determined by NASA/JPL using the DE200/LE200 ephemeris. The position of the center of mass (as seen by an observer on Earth) is slightly different than the actual "center of figure" which shifts depending on libration (slight wobble of the moon) and the position on Earth of the observer. The actual center of lunar mass is about 2 kilometers closer to Earth. Views from various points along the eclipse path see a different profile of the moon. The resulting shift means that the observed position of the moon can be almost 0.5 seconds of arc different than the calculated center of mass position. For the majority of eclipses the deviation is less than a second in totality duration time.

Lunar Limb Profile Corrections: When the lunar limb corrections are incorporated the actual observed center of figure is determined and used. Corrections may be several seconds of time at either or both 2nd and 3rd contacts. The majority of the correction value is the result of the lunar profile.

To compute the corrections this program uses either the Watts Lunar Limb Profile data from CDS along with correction algorithms developed through the study of a large data set of lunar-stellar occultation timings (links below) or a more recent set of data provided by Dave Herald after reducing laser altimeter readings from the Japan Aerospace Exploration Agency's (Kaguya) Selene lunar orbiter. The difference between the center of mass and center of figure are also included. When run the program reads a copy of the Watts or Kaguya/Herald data on the eclipse-chasers server and creates a list of points every 0.2 degrees describing the profile. The profile is then compared against a sliding circle that represents the solar disk. When the disk of the sun is completely obscured the eclipse is total and the amount of shift required determines the time change. The approach compares favorably with other methods of contact corrections and better accounts for profile features near, but not exactly at, the computed points of contact.

The Kaguya/Herald profile was derived from the Kaguya Laser-altimeter time series dataset by Dave Herald of Canberra Australia. It provides the angular height of the lunar limb above a mean lunar limb centered on the center of mass of the moon, with the moon being at its mean distance. The dataset has been tested against the historical list of lunar occultations to validate the accuracy of the conversion. The reference point for the lunar profile is the center of mass of the moon. When using the dataset the position of the moon as derived from DE421 (or previous versions of the JPL Development Ephemeris) does not need to be corrected for any difference between center of mass and center of figure.

Constants: In almost all cases, astronomical constants in use are based on the IAU (International Astronomical Union) values provided in this paper from the US Naval Observatory (see page viii).

Graphic Presentation: The eclipse path shown inside Google Maps is an approximation. The path was generated with an elevation of zero meters above sea level and does not account for terrain changes. Specific location input for the latitude and longitude are processed by a different calculation for the local circumstances. The centerline graphics are meant to serve as a general guideline to the eclipse path. In some places the actual edge or center may be shifted by several kilometers. Use the Do the Calculation button to determine local circumstances that account for elevation and the lunar limb profile.

Baily's Beads: When the photosphere of the sun peeks through valleys along the lunar profile a series of bright points of light are visible. The rugged profile of the moon can sometimes cause a string of bright points just as the eclipse goes total (or the total phase ends). The term "beads" was first coined by the 19th century British eclipse chaser Francis Baily hence they are known as Baily's Beads. A side effect of the lunar limb profile correction calculation is that the same data can be used to render Baily's Beads configurations for times near the umbra contacts. Comparisons to actual observed bead configurations are welcomed by the web master of eclipse-chasers.

Elements Data - The Besselian Elements used by the calculator can be supplied from various sources. Most of them come from the NASA GSFC web site. The common aspect is that they all use the center of mass for the moon. Very short eclipses and grazing eclipse conditions are difficult to predict well in advance. The accuracy of the calculation needs to be verified by multiple sources. If you notice that the elements data in use is out dated or that a more recent set of exists then please alert the webmaster so that the files can be updated.

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