File:Lunar eclipse umbra lightcurve arcmins.png

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Original file ‎(1,421 × 1,033 pixels, file size: 46 KB, MIME type: image/png)

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Description: Intensity curve of Earth's shadow at 380,000 km distance (typical Moon distance). The angle coordinate (or umbral magnitude) is with respect to the rim of the umbra (ru = 0), the curve ends at the centre of the umbra (u-mag = +41.6'). The umbra is defined here as that of the solid body of the Earth without the atmosphere. The 'visual' umbra is about 2% larger due to the atmosphere's extinction and refraction. The lower (orange) curve shows the (absolute value of the) gradient of the logarithm of the intensity, which is approximately proportional to the visual gradient. The visual rim of the umbra is marked by the point of steepest gradient. The unusual choice of x-axis is for compatibility with the umbral magnitude (which normally is given in Lunar angular diameter rather than in arcminutes).

  • Author: SiriusB
  • Source: Own theoretical model based on 1976 standard atmosphere and atmospheric extinction curves from dtv-Atlas zur Astronomie, 9th edition 1987. Plotted with Gnuplot. Short description how to get these images:
    1. Calculate and tabulate atmospheric refraction angles and extinction of a light beam of certain wavelength (e.g. 630 nm). This requires numerical integration of both variables. To save computing time for later usage, a cubic spline is calculated from the tabulated values.
    2. Given the solar middle-edge-intensity function (the Sun's disk becomes darker at the rim) integrate the intensities of each point of the obscured disk of the Sun (which is at a given angular distance s from the center of the Earth's disk as seen from the Moon) after the "mapping" through the Earth's atmosphere. Use the spline from above as a good approximation. The result is the total intensity of the refracted and partially extinted light from the Sun as received on a point on the Moon. The direct sunlight has to be added to this, of course.
    3. Repeat the previous calculation for every Sun-Earth angular distance s and transform it to the actual angle (a Sun's diamater is about 32 arcminutes).

To get the actual brightness of the Moon for a terrestrial observer, this curve has to be integrated once more (using another interpolation to save CPU time) over the Moon's disk.

Date 22 April 2005 (original upload date)
Source No machine-readable source provided. Own work assumed (based on copyright claims).
Author No machine-readable author provided. SiriusB assumed (based on copyright claims).

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I, the copyright holder of this work, hereby publish it under the following licenses:
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Date/TimeThumbnailDimensionsUserComment
current11:58, 22 April 2005Thumbnail for version as of 11:58, 22 April 20051,421 × 1,033 (46 KB)SiriusB (talk | contribs)Same as Image:Lunar_eclipse_umbra_lightcurve.png but plotted against angle (arcmins) instead of time (minutes) {{GFDL}}

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