Absolute Magnitude of the Full Moon

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SUMMARY

The absolute magnitude of the Full Moon is calculated using the square root of its albedo to adjust for the logarithmic scale of light intensity. A factor of 100 in albedo results in a 5-unit difference in apparent magnitude, necessitating the square root to maintain accuracy in calculations. The formula incorporates the log base 100, allowing the use of the ratio of the Moon's apparent brightness to its distance squared as the argument. This method ensures precise representation of the Moon's luminosity in astronomical terms.

PREREQUISITES
  • Understanding of astronomical concepts such as absolute magnitude and apparent magnitude
  • Familiarity with albedo and its role in light reflection
  • Basic knowledge of logarithmic functions and their applications in astronomy
  • Experience with mathematical formulas involving ratios and square roots
NEXT STEPS
  • Research the relationship between albedo and light intensity in astronomical bodies
  • Explore the mathematical principles behind logarithmic scales in astronomy
  • Learn about the calculation of absolute magnitude for different celestial objects
  • Investigate the significance of distance in determining apparent brightness
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Astronomy students, astrophysicists, and anyone interested in the mathematical calculations related to celestial bodies and their luminosity.

Fabio010
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Hey guys, I was doing some homework and found something I don't quite understand. When calculating the absolute magnitude of the Full Moon, I came across a square root of its Albedo.

(here - http://space.wikia.com/wiki/Absolute_magnitude). No idea why it's squared, but I can't get the +0,25 any other way so I guess it's there to stay?b]
 
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The square root is used to get the log scale right:
As an example: A factor of 100 in the albedo corresponds to a factor of 100 in the light intensity, which is a difference of 5 in the apparent magnitude and therefore a difference of 1 in the logarithm, which corresponds to a factor of 10 in the argument of the logarithm. Therefore, you need the square root of the albedo in that formula.

Take the log with base 100 (or 2.5*log instead of 5*log), and you can use ##\frac{ar^2}{d^2}## as argument, which directly corresponds to the intensity.
 

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