What's the definition of magnitude?
In astronomy the magnitude is the measure of the brightness of an object in logarithmic scale, measured in a certain band, for example the near IR (Infra-Red) or V (violet).
Define the apparent and absolute magnitude and explain how to link the two.
The apparent magnitude m of a celestial object is the brightness of an object as seen from earth, without the influence of the atmosphere.
The formula to remember is:
\[m_{2} -m_{1} = -\log\bigg(\frac{F_{2}}{F_{1}}\bigg)\]
where F2 is the observed flux in a certain band, for example the V one and F1 and m1 are respectively the reference flux and magnitude calibrated for example with the star Vega.
The absolute magnitude M of a star is the apparent magnitude it would have if it were at 10 parsecs.
I can derive the absolute magnitude from the apparent one if I know the distance, so I use the distance modulus relation:
\[m - M = 5\cdot \log(D) - 5\]
D is measured in parsecs.
Reference: http://en.wikipedia.org/wiki/Magnitude_%28astronomy%29
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