Today let's talk about Magnitudes

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