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Apparent magnitude is a rather complex way to determine the brightness of a star. Quoting the introduction text from the linked to Wikipedia page:

The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere. The brighter the object appears, the lower the value of its magnitude. Generally the visible spectrum (vmag) is used as a basis for the apparent magnitude, but other regions of the spectrum, such as the near-infrared J-band, are also used. In the visible spectrum Sirius is the brightest star in the night sky, whereas in the near-infrared J-band, Betelgeuse is the brightest.

While it is of course a useful measure also for the slightly more casual, non-scientific observer to help determine the observed star from its neighboring cluster, or identification in general, I always wondered if there is a way to measure apparent magnitude with enthusiast-class equipment, and what would these procedures be?

                              apparent magnitude

                              Apparent magnitude scale and observational limits (Source: ESA Science)

Also interesting would be a description of what level of precision and enthusiast can get with such equipment while measuring apparent magnitude of a distant star. If you need specifics to answer the question, such as precise available equipment or subject of observations, please feel free to choose at will any that would broadly match the capabilities of enthusiast-grade equipment.

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You may already have a DSLR, but if you're ready to buy it, a CCD would cost as much. Do you want an answer with CCDs? –  Cheeku Sep 28 '13 at 2:17
    
@Cheeku - Sure, any method that's accessible to enthusiasts will do, thereof my last sentence. If you know of more ways, then the better. There ought not be many ways anyway, so I thought to ask it like that, have answerers demonstrate their ingenuity a little LOL –  TildalWave Sep 28 '13 at 4:21

1 Answer 1

up vote 13 down vote accepted

The easiest way to determine the magnitude of a given star is probably to use the Pogson relation. The idea is to determine the magnitude of a star knowing the magnitude of a reference star; it is thus quite easy, using a well-known reference as Vega or Sirius.

The Pogson relation is given by:

$$m_1-m_2=-2.5\ log\ \left({\frac{E_1}{E_2}}\right)$$

where $m_1$ and $m_2$ are the magnitudes of star 1 and star 2 (your reference star), and $E_1$ and $E_2$ brightness (that could be in arbitrary units, which is a good news for you).

With a CCD detector the brightness is easy to determine since it's just the flux of a pixel. You don't have to convert it in physical units (as Watt per square meter) since you have a ratio $\left({\frac{E_1}{E_2}}\right)$, so the raw intensity is enough to determine the magnitude.

As for any other measurement with a CCD camera, you have of course to determine the bias, dark and flat-field and to reduce your data before estimating any magnitude. The precision will depend on the number of observations performed and, as always, it is better to perform several short exposure images than a single long exposure one.

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