to the airmass at the target's position. Such calibration obtains the brightness as would be observed from above the atmosphere, where apparent magnitude is defined. For those new to astronomy, Apparent Magnitude scales with the received power (as opposed to amplitude), so for astrophotography you can use the relative brightness measure to scale the exposure times between stars. Apparent magnitude also adds up (integrates) over the entire object, so it is focus independent. This needs to be taken into account when scaling exposure times for objects with significant apparent size, like the Sun, Moon and planets. For example, directly scaling the exposure time from the Moon to the Sun works, because they are approximately the same size in the sky, but scaling the exposure from the Moon to Saturn would result in an overexposure, if the image of Saturn takes up a smaller area on your sensor than the Moon did (at the same magnification or more generally f/#). Calculations The dimmer an object appears, the higher the numerical value given to its magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Therefore, the magnitude , in the spectral band , would be given by which is more commonly expressed in terms of common (base-10) logarithms as where is the observed irradiance using spectral filter , and is the reference flux (zero-point) for that photometric filter. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor (Pogson's ratio). Inverting the above formula, a magnitude difference implies a brightness factor of Example: Sun and Moon What is the ratio in brightness between the Sun and the full Moon? The apparent magnitude of the Sun is −26.832 (brighter), and the mean magnitude of the full moon is −12.74 (dimmer). Difference in magnitude: Brightness factor: The Sun appears about times as bright as the full Moon. Magnitude addition Sometimes one might wish to add brightness. For example, photometry on closely separated double stars may only be able to produce a measurement of their combined light output. To find the combined magnitude of that double star knowing only the magnitudes of the individual components, this can be done by adding the brightness (in linear units) corresponding to each magnitude. Solving for yields where is the resulting magnitude after adding