Understandings: Luminosity and apparent brightness
Applications and skills: Solving problems involving luminosity, apparent brightness and distance.
Data booklet equations:
Luminosity is the total power output of an object, normally in this context a star or galaxy. The SI derived units of luminosity are watts (or joules per second), but astronomers and astrophysicists sometimes use multiples of the sun's luminosity, where 1 L☉ = 3.828×1026 W.
If we assume a star is an ideal (black body) emitter of radiation , its luminosity can be calculated using the Stefan-Boltzmann law as given in the data booklet.
For radiation emitted in all directions from a point source (and on astronomical scales that is a fair assumption for a star) the radiation spreads out on the surface of a sphere. As the equation for the surface area of a sphere is A=4πr2 this means that the radiation incident on a square meter falls off as you move away from the object in this ratio. Which leads to the brightness.
The (apparent) brightness of an object is defined as the radiation from that object incident on a square metre at a distance d from that object. As a result of the inverse square law we can calculate the brightness from the luminosity using the equation in the data booklet. The units of brightness are normally watts per metre-squared [ Wm-2 ].
The brightness equation has three variables, L - the luminosity (measured in W), b - the brightness (measured in Wm-2) and d - the distance (measured in m).
If we know two of these we can calculate the third.
Brightness can normally be measured directly on Earth using a telescope and a photometer. Potential difficulties include the response of the devices (they are not equally sensitive to all parts of the spectrum) and absorption of some of the light by the atmosphere or even gas clouds in space between the source and the observer.
For close objects we can measure their distance using techniques like parallax, and use them to calculate their luminosity.
For more distant object we can estimate their luminosity (for example from their temperature using Wien's displacement law - see the next section) and use that to calculate an estimate for their distance.
Oxford Physics: pp 647-648 with a good worked example on page 647.
Hamper HL (2014): pp 538-539 with exercises on page 539
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