How are we to understand the brightness of stars and planets?

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+5.7 this one and minus -1.5 magnitude that one....

(it is suggested that our eyes can see no fainter than +5.5 and that approximately 2,800 stars (globally, so on average 1,400 above your horizon) are therefore visible in the night sky.

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Well, very simply put, the higher the figure i.e. +..... the dimmer it appears and the smaller the figure i.e. a minus -.... the brighter it appears.

So for example, the International Space Station can have a brightness of -6 maganitude, whereas the moon can have a brightness rating around -13 and the sun, which remember is too bright to look at safely with the naked eye (so don't do that or even think about doing that!) can be -27!

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There are also two ways of considering this - 'apparent' magnitude and 'absolute' magnitude.

Apparent magnitude is how bright any particular planet or star appears to us from earth. Then by contrast, absolute magnitude gives any cosmos object a rating of brightness. Apparently, the star Vega, that was the initial baseline standard and first given  a magnitude of 0, has now, with much better precision measuring instruments, been given a photometric rating of +0.03.” 

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As you can appreciate a star may look brighter in the sky than another one but a dimmer looking star could simply be very much further away and therefore in 'absolute' terms could actually in real terms be a much brighter star! 

The web site 'Space.com' has a table of the brightest 26 objects at https://www.space.com/21640-star-luminosity-and-magnitude.html. (look towards the end of their article)

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So for another example our brightest star (not planet!) 'Sirius' which is 8.6 light years away, in 'Apparent' terms has an apparent brightness is -1.46 but has an 'Absolute' brightness of +1.4 and if it could be placed next to our Sun would outshine it by about 20x.

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Proxima Centauri (Alpha Centauri is a star system) is our closest star at only approximately 4.25 light years away, so nearly half the distance of 'Sirius',  but not as bright at -0.27 compared to the -1.46 of 'Sirius'.