In: Physics
The Sun has an apparent magnitude of -26.74. The closest star system to us, Alpha Centauri, has an apparent magnitude of +0.01 and a luminosity of 1.1519 times that of the Sun. How much brighter is the Sun compared to Alpha Centauri? How close is this star system to us?
Apparent magnitude of Sun, m1 = - 26.74
Apparent magnitude of Alpha Centauri, m2 = + 0.01
Let L2 and L1 be the luminosity of Alpha Centauri and the Sun respectively
Since the apparent magnitude of Sun is lower than that of Alpha Centauri, Therefore, Sun is more brighter.
How much brighter, is given by going through the relation that exist between their apparent magnitude and the flux.
(because, how much brighter a star really is, is determined by it's flux)
where F1 and F2 are the flux of Sun and Alpha Centauri
Putiing the values of m1 and m2
Therefore, Sun is about 5.01 * 1010 times brighter than the Alpha Centauri
Now, By the relation of Flux and Luminosity
where F is the flux, L is luminosity and D is the distance from the star
Dividing first by second : -
Putting values of F1 / F2 and L1 / L2 in relation above : -
Therefore, Alpha Centauri star system is about 2.402 * 105 times far as compared to the Sun.