Question

(a) The distance modulus of the star Vega is

— 0.5. At what distance is it from us ? ​

Answer 1

Solution:

Distance Modulus of Star Vega = -0.5 = m - M

Distance Modulus is the difference between the apparent magnitude(m) and absolute magnitude(M) which also defines the distance in parsecs which is,

Distance Modulus , $m - M = -5 + 5 log_{10} d$

$-0.5 = -5 + 5 log_{10}d$

$-0.5 + 5 = 5 log_{10}d$

$4.5 = 5 log_{10}d$

$\frac{4.5}{5} = log_{10}d$

$0.9 = log_{10}d$

Now we will use logarithm property,

$log_{a} (b) = c \ then \ b = a^{c}$

Therefore,

$d = 10^{0.9}$

$d = 7.943$

The distance of star Vega from us is 7.943 parsecs.