How far away is a RR Lyrae variable star if it has a period of 0.5 days and a brightness of 2.3 x 10^-11 W/m^2?

The answer is d = 10^6.43 Mpc

Explanation:

Solution

To calculate the absolute magnitude of the star, we apply or use the relation with the period

Mv = - [ 2.76 (log₁₀ (P) - 1.0) ] - 4.16

Here P = + 0.5 days

Mv = - 0.569

To calculate m, we have the following relation given below:

Mₓ = - 2.5 Log₁₀ (Fₓ/Fₓ,0)

Fₓ,0 = 1 w/m² (This is assumed)

Fₓ = 2.3 * 10^-11 W/m^2 (Given)

Thus

Mₓ = - 2.5 Log₁₀ (2.3 * 10^ ⁻11

Mₓ = 26.595

Now, applying the formula we have the following given below:

d = ₁₀ (Mₓ - Mv + 5) / 5

d = ₁₀ (26.595 - 0.569 + 5) / 5

d = 10^6.43 Mpc