Answer to Question #176413 in Astronomy | Astrophysics for Harshdeep

Question

Using parallax, you establish that a particular star cluster is 30 parsecs from the Earth. You measure the colours and fluxes of all the main sequence stars in this cluster.

You next want to work out the distance to a dwarf galaxy orbiting our own Milky Way. You measure the colours and fluxes of the stars in this galaxy, and find that they have fluxes that are typically one million times fainter than comparable colour stars in the nearby star cluster.

What is the distance to the dwarf galaxy (in parsecs)

Answer 1

Let's denote $d_1 =30 \;pc$ distance to the star cluster, $F_1$ - its flux, $d_2$ distance to the dwarf galaxy and $F_2$ - its flux.

$\displaystyle F \propto \frac{1}{r^2}$

Then,

$\displaystyle \frac{F_1}{F_2} = \frac{d^2_2}{d_1^2} = 10^6$

$d_2^2 = 10^6 \times d_1^2$

$d_2 = 10^3 \times d_1 =10^3 \times 30\; pc = 30\, 000 \; pc = 30 \; kpc$

Answer: 30 kpc.