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## Homework Statement

The main sequence can be approximated by a relation of the form L[itex]\propto[/itex]T^5 .

In Cluster A, a main sequence star called Star α has the same B – V colour as the Sun, and a V-band apparent magnitude of 11.3.

The effective temperature of Star α is 5800K. In Cluster B, a main sequence star called Star β has an effective temperature of 9000K and a V-band apparent magnitude of 17.0.

Derive an approximate value for the distance to Cluster B. {9}

I have already shown that Cluster A lies at an approximate distance of 200pc by using its absolute magnitude as 4.8 which was stated.

## Homework Equations

m[itex]_{a}[/itex]-M[itex]_{a}[/itex]=5log[itex]_{10}[/itex](d[itex]_{a}[/itex])-5

m[itex]_{b}[/itex]-M[itex]_{b}[/itex]=5log[itex]_{10}[/itex](d[itex]_{b}[/itex])-5

L=4[itex]\pi[/itex]σR[itex]^{2}[/itex]T[itex]_{eff}[/itex][itex]^{4}[/itex] ( However as in the question earlier on it says L is proportional to T^5 I don't think we can use this equation)

## The Attempt at a Solution

I have tried numerous ways but I can't seem to get the distance for cluster B on its own.

Also I do not really see how you can use L[itex]\propto[/itex]T[itex]^{5}[/itex] in the equations for the apparent and absolute magnitude.

I am so confused any help would be great, thanks