Q: What is the average apparent magnitude in the V filter for
RR Lyrae stars in the Draco dwarf galaxy?
The average of the V-band apparent magnitudes is about
m(V) = 20.20
Q: The absolute magnitude of RR Lyrae stars in the V filter is approximately
M(V) = +0.77
What is the distance to the Draco dwarf galaxy?
First, we compute the difference between apparent and absolute
magnitudes, which is called the "distance modulus"
m(V) - M(V) = 20.20 - (+0.77) = 19.43 mag
Next, we use the distance modulus formula to calculate the
distance to the cluster:
(m - M) = 19.43 = 5*log(d) - 5
5*log(d) = 24.43
log(d) = 4.89
d = 10^(4.89) = 77,000 pc = 77 kpc