Q: What is the average apparent magnitude in the K filter for
RR Lyrae stars in the cluster M3?
The average of the K-band apparent magnitudes is about
m(K) = 14.70
Q: The absolute magnitude of RR Lyrae stars in the K filter is approximately
M(K) = -0.35
What is the distance to the cluster M3?
First, we compute the difference between apparent and absolute
magnitudes, which is called the "distance modulus"
m(K) - M(K) = 14.70 - (-0.35) = 15.05 mag
Next, we use the distance modulus formula to calculate the
distance to the cluster:
(m - M) = 15.05 = 5*log(d) - 5
5*log(d) = 20.05
log(d) = 4.01
d = 10^(4.01) = 10,200 pc