 # Distance And Age Of M52

The upper point on the main sequence which is the most densely populated with stars where the red giants seem to begin is called the turnoff point; the exact location of turnoff point indicates the age of the cluster.
Deriving the distance and age of M52

We have already identified main sequence, turnoff point, and giant red for M52 shown in figure by comparing with Figure 1. A best fit line this will help to find the distance to open cluster M52 by using the techniques of best fit line.

In table 1 (The Open University, 2015, p.11) the value for colour excess E (B-V) = 0.65 noted for the M52 cluster; E(B-V) indicates an interstellar extinction which is caused by gas and dust in the line of sight resulting in dimmer magnitudes of stars than
The turnoff point located 11.4 indicating the rough age of the M52 cluster.

Deriving the distance and age of M39

In comparison with Figure 1 the main sequence, turnoff point, and giant red for M39 are identified and clearly shown in figure 3.

As before the colour excess for M39 is 0.01 resulting Av = 3× 0.01 = 0.03. The apparent magnitude mv is 8.8 and the absolute magnitude Mv is +0.70. The uncertainty in the main sequence recorded the maximum value 15.00 and minimum value 9.00 in Y-axis which gives 15.00-9.00 = ± 6.00. Now we need to plug all known values in equation 1 to calculate distance in parsec as below:

d = 10 (8.8-0.70+5-0.03) /5 = 10 2.6 = 398.10 ± 6.00 parsec= 392.10 parsec × (3.261 light year/ 1 parsec) = 1278.86 light year= 1.279 × 103 light year

The published distance for M39 is 326 parsec (Mavers, 1940). To calculate the percentage error, using equation 2 we get

Gives us percentage error = ((392.10-326)/326) ×100

Percentage error = 20.27 %. The turnoff point located at 8.8 indicating the rough age of the M39 cluster. Also, points lying lower than the 16th magnitude below to the left of the Main Sequence for M39 are considered to be interpolar