# Measuring Angular Diameters of Star Clusters or Galaxies

Measuring angular sizes

• Use the measurement tool in Afterglow. Record measurements in arc minutes.
• For star clusters make four diameter measurements, along the horizontal, vertical and two diagonals.
• For spiral galaxies, measure only the major axis but take at least independent 3 measurements.
• Record these measurements in a table.
• Take an average of the measurements for the final estimate.

Calculating distances from angular size

Once you have the angular size of an object, it is fairly easy to find the distance if you know the true physical size.  Remember, there is a direct relationship between the angular size (diameter) and the distance to that object.  The relationship can be described by,

D1 × θ1 = D2 × θ2 .

In this equation, one is saying that the distance (D) to a cluster, for example, times its angular size θ is the same for all clusters.  This holds true as long as the open clusters have the same physical size.

#### Clusters

In order to find the actual distance to a cluster, we need to have a reference cluster for which we know the distance.  Fortunately, there is just such a cluster, the Hyades.  Using a different method, we know that the Hyades is 47 parsecs away, and measures 400′ in diameter.  Therefore, you can find the distance (in parsecs) to any one of your clusters by simply using,

Dθ = 18,800 / θ  where θ is measured in arcminutes

#### Spiral Galaxies

For spiral galaxies, the reference is just the typical size of a galaxy,

Dθ = 30 kpc/ θ where θ is measured in radians

There are 206265 arcseconds or 3438 arcminutes per radian

Record your distances in your table and include this table with your report.