**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,

D_{1} × θ_{1} = D_{2} × θ_{2 .}

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,

D_{θ} = 18,800 / θ where θ is measured in arcminutes

#### Spiral Galaxies

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

D_{θ} = 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.*