Can someone help me find the D (Mpc) of the group, pair and cluster?

Question

Below is a table of data for pairs/groups/clusters of galaxies. The apparent angular diameter in mm of the largest spiral galaxy in each has been measured on the Lick Sky Atlas or Canterbury Sky Atlas (northern and southern hemisphere 15 degree square photograph prints). If we assume that the largest spiral in any group or cluster has the same linear diameter as M31 (the largest spiral in our local group of galaxies) then the distance to the other galaxies can be calculated since we know the angular diameter of M31 (28mm) and its distance (about .7 Mpc). The relation is:
Dgalaxy=dM31x(theta)M31/(theta)galaxy
What?

Can you show me the correct way to use the formula to find this out? Also plug in the numbers so I can see what you did.

D= distance

Galaxy Largest Spiral D(Mpc) Radial Velocity (km/sec)
Sculptor Group/ NGC 55 / ?/ 279/
Formax Cluster/ NGC 1380/ ?/ 1384/
NGC 2985 Pair/ NGC 3027/ ?/ 1327

Formula: Dgalaxy=dM31x(theta)M31/(theta)galaxy

continued:
(theta)galaxy

Answer 1

Hi. The formula simply determines an estimate of the distance of large (M31 sized) galaxies based on the number of millimeters of size on an image. Lots of assumptions here, as with all far away astronomy, but on average it should be a good estimate. They use M31 because it's distance is known. (Mpc is a Mega Parsec. 1 parsec is the distance at which an object shifts 1 arc second against the far background due to Earth's moving from one point in it's orbit to the point half way around, or about 93 million miles times two. http://en.wikipedia.org/wiki/Parsec )