# How to find if a set of objects lies within a given resolution (5 arcsec) on a telescope?

I am new to astronomy and I was given the task of finding out if there are objects which can't be resolved by a telescope of resolution 5 arcseconds.

I was given the values of RA and Dec of these objects in degrees.

   RA              DEC
201.1999388    27.49294258
201.2048319    27.49212959
201.1984702    27.4978016
201.2025157    27.51610266
201.1997827    27.51743447 ...etc


How can I find these in the simplest way? Is there any simple formula which can be used to achieve this which is computationally efficient as well?

• Not clear what you mean. Do you mean you have a list of object positions and need to find out which pairs are unresolved or which objects are confused with at least one other object. Oct 8 '17 at 13:20
• @RobJeffries Yes, how to find which pairs that don't lie within 5 arcsec of each other. So by that definition find the pairs which might lie within that 5 arcsec resolution which might be confused with each other. Oct 8 '17 at 14:36
• Google "angular distance sphere"; you can actually use a shortcut if you know the points are close, but "premature optimization is the root of all evil", so try the precise formula first.
– user21
Oct 8 '17 at 17:02
• Is this an astronomy issue? If you know how to calculate the angular separation (simple trig formula), then the rest is an algorithmic problem, which doesn;t really belong here. Oct 8 '17 at 18:06