# Object in or out of a circular field of view? (celestial coordinate system)

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In summary, to check if an object with position RA and dec is within a given circular field of view of radius R (in arcminutes) and centred at (0,0), you need to compute the distance d of the object from the center using the formula d = (RA^2+dec^2)^0.5 and check that d is less than R. However, this may not be accurate for small angular separations, as a change in RA gets smaller as you get nearer to the poles. A more accurate formula is sqrt(δdec^2 + cos^2(dec)*δRA^2), which can be found in the provided reference.

TL;DR Summary
Check that object with position RA and dec is within circle of radius R (in arcminute) ?
In celestial coordinate system (right ascension/declination), how to check if an object with position RA and dec is within a given circular field of view of radius R (in arcminutes) and centred at (0,0)?
R is small in this case so I assumed that I could compute the distance d of the object from the center as in cartesian coordinates: d = (RA^2+dec^2)^0.5 and check that d is less than R. Is that correct (at least for small angular separation) ?

Thanks !

Summary:: Check that object with position RA and dec is within circle of radius R (in arcminute) ?

In celestial coordinate system (right ascension/declination), how to check if an object with position RA and dec is within a given circular field of view of radius R (in arcminutes) and centred at (0,0)?
R is small in this case so I assumed that I could compute the distance d of the object from the center as in cartesian coordinates: d = (RA^2+dec^2)^0.5 and check that d is less than R. Is that correct (at least for small angular separation) ?

Thanks !
Not really. A change δdec is the same size everywhere, but a change δRA gets smaller as you get nearer the poles. So for small changes, the angular separation between two objects is give by sqrt(δdec^2 + cos^2(dec)*δRA^2). Of course this won't make much difference if you are at (0,0), which is on the equator.

Thanks a lot and sorry for the late reply. Do you have any reference for the formula that you give? I'd like to see how it is derived.
Thanks again.

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