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

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Discussion Overview

The discussion revolves around determining whether an object, defined by its right ascension (RA) and declination (dec) in the celestial coordinate system, lies within a specified circular field of view of radius R (in arcminutes) centered at the coordinates (0,0). The focus is on the mathematical approach to calculating angular separation and the implications of small angular separations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant proposes calculating the distance d from the center using d = (RA^2 + dec^2)^0.5 and checking if d is less than R, assuming small angular separations.
  • Another participant challenges this approach, noting that a change in declination (δdec) is consistent, while a change in right ascension (δRA) varies with declination, suggesting that the angular separation should be calculated using the formula sqrt(δdec^2 + cos^2(dec)*δRA^2).
  • A request for references to support the formula provided is made, indicating interest in its derivation.
  • A later reply provides a link to a resource that includes the formula and additional general formulae for larger differences in coordinates.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial method proposed for calculating angular separation, as one participant offers a correction and an alternative formula. The discussion reflects differing views on the appropriate approach to the problem.

Contextual Notes

The discussion highlights the dependence of angular separation calculations on the position in the celestial coordinate system, particularly the variation of δRA with declination. There is an acknowledgment of the limitations of the initial approach for larger angular separations.

vladivostok
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TL;DR
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 !
 
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vladivostok said:
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.
 
vladivostok said:
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.
Here's a good link. The formula I gave is down near the bottom of the page. It also has more general formulae for when the differences of the coordinates are not small.
http://spiff.rit.edu/classes/phys373/lectures/radec/radec.html
 
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Great, thanks !
 

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