A friend in astronomy had a question which stumped me. Astronomical telescope observations are typically pointed at a center coordinate provided in right ascension in [0º, 360º] and declination in [+90º, -90º]. The region of the sky that is imaged on the (usually rectangular) detector is typically quoted in angle subtended in each direction (e.g. 1 degree by 1 degree).
Suppose you have some points that define corners of this field of view, like (-0.5º, 0.5º), (0.5º, 0.5º), (0.5º, -0.5º), (-0.5º, -0.5º).
Then you point the telescope at (RA, Dec) = (0º, +90º).
How can you compute the angular coordinates of the corners? The spherical coordinates mean it's not simple addition, of course. I tried converting from spherical coordinates to (x, y, z) Cartesian coordinates (taking r = 1), but I'm having difficulties making sense of "1 degree square" at the pole.
I know it's not formally correct to say that, but this visualization he's making should look approximately correct to an astronomer if we treat the coordinates appropriately. There's another free parameter for the rotation of the footprint, I guess, but one sensible representation could be (0, 89.5º), (90º, 89.5º), (180º, 89.5º), (270º, 89.5º).
Is there a "sensible" interpretation to use there? How would I go about calculating these points?