I am sure I get parts of the terminology wrong but if anyone can shed some light in the following:

I understand that for a given right ascension (RA) and declination (DEC), one has defined a ray (half-line) in the sky starting from the center of the earth towards infinity.

Now, if I also provide a angle, say`d`

degrees around that ray, I have essentially defined a cone in the sky. My question is the following:

Which steps (`RA_step`

and`DEC_step`

) should I use in the following loop, as a function of`d`

to ensure that I cover the entire sky and don't leave any patches anywhere?.

`for (RA = 0 ; RA <= 360 ; RA += RA_step) for (DEC = -90 ; DEC <= 90 ; DEC += DEC_step) examine-cone(RA, DEC, d)`

Imagine you are patching a plane with circles, instead of patching the sky sphere with circles (which is the same as filling the space with cones). Now, for every circle of diameter D define a square of diagonal D (D=2d). It is easier to patch the plane with squares, isn't it? So you have squares of side D/2*sqrt(2), and that is exactly your DEC_step, for each vertical sweep, and your RA_step, from sweep to sweep.

This will lead to a lot of duplicated examination (in fact you will examinate exactly the same place at the Poles once for each sweep) but you can be sure you'll not leave anything out of your squares.