I am using the SIMBAD database for Alnitak, Saiph, and Sirius:
Alnitak ; FK5 coord. (J2000): RA = 05 40 45.527 DEC = -01 56 33.26;
Saiph ; FK5 coord. (J2000): RA = 05 47 45.389 DEC = -09 40 10.58;
Sirius ; FK5 coord. (J2000): RA = 06 45 08.917 DEC = -16 42 58.02;
What is the trigonometric relationship in degrees (length of sides and inclusive angles to four decimal places) between these three stars when they are used to form a triangular aterism?
This is a relatively straightforward application of spherical trigonometry. (See also: About coordinate systems and angle differences and Angular Distance Between Two Points on a Sphere)
The expression to compute the angle on the celestial sphere between to points is: $$\Psi = \arccos\left(\sin\theta_1\sin\theta_2 + \cos\theta_1\cos\theta_2\cos(\phi_1-\phi_2)\right)$$ where $\Psi$ is the angular separation, $\phi_1$ and $\phi_2$ are the right ascensions of the first and second direction, and $\theta_1$ and $\theta_2$ are the declinations of the first and second direction.
| Star Pair | Separation (deg) |
|---|---|
| Alnitak - Saiph | 7.9203 |
| Alnitak - Sirius | 21.6568 |
| Saiph - Sirius | 15.6351 |
I am including my conversion of the RA and DEC to degrees in case I have made a mistake if anyone wants to check my computations.
| Star | RA (HH MM SS) | RA (deg) | DEC (DD MM SS) | DEC (deg) |
|---|---|---|---|---|
| Alnitak | 05 40 45.527 | 85.1897 | -01 56 33.26 | -1.9426 |
| Saiph | 05 47 45.389 | 86.9391 | -09 40 10.58 | -9.6696 |
| Sirius | 06 45 08.917 | 101.2872 | -16 42 58.02 | -16.7161 |
