Final answer:
The angular separation between Proxima Centauri and Alpha Centauri is calculated using their celestial coordinates and applying the spherical law of cosines. The coordinates in Right Ascension and Declination are converted to decimal form and then used in the formula to determine the angular distance.
Step-by-step explanation:
The angular separation between Proxima Centauri and Alpha Centauri can be found by using their celestial coordinates given in Right Ascension (RA) and Declination (Dec). To calculate the angular distance, we use the spherical law of cosines which is applied to celestial sphere coordinates. For Proxima Centauri (RA=14:29:42.95, Dec=-62:40:46.1) and Alpha Centauri (RA=14:39:36.50, Dec:-60:50:02.3), the angular separation δ can be calculated using the formula:
δ = cos-1 [sin(Dec1)sin(Dec2) + cos(Dec1)cos(Dec2)cos(RA1 - RA2)]
To get the RA and Dec in decimal form, we convert the given times and angles into degrees, minutes, and seconds, remembering that there are 15 degrees in one hour of RA since the celestial sphere is 360 degrees and there are 24 hours in a celestial day. We then use these values in the formula above to get the angular distance in degrees.
The angular separation is important for observational astronomy as it helps to determine the position and distance between stars. Proxima Centauri and Alpha Centauri, as part of the same system, have a small angular separation as viewed from Earth, but they are separated by more than 0.2 light-years in space.