Angular separation

Angular separation or angular distance is a measure of the apparent distance between two points or objects, expressed in radians, assuming the observer at the vertex of the angle whose ends are the two points in question. The angular diameter is a particular case of angular separation.

Angular separation is a fundamental magnitude in Astronomy to determine the position of any object on the celestial sphere through its celestial coordinates, either in angular units or time units. The azimuth, height, declination, or right ascension of an object in the sky are, among others, celestial coordinates. Any of them is an angular distance to a reference point or plane: the horizon, the celestial equator, the southern meridian, etc.

Given the positions of two objects in the celestial sphere through their respective values of straight ascensions ${displaystyle alpha }$ and declines ${displaystyle delta }$ (Equatorial coordinates) expressed in shape angles ${displaystyle alpha in [0.2pi]}$ and ${displaystyle delta in [-pi /2,pi /2]}$ the angular separation between both objects is calculated by:

${displaystyle theta =arccos {Big [}operatorname {sen}(delta _{1})operatorname {sen}(delta _{2})+cos(delta _{1})cos(delta _{2})cos(cos(alpha _{1}-alpha _{2}){big}}}}}}}}}}{$

This expression is derived from basic spherical trigonometry and is therefore applicable not only to the positions of objects on the celestial sphere given by right ascension and declination, but also to those defined by any other pair of orthogonal great circles taken as angle reference, therefore we can use the same expression for, for example:

• Ecliptical coordinates, considering then that ${displaystyle alpha in [0.2pi]}$ is the ecliptic length and ${displaystyle delta in [-pi /2,pi /2]}$ ecliptic latitude
• Horizontal coordinates, considering then that ${displaystyle alpha in [0.2pi]}$ It's the Acimut. ${displaystyle delta in [-pi /2,pi /2]}$ the height

For visual observations without claims to accuracy, angular separation is also very useful, of course with approximations of the order of the degree, and of course very roughly. The hand and fingers are the measuring instrument, keeping the arm extended:

• The end of the finger covers approximately 1o
• If it's the thumb, it's 2nd.
• Index, middle and ring fingers, townhouses, 5o
• The fist closed, 10th
• From the end of the index to the of the meñique, extended, 15o
• Open hand, about 20th

Individual variations - length of the arm, thickness of the fingers, etc. - make the above values first approximations, but no less valid for locating a star or planet with the naked eye, or relating a constellation with their neighbors.

Angular separation is accurately measured using goniometers, sextants, and astronomical sextants.