Star Cluster
Clusters of stars
A star cluster is a group of stars that are gravitationally bound and typically formed from the same giant molecular cloud in space. These clusters can vary in size, composition, and age.
Type Of Clusters
There are two main types of star clusters:
I. Galactic Clusters (Open Clusters)
II. Globular Clusters
technique for determining distances
Distances to moving clusters
When a star (or cluster) is in motion through space with a velocity v, and this velocity forms an angle A with the line of sight, the velocity can be divided into two components:
- Radial Velocity (vr):
- Parallel to the line of sight.
- Responsible for the Doppler shift observed in the star's spectrum.
- Transverse Velocity (vT):
- Perpendicular to the line of sight is the transverse velocity (vT).
- Responsible for the star's motion across the sky, known as proper motion.
The velocity of the star is v, which makes an angle A with the line of sight. The radial and tangential components of the velocity are vr and vT, respectively.
\[v^2=v_r^2+v_T^2\]
\[v_r=v\ \cos A\]
\[v_T=v\ \sin A\]
\[\tan A=\frac {v_T}v_r \]
The proper motion µ, expressed in radians per second, is just the transverse velocity divided by the distance to the star d:
The dependence of the proper motion on the distance d and tangential speed
\[\mu [rad/s]=\frac {v_T\ [km/s]}{d \ [km]}\]
The apparent motion of a star across the sky, known as proper motion, is determined by its transverse velocity. A higher transverse velocity results in a faster observed motion. The proximity of the star also affects its apparent motion, with closer stars exhibiting more significant motion across the sky. Proper motions are generally small, typically a few arc seconds per year or less.
The relationship between proper motion (µ), velocity (v), and distance (d) can be expressed more conveniently by considering µ in terms of in arc seconds per year:
\[\frac {v_T}{[km/s]}=\frac {\mu}{[rad/s]} \frac {d}{[km]}\]
\[\mu \ [arc\ sec/yr]=\frac 1{4,74} \frac {v_r\ [km/s]}{d\ [pc]}\]