Positions and Velocities of Stars

Determining Positions and Velocities of Stars

Understanding the galaxy requires knowing the positions and velocities of celestial objects.
Positions and velocities are essential for determining:
- The orbit of the solar system around the galaxy.
- The locations and trajectories of nearby stars.
To fully define the phase space of position and velocity in a three-dimensional universe, six parameters are needed.
- Three dimensions for position (x, y, z).
- Three velocity components (velocity in x, y, z).

Instead of Cartesian coordinates, a spherical coordinate system is typically used.
Components:
- Distance: Determined using parallax. The inverse of parallax gives the distance to the object.
- Two Coordinates: Define the direction of the star in the sky.
  - Right Ascension and Declination (common).
  - Galactic coordinates, ecliptic coordinates, or other systems could also be used.
Together these parameters fully constrain the position of a star relative to Earth.

Velocity is not measured in x, y, and z components because stars are observed on a flat plane of the sky.

Velocity component in the plane of the sky.
Transverse to the line of sight.
Needs two directions (e.g., up/down, left/right in the sky).
Measured as the angular change of a star's position over time.
Observed by measuring the star's position over a year. The star will appear to move, tracing a curlicue spring pattern due to the combination of parallax and proper motion.
Units: milliarcseconds per year (mas/yr).
Requires precise instrumentation, and large surveys like the Gaia mission are dedicated to measuring proper motions.

European Space Agency telescope.
Undertaking a ten-year survey to measure:
- Parallaxes.
- Proper motions.
- Other properties of a billion stars across the galaxy.

Velocity component along the line of sight (towards or away from us).
Hardest to measure.
Determined using the Doppler shift of spectral lines.
Stars have unique spectral signatures at specific wavelengths.
The observed wavelengths are shifted depending on the star's motion.
Analogy: Similar to how the frequency of an ambulance siren changes as it moves towards or away from you.
Radial velocities can also change due to:
- The presence of exoplanets.
- The star being part of a binary system.
  - The star exhibits periodic motion toward and away from the observer as it orbits the center of mass of the system.

Catch-all term for parallax and proper motion measurements.
Can also be used to detect exoplanets.
The presence of a planet causes small deviations in the star's astrometric motion.

Radial velocity only measures motion along the line of sight.
Motion perpendicular to the line of sight is not detected.
Example: In a binary star system orbiting in a plane transverse to the observer, radial velocity shifts may be minimal.

Position:
- Right ascension, declination, and parallax.
Velocity:
- Proper motion (two components).
- Radial velocity.
These six parameters fully define a star's position and velocity, which are essential for understanding the structure and dynamics of the galaxy.