The Balmer Hαabsorption line in the spectrum for the star...

The Balmer $\mathrm{H}_\alpha$ absorption line in the spectrum for the star Vega is observed to be shifted to $6562.5 \AA$, the star is observed to change its angular position on the celestial sphere by 0.35 " per year, and the parallax shift of Vega is found to be $0.130 "$. What are the radial, tangential, and space velocities for Vega?

Key Concepts

Doppler Effect

The Doppler effect in astronomy refers to the change in the observed wavelength (or frequency) of light from an object moving relative to the observer. When a star moves toward or away from us, its spectral lines shift from their rest wavelengths. This shift can be measured to determine the star's radial velocity, which is the component of the star’s motion along the line of sight.

Proper Motion

Proper motion is the apparent angular motion of a star across the sky, typically measured in arcseconds per year. It reflects the star's movement tangentially, across the line of sight. When combined with the distance to the star, proper motion can be converted into a tangential velocity, representing the actual speed of the star perpendicular to our line of sight.

Parallax

Parallax is the apparent shift in the position of a nearby star against the background of distant stars due to the Earth’s orbit around the Sun. By measuring this shift, astronomers can calculate the distance to the star using trigonometric methods. Knowing the distance is essential for converting angular measurements, such as proper motion, into physical velocities.

Space Velocity

Space velocity is the total velocity of a star through space, taking into account both its radial and tangential components. It is computed by combining the radial velocity (from the Doppler shift) and the tangential velocity (derived from proper motion and distance). This gives a complete picture of the star's motion relative to the observer.

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