A star is orbiting the galactic center, and at a point in...

A star is orbiting the galactic center, and at a point in its orbit when it's heading in the direction toward Earth, it's moving at $64.8 \mathrm{~km} / \mathrm{s}$. An astronomer observes a spectral line emitted by hydrogen atoms in the star's atmosphere; the wavelength relative to the emitting atoms is $656.28 \mathrm{nm} .$ By how much will the astronomer observe this wavelength to be shifted?

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Key Concepts

Spectral Lines

Spectral lines are specific wavelengths of light that are either emitted or absorbed by atoms or molecules, characterizing the transitions between energy levels within these particles. In astronomical spectroscopy, these lines serve as fingerprints for identifying elements and measuring the Doppler shift caused by the relative motion of astronomical objects.

Radial Velocity

Radial velocity is the component of an object's velocity that is directed along the line of sight toward or away from the observer. It is a crucial concept in understanding the observed Doppler shifts in spectral lines since only the velocity component along the observer’s line of sight affects the wavelength measured. This concept allows astronomers to infer the motion of stars and other celestial bodies in space.

Doppler Effect

The Doppler Effect describes the change in wavelength (or frequency) of waves, including light, due to the relative motion of the source and the observer. When a light-emitting object moves toward the observer, the wavelengths are compressed (resulting in a blueshift), and when it moves away, they are stretched (resulting in a redshift). This effect is key in astrophysics for determining the velocities of stars and galaxies relative to Earth.

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