The displacement of a star through the universe is not directly determined by the wavelength of light it emits. The displacement of a star, or any celestial object, is primarily determined by its motion relative to an observer, such as Earth. This motion is typically described in terms of its velocity and direction.
However, the wavelength of light emitted by a star can provide important information about its motion relative to the observer through the phenomenon known as the Doppler effect. The Doppler effect describes how the observed wavelength of light is affected by the relative motion between the source of light and the observer.
When a star is moving away from the observer, the wavelength of the light it emits is stretched or "redshifted." This means that the observed wavelength is longer than the wavelength of the emitted light. On the other hand, if the star is moving towards the observer, the observed wavelength is compressed or "blueshifted," resulting in a shorter wavelength compared to the emitted light.
By measuring the redshift or blueshift of the light from a star, astronomers can determine its radial velocity, which is the component of its velocity directly along the line of sight. This radial velocity information, along with other observations and techniques, can be used to study the motion of stars, galaxies, and other celestial objects in the universe.
It's important to note that while the wavelength of light can provide information about an object's motion, it is not the sole determinant of displacement. Other factors such as proper motion, gravitational interactions, and the overall structure and dynamics of the universe play significant roles in understanding the motions and displacements of celestial objects.