91Ó°ÊÓ

Redshift occurs when light or other electromagnetic radiation from an object undergoes an increase in wavelength, or shift toward the red end of the spectrum. This typically happens due to the object moving away from the observer.
Redshift is a key concept in astrophysics as it helps measure the speed and distance of galaxies moving away from us due to the expanding universe.

• The amount of redshift can tell us how fast the object is moving away.
• Measured by the change in wavelength, compared to the light emitted by the object in a stationary state.

The formula for redshift (\(z\)) is given by:\[z = \frac{\lambda_{observed} - \lambda_{emitted}}{\lambda_{emitted}}\]where \(\lambda_{observed}\) is the observed wavelength and \(\lambda_{emitted}\) is the emitted wavelength in a non-moving frame. This ratio helps astrophysicists to determine how the universe is expanding by observing distant quasars and galaxies.

Recession velocity describes the speed at which an astronomical object is moving away from the observer. It is a key measure in cosmology for understanding the expansion rate of the universe.
The recession velocity leads to the observed redshift due to the Doppler Effect.

• In classical physics, recession velocity can be calculated using the simple Doppler shift formula.
• However, as seen in our exercise, it can sometimes suggest speeds faster than light, which is not physically possible.

For such high velocities, relativistic physics comes into play to provide an accurate description. Instead of being limited by the speed of light, recession velocity in an expanding universe is based on an understanding from Einstein's theory of relativity.

Relativistic physics deals with conditions where speeds approach the speed of light, requiring adjustments to classical mechanics. In our context, this especially influences how we calculate recession velocity.
In relativistic physics, the Doppler effect is modified to accommodate the high speeds by using the relativistic Doppler equation: \[\frac{\lambda_{observed}}{\lambda_{emitted}} = \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}\]where \(v\) is the velocity of the source, and \(c\) is the speed of light. This formula avoids implying any object can move faster than light.

• It combines time dilation with the classical Doppler effect.
• Ensures velocity calculations remain within the bounds set by relativity.

Thus, relativistic physics provides tools to continue analyzing objects in motion near or at the speed of light, offering a more accurate understanding of cosmic expansion and high-speed astronomical phenomena.