Suppose when we look in one half of the sky, the CMBR appears to be at a temperature of 2.72K. What is the peak wavelength in that direction? Are we moving toward or away from the region of space? What is our velocity with respect to the CMBR?
To determine the peak wavelength in the direction you mentioned, we need to use Wien's displacement law. The formula for calculating the peak wavelength is given by:
λ = (2.89777 × 10^-3 m·K) / T
where λ is the peak wavelength in meters, 2.89777 × 10^-3 m·K is the Wien's displacement constant, and T is the temperature in Kelvin.
Substituting the temperature of the CMBR (2.72K) into the formula, we get:
λ = (2.89777 × 10^-3 m·K) / 2.72K
Simplifying the calculation, we find that the peak wavelength in the given direction is approximately 1.066 × 10^-3 meters or 1.066 millimeters.
To determine whether we are moving toward or away from the region of space, we need to consider the Doppler effect. The Doppler effect describes the change in frequency or wavelength of a wave due to the relative motion between the source and the observer.
The CMBR represents the radiation leftover from the Big Bang and is isotropic on large scales, meaning it appears the same in all directions. Therefore, the observed temperature of the CMBR is independent of the motion of the observer.
However, if we want to calculate our velocity with respect to the CMBR, we need to consider the motion of our Galaxy, the Milky Way, in the universe. Our Galaxy moves relative to the CMBR due to its peculiar velocity.
The Milky Way is moving towards a region of space known as the Great Attractor, which is a massive concentration of matter. But in addition to this motion, our Galaxy is orbiting around the center of the Local Group of galaxies, which includes the Milky Way and nearby galaxies such as Andromeda.
The exact velocity of the Milky Way with respect to the CMBR can be complex to determine precisely. However, estimates indicate that the Milky Way's peculiar velocity with respect to the CMBR is around 630 km/s.
Therefore, our velocity with respect to the CMBR is roughly 630 km/s, carrying out the motion caused by the Milky Way's motion through the universe.