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 of the Cosmic Microwave Background Radiation (CMBR) in the specified direction, we can use Wien's displacement law. This law states that the peak wavelength (λ_peak) of a black body at a given temperature (T) is inversely proportional to the temperature:
λ_peak = b / T,
where b is Wien's displacement constant (approximately 2.898 × 10^(-3) m·K). Substituting the given temperature of 2.72K, we find:
λ_peak = 2.898 × 10^(-3) m·K / 2.72K.
Performing the calculation:
λ_peak ≈ 1.064 × 10^(-3) m,
or approximately 1.06 millimeters.
Now, let's move on to determining our motion with respect to the CMBR. The observed temperature of the CMBR is not affected by our motion directly but can be influenced by the Doppler effect due to our relative velocity. The Doppler effect results in a shift in the measured temperature.
If the CMBR appears at the expected temperature of 2.72K, it implies that we are not moving towards or away from the region of space where the CMBR is observed. In other words, our velocity relative to the CMBR in that direction is negligible.
To recap:
- The peak wavelength in the specified direction is approximately 1.06 millimeters.
- We are not moving towards or away from the region of space where the CMBR is observed.
- Our velocity with respect to the CMBR in that direction is considered negligible.