Suppose when we look in one half of the sky, the CMBR appears to be at a temperature of 2.725K. What is the peak wavelength in that direction? Are we moving toward or away from the region of space?
To determine the peak wavelength of the Cosmic Microwave Background Radiation (CMBR), we can use Wien's displacement law. It states that the peak wavelength (λpeak) of blackbody radiation is inversely proportional to its temperature (T).
The equation for Wien's displacement law is:
λpeak = (2.898 × 10^−3 m·K) / T
Given that the temperature is 2.725K, we can substitute this value into the equation:
λpeak = (2.898 × 10^−3 m·K) / 2.725K
Calculating this, we find:
λpeak ≈ 1.06 × 10^−3 meters
So the peak wavelength in that direction of the CMBR is approximately 1.06 millimeters.
To determine if we are moving toward or away from the region of space, we need additional information. The CMBR is considered to be the remnant radiation from the Big Bang, which uniformly fills the entire observable universe. However, on smaller scales, there can be slight variations in temperature due to the expansion of the universe and the motion of galaxies.
To determine our motion relative to the CMBR, we would need to know the CMBR dipole anisotropy, which represents the temperature fluctuations caused by our motion with respect to the CMBR rest frame. The CMBR dipole anisotropy shows that our galaxy, the Milky Way, is moving at a speed of approximately 371 km/s towards the direction of the constellation Hydra.
Therefore, based on the current understanding, we are moving towards the region of space from where the dipole anisotropy originates, which is in the direction of Hydra.