Doppler Effect For A Moving Black Body
The relativistic Doppler effect causes a shift in the frequency f of light originating from a source that is moving in relation to the observer, so that the wave is observed to have frequency f':
where v is the velocity of the source in the observer's rest frame, θ is the angle between the velocity vector and the observer-source direction measured in the reference frame of the source, and c is the speed of light. This can be simplified for the special cases of objects moving directly towards (θ = π) or away (θ = 0) from the observer, and for speeds much less than c.
Through Planck's law the temperature spectrum of a black body is proportionally related to the frequency of light and one may substitute the temperature (T) for the frequency in this equation.
For the case of a source moving directly towards or away from the observer, this reduces to
Here v > 0 indicates a receding source, and v < 0 indicates an approaching source.
This is an important effect in astronomy, where the velocities of stars and galaxies can reach significant fractions of c. An example is found in the cosmic microwave background radiation, which exhibits a dipole anisotropy from the Earth's motion relative to this black body radiation field.
Read more about this topic: Black-body Radiation
Famous quotes containing the words effect, moving, black and/or body:
“Thinking is seeing.... Every human science is based on deduction, which is a slow process of seeing by which we work up from the effect to the cause; or, in a wider sense, all poetry like every work of art proceeds from a swift vision of things.”
—Honoré De Balzac (1799–1850)
“O what venerable and reverend creatures did the aged seem! Immortal Cherubims! And young men glittering and sparkling Angels, and maids strange seraphic pieces of life and beauty! Boys and girls tumbling in the street, and playing, were moving jewels. I knew not that they were born or should die; but all things abided eternally as they were in their proper places.”
—Thomas Traherne (1636–1674)
“It’s not like I was out there running and not knowing what’s going on in the country. I knew what was going on, but I felt this is not something that is going to bog me down and not let me participate. The only way I was going to make a difference for myself or any other black person is to say the hurdles were there and do what I had to do.”
—Wyomia Tyus (b. 1945)
“The body prospered, teeth in the marrowed gums,
The growing bones, the rumour of manseed
Within the hallowed gland, blood blessed the heart....”
—Dylan Thomas (1914–1953)