[Physics of Binary Stars] [Astronomy] [Topics]
The Doppler effect is the apparent change in the frequency of a wave motion when there is relative motion between the source of the waves and the observer.Well known examples include the change in pitch of an ambulance or police siren, as it approaches and then recedes from you, or the same effect from a passing train. The Doppler effect is observed for ALL wave motions (from g to radio), where there is relative motion. It is extensively used in astronomy to deduce the component of velocity in the line-of-sight of an approaching or receding planet/star/galaxy etc. Some examples are discussed below. Details of the Doppler effect may be found in any A-level (or equivalent) textbook, including a derivation of the general formulae for the Doppler effect:
D f/f = v/c
Note that these equations
use v as the velocity of the source and that v is assumed positive
when the source is approaching the Earth (ie. if the source
moves towards the Earth,)
Df is +ve (f increases)).
These equations are
they are only true
when v << c.
and the Expansion of the Universe:
We can observe features in the spectra obtained from distant galaxies and compare
their wavelengths/frequencies with those measured in the laboratory. We find that,apart from galaxies within our Local Group (such as the Andromeda spiral), the light from distant galaxies has been "red-shifted" - the wavelengths of spectral lines are longer than those measured on Earth (ie. Dl is +ve) SO THESE GALAXIES ARE MOVING AWAY FROM US. This is a consequence of the general expansion of the Universe: all clusters of galaxies are moving away from each other.
(ii) Hubble's Law and the Age of the Universe:
and, even more useful:
VELOCITY OF GALAXY µ DISTANCE OF GALAXY FROM EARTH
This relation is expressed
in Hubble's Law:
The most distant galaxies
observed through the world's largest telescopes have recession velocities
approaching that of light. Setting v = c in Hubble's equation gives a distance
to the edge of the observable universe of d = c/H = 6000Mpc, around about
We can also use Hubble's Constant (H) to estimate the age of the universe if we assume that the universe has always expanded at its present rate. Of course, this is probably not true, but at least it gives us an order of magnitude for how long the universe has existed. The idea is as follows:
Suppose we measure the distance to galaxy "Z" by some means other than the Doppler effect, and find that Z is 50Mpc away. The value of H = 50000ms-1 Mpc-1 , giving the recession velocity of this galaxy (ie. its speed away from us) as v = Hd = 2.5 x 106 ms-1 . So now calculate how long it has taken (T), at this speed, to move 50Mpc away from us - this will be the time since our galaxy and galaxy Z were together in the Big Bang.
1pc = 3.26ly = 206265AU = 3.09 x 1016 m, so 50Mpc = 1.55 x 1024 m
T = Distance gone/speed = 2 x 1010y
Note that we must use
a value for the distance to Z that has been obtained independently of v
= Hd, otherwise we are simply proving that x = x !
At position X, star S1 is approaching the Earth and its line is blue-shifted, while S2 is receding from the Earth and its line is red-shifted.
(a) A continuous
spectrum plus some absorption lines:
these are the features produced
by the Sun itself, just being reflected to us,
(b) Additional absorption lines due to certain wavelengths of the solar radiation having been absorbed by materials in the atmosphere of the planets. These extra absorption features allow us to deduce the chemical composition of the atmospheres of Jupiter, Saturn etc.
(c) Since the planet is rotating, the light that it reflects is Doppler shifted. Light from the edge of the planet approaching us is blue-shifted, and vice versa.
(v) Doppler Broadening of spectral lines:
The atoms/molecules/ions that are emitting light within a star are not at rest: they are moving around in random directions, at high speed - the speed is determined by the temperature of the hot gas. The radiation emitted therefore suffers a Doppler shift, depending on the motion of the atom when it was emitted. Since the atom could be directly away from us, directly towards or somewhere in between, the radiation produced is not observed at one specific wavelength, but a slight spread in l occurs. This effect is called Doppler Broadening.
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