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Ambulance analogy
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First the pitch became higher, then lower.
Originally discovered by the Austrian mathematician and physicist, Christian
Doppler (1803-53), this change in pitch results from a shift in the frequency of the
sound waves
As the ambulance approaches, the sound waves from its siren are compressed
towards the observer.
The intervals between waves diminish, which translates into an increase in
frequency or pitch.
As the ambulance recedes, the sound waves are stretched relative to the observer,
causing the siren's pitch to decrease.
By the change in pitch of the siren, you can determine if the ambulance is coming
nearer or speeding away.
If you could measure the rate of change of pitch, you could also estimate the
ambulance's speed.
Redshift
• A redshift is a shift in the frequency of a photon toward
lower energy, or longer wavelength.
• The redshift is defined as the change in the wavelength
of the light divided by the rest wavelength of the light
• The Doppler Redshift results from the relative motion
of the light emitting object and the observer.
• If the source of light is moving away from you then the
wavelength of the light is stretched out, i.e., the light is
shifted towards the red.
• These effects, individually called the blueshift, and the
redshift are together known as doppler shifts
Gravitational Redshift
• According to General Relativity, the wavelength of light
(or any other form of electromagnetic radiation)
passing through a gravitational field will be shifted
towards redder regions of the spectrum.
• To understand this gravitational redshift, think of a
baseball hit high into the air, slowing as it climbs.
• Einstein's theory says that as a photon fights its way
out of a gravitational field, it loses energy and its color
reddens.
• Gravitational redshifts have been observed in diverse
settings.
Cosmological Redshift
• Atoms emit or absorb light in characteristic wavelengths: hydrogen,
helium, and all the other atomic elements have their own spectrum
signatures.
• In the early part of this century, Vesto Slipher was studying the
spectra of light emitted from nearby galaxies.
• He noticed that the light coming from many galaxies was shifted
toward the red, or longer wavelength, end of the spectrum. The
simplest interpretation of this "redshift" was that the galaxies were
moving away from us.
• Hubble, who had been the first to establish that the universe
included many other galaxies outside of our own, noticed
something else: the galaxies were receding from us at a velocity
proportional to their distance. The more distant the galaxy, the
greater its redshift, and therefore the higher the velocity, a relation
known as Hubble's Law.
Dynamical Timescales
• For a star, the dynamical time scale is defined as
the time that would be taken for a test particle
released at the surface to fall under the star's
potential to the centre point, if pressure forces
were negligible.
• In other words, the dynamical time scale
measures the amount of time it would take a
certain star to collapse in the absence of any
internal pressure.
• As an example, the Sun dynamical time scale is
approximately 2250 seconds
Thermal Timescale
The Law of Orbits
Other
applications
of the
Electric field Light
inverse
square law
Sound
Radiation
The elliptical shape of the orbit is a result of
the inverse square force of gravity
The Law of Areas
This is one of Kepler's
laws.This empirical law
discovered by Kepler arises
from conservation of
angular momentum. When
the planet is closer to the
sun, it moves faster,
sweeping through a longer
path in a given time.
L = mvr
The Law of Periods
Binary Stars
Eclipsing binary stars are those whose orbits form a horizontal line from
the point of observation; essentially, what the viewer sees is a double
eclipse along a single plane; Algol for example.
A visual binary system is a system in which
two separate stars are visible through a
telescope that has an appropriate resolving
power. These can be difficult to detect if one of
the stars’ brightness is much greater, in effect
blotting out the second star.
Spectroscopic binary stars are those systems in
which the stars are very close and orbiting very
quickly.
•These systems are determined by the
presence of spectral lines – lines of color that
are anomalies in an otherwise continuous
spectrum and are one of the only ways of
determining whether a second star is present.
• It is possible for a binary star system to be
both a visual and a spectroscopic binary if the
stars are far enough apart and the telescope
being used is of a high enough resolution.
•Black holes are the result of a massive star (approximately greater than 4 solar masses)
that ends its life cycle (nuclear fusion) and collapses in on itself
•Discuss the life cycle of a star
•Photons always travel at the speed of light, but they lose energy when travelling out of a
gravitational field and appear to be redder to an external observer (because red is less
energetic than blue, for instance)
•The stronger the gravitational field, the more energy the photons lose because of this
gravitational redshift
• The extreme case is a black hole where photons from within a certain radius lose all their
energy and become invisible
•Black holes ‘trap’ light, but at the same time force light to move at a constant speed C
•Black holes bend spacetime over on itself to force light to go towards the center referred
to as ‘singularity’
•Just as travelling in a straight line, no matter the direction, on a three dimensional object
like Earth will bring you back to the same point, singularity works the same way in four
dimensions
•Singularity is a point believed to be in black holes of infinite density
•Black holes cannot be directly observed, which is really frustrating
•Instead, we observe objects around them
•Stars moving in binary systems without a noticeable companion are generally candidates
for black holes
•Stars forming accretion disks are also candidates for black holes
•As the matter in the accretion disk loses energy and spirals downward into the black hole
it is heated to very high temperatures and emits X-rays.
•Generally, any binary star system in which there is a strong X-ray source and in which one
of the stars is not seen but is very massive is a good candidate for a black hole.
1. An x-ray source was discovered in the constellation Cygnus in 1972 (Cygnus X-1). X-ray
sources are candidates for black holes because matter streaming into black holes will be
ionized and greatly accelerated, producing x-rays.
2. A blue supergiant star, about 25 times the mass of the sun, was found which is
apparently orbiting about the x-ray source. So something massive but non-luminous is
there (neutron star or black hole).
3. Doppler studies of the blue supergiant indicate a revolution period of 5.6 days about
the dark object. Using the period plus spectral measurements of the visible companion's
orbital speed leads to a calculated system mass of about 35 solar masses. The calculated
mass of the dark object is 8-10 solar masses; much too massive to be a neutron star
which has a limit of about 3 solar masses - hence black hole.
This is of course not a proof of a black hole -- but it convinces most astronomers.