Ambulance analogy First the pitch became higher, then lower.

2. Ambulance analogy • 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.

3. 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

4. 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.

5. 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, VestoSlipher 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.

6. 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

7. Thermal Timescale

8. The Law of Orbits

9. The elliptical shape of the orbit is a result of the inverse square force of gravity

10. This is one of Kepler'slaws.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. The Law of Areas L = mvr

11. The Law of Periods

12. Binary Stars

13. 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.

14. A visual binary systemis 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.

15. 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.

16. 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

17. 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.