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Doppler Shift. Consider a stationary point source emitting light waves. Doppler Shift. If source moves away, light appears redder than it is. If source moves towards us, light appears bluer. Visible light.
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Doppler Shift Consider a stationary point source emitting light waves
Doppler Shift If source moves away, light appears redder than it is. If source moves towards us, light appears bluer.
Visible light The shift in the light waves is proportional to the relative speeds of the source and observer
Doppler Shift Wavelength is shorter when approaching Stationary waves Wavelength is longer when receding
Wavelength shift -v l - lo Dl l c lo Assume radial speed, v, of glowing object is small compared to speed of light, c v << c. l0 is reference wavelength of medium at rest. = =
Frequency shift v f - fo f c Df = = f
Example calculation • The star Vega has a hydrogen line of 656.255nm, which is shifted from the reference value of 656.285 nm. • Is it moving towards us or away? • Calculate its speed Red shifted to LONGER wavelength so moving away. Speed is –13.7 km/s.
Rotation speed of galaxy from 21-cm spectral line of Atomic hydrogen
Historical Note • Using the Doppler shift, Edwin Hubble observed that the Universe is expanding!
What Hubble Found The Hubble constant Ho = 558 km s -1Mpc -1 is the slope of these graphs Compared to modern measurements, Hubble’s results were off by a factor of ten!
Hubble’s Law v = Ho d Ho is called the Hubble constant. It is generally believed to be around 65 km/sec/Mpc… plus or minus about 10 km/sec/Mpc. • Note: The further away you are, the faster you are moving!
Implications of Hubble’s Law Distance = velocity/(Hubble constant) • To get a rough idea of how far away a very distant object is from Earth, all we need to know is the object's velocity. • The velocity is relatively easy for us to measure using the Doppler effect, or Doppler shift.
Caveat! Space between the galaxies expands while galaxies stay the same size
The Tools of All Astronomy • Light Curves – examining how bright something is • as a function of time • Images – examining what something • looks like spatially • Spectra – examining how much energy an object • emits as a function of energy
The Atom’s Family • Bohr atom • Electrons in fixed orbits around… • Protons and neutrons in the nucleus • Only certain electron orbits are allowed • Electrons jump between orbits to make photons of specific energies
Periodic Table Electrons fill shells labeled s, p, d, f, etc. New shells are added
The Atom’s Family Dx Dp = h/2 > • Quantum atom • Electrons are clouds of probability density • No two electrons can have identical quantum numbers Pauli exclusion principle • Heisenberg Uncertainty principle limits knowledgeour simultaneous knowledge of: • position & momentum • energy & time
Gravitational Force The gravitational force is weak, but very long ranged. Furthermore, it is always attractive, and acts between any two pieces of matter in the Universe since mass is its source.
Remember the Tortoise and the Hare? Gravity has basic properties that set it apart from the other forces: (1) it is long-ranged and thus can act over cosmological distances; (2) it always supplies an attractive force between any two pieces of matter in the Universe. Thus, although extremely weak, it always wins over cosmological distances and is the most important force for the understanding of the large scale structure and evolution of the Universe.
So, let us deal with GRAVITY • We’ll need a bit of a history lesson: • Brahe • Kepler • Newton • Einstein Pay close attention, gravity has many implications!
Tycho Brahe 1546 - 1601 A wild Dane, but he made and recorded large quantities of accurate measurements of the motions of the planets around the Sun. Began working with Johannes Kepler in 1600.
Kepler’sThree Laws of PlanetaryMotion • Landmarks in the history for astronomy and mathematics, for in the effort to justify them Isaac Newton was led to create modern celestial mechanics. The three laws are: • 1) The planets move abort the sun in elliptical orbits with the sun at one focus. • The radius vector joining a planet • to the sun sweeps over equal areas • in equal intervals of time. • The square of the time of one compete • revolution of a planet about its orbit is proportional • to the cube of the orbit's semi-major axis T12/ T22 =R13/ R23 or T2=k.R3 The empirical discovery of these laws from Tycho Brahe's mass of data constitutes one of the most remarkable inductions ever made in science.
Isaac Newton • Born 1642, the year Galileo died • Loner, tinkerer, paranoid • 1665-1666 Plague was very good for him • Suffered mental breakdown 1675 • Math, Chemistry, Theology, Parliament • Died 1727 • Has his picture on the British pound note He put the physics and mathematics to Kepler’s Laws!
Was there really an apple? • We know: he was on a farm • We don’t know anything else
Newton’s Laws of Motion • First Law - A body remains in its state of motion unless acted upon by an outside force • Second Law - A body acted upon by an external force will change its momentum in the direction of the force such that the greater the force the greater the change in momentum (F= ma) • Third Law - Forces always occur in pairs, i.e. for every action there is an equal and opposite reaction
Universal Law of Gravitation • All objects in the Universe attract each other with a force that varies directly as the product of their masses and inversely as the square of their separation from each other. F = G m m r 1 2 gravity 2
Albert Einstein Besides having great hair, he taught us a few fundamentally important things: E = m c2 • Energy can be neither created nor destroyed. It can just • change from one form to another. Light, heat, kinetic, potential, • etc. etc. etc. • No object can move faster than the speed of light. • Space and time are linked together.
