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Tools We Will Need on our Journey through the Universe

Tools We Will Need on our Journey through the Universe. Don’t Panic… but it IS physics and math. Quick Review of Scientific Notation. Powers of Ten. Scientific Notation 10 n means 10 x 10 x 10 x 10 … [n times] 10 -n means 1/(10 x 10 x 10 ….) [n times]

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Tools We Will Need on our Journey through the Universe

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  1. Tools We Will Need on our Journey through the Universe Don’t Panic… but it IS physics and math

  2. Quick Review of Scientific Notation

  3. Powers of Ten • Scientific Notation • 10n means 10 x 10 x 10 x 10 … [n times] • 10-n means 1/(10 x 10 x 10 ….) [n times] • There are 1010 –1011 stars in our Galaxy, and a similar number of galaxies in the Universe

  4. Units for Distance, not Time • Kilometer (km) = .621 miles • Light-year (lt-yr) = The distance light travels in one year in a vacuum. 1 lt-yr = 9.5 x 1012 km • Parsec = 3.3 light-years (Mpc = 1,000 pc) • arc-second = (1 degree/3600)

  5. Forces in the Universe • Weak • Strong • Electromagnetic • Gravitational

  6. Strong Force The strong interaction is very strong, but very short-ranged. It acts only over ranges of order 10-13 centimeters and is responsible for holding the nuclei of atoms together. It is basically attractive, but can be effectively repulsive in some circumstances.

  7. Weak Force The weak force is responsible for radioactive decay and neutrino interactions. It has a very short range and, as its name indicates, it is very weak.

  8. Electromagnetic Force The electromagnetic force causes electric and magnetic effects such as the repulsion between like electrical charges or the interaction of bar magnets. It is long-ranged, but much weaker than the strong force. It can be attractive or repulsive, and acts only between pieces of matter carrying electrical charge.

  9. Light is Electromagnetic!

  10. The Wave Nature of LightProvides us with Important Probes for Understanding Our Universe

  11. Let There Be Light! c = 3 x 108 m/s It’s not just a good idea, it’s the law!

  12. A Brief Review of ...

  13. Seeing the Light VLA COBEIRASEUVEChandraCGRO HST/Keck

  14. Looking back through space and time Constellation-X NGST, FIRST Explorer MAP, Planck clusters and groups of galaxies LISA, GLAST first stars, galaxies, and black holes OWL matter/radiation decoupling microwave background Big Bang inflation Early Universe Gap First Stars Gap

  15. Falloff and Shift Two things we must understand: 1.) Intensity of light falls off as we move away from the source 2.) Wavelength of light we see shifts as source moves

  16. Light at a Distance • Objective: Your detector in orbit around Earth has measured a certain amount of energy from the direction of a faraway source. Your job is to determine how much energy the source actually emitted. Assume the source emits energy equally in all directions.

  17. Think About It! • A light emits equally in all directions. • What does this mean about the amount of light you will measure in any given square cm as you move further and further away from the light source?

  18. Add the Mathematics! • At r1, the light per unit area, • L1 = L/4p(r1)2. • And at r2, the light per unit area, • L2 = L/4p(r2)2. • Solving each equation for L gives us • L= L1 x 4p(r1)2 = L2 x 4p(r2)2. Think of it in terms of a ratio... the amount of light per unit area at r2 relative to the amount of light per unit area at r1 is then L2/L1 = (r1)2/(r2)2.

  19. Conclusion • We say that the intensity, or amount of light per square cm, changes as 1/distance squared (i.e., 1/r2) away from the source. • How does this help us to achieve our Objective? If we • measure X amount of energy per square cm in our detector, then we know that the source must have emitted energy equal to 4pr2 times X!

  20. Now Confirm It…Low-Tech Want to convince yourself that light really does fall off as 1/r2? Here is a quick, easy, low-tech way! Materials: tape measure flashlight - with a well focused emission of light - light end no more than 5cm in diameter graphics calculator

  21. Look!

  22. Keep Looking!

  23. Doppler Shift If source approaches, light appears bluer than it is. If source recedes, light appears redder than it is.

  24. Doppler Shift Wavelength is shorter when approaching Stationary waves Wavelength is longer when receding

  25. What It Looks Like Comparison of laboratory to blue-shifted object Comparison of laboratory to red-shifted object

  26. Doppler Shift / Redshift v l - lo Dl = = = z l c lo Redshift, z, is a non-relativistic approximation to the Doppler shift

  27. Historical Note • Using the Doppler shift, Edwin Hubble observed that the Universe is expanding!

  28. 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!

  29. 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!

  30. 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.

  31. Caveat! Space between the galaxies expands while galaxies stay the same size

  32. 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

  33. Kinds of Spectra

  34. Another Way to Look at a Spectrum

  35. 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

  36. Periodic Table Electrons fill shells labeled s, p, d, f, etc.  New shells are added 

  37. 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

  38. 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.

  39. 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.

  40. 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!

  41. 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.

  42. 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.

  43. 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!

  44. Was there really an apple? • We know: he was on a farm • We don’t know anything else

  45. 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

  46. 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

  47. 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.

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