# IB Physics - Astronomy

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1 Solar System Our Solar System has eight planets. The picture below shows their relative sizes, but NOT their relative distances. A planet orbits the sun, and has gravitationally cleared its orbital area of other orbiting objects. The orbits are elliptical, but are very close to circular. The sun is at one of the foci of the ellipse. The planets have a common orbital plane. Asteroids orbit the sun as if they were a large disintegrated planet. Why do they not count as planets? Comets are dirty snowballs that have extreme elliptical orbits that can be out of the orbital plane of the planets. 1 of 1

2 Moons are objects that orbit planets. The Earth has one moon, Jupiter and Saturn have many moons. Outside of the Solar System, distance are vast, and the unit of the light year can be used to describe distance. A light year is the distance that light travels in one year. 1 ly = 9.46 x m A parsec (pc) is 3.26 ly. It is also, coincidentally the average distance between stars in a galaxy. Using the data on p. 488 (handout) calculate the distances and sizes of a scale model of the solar system if the earth is a dot with a diameter of 1 mm. 2 of 2

3 The size of the universe is vast. We are truly an insignificant amount of matter in the Universe. The universe is organized upon gravitational principles. Bodies that are gravitationally connected are considered units. The constellations we see appear to be groups, but the stars can be very far apart and not gravitationally related. The first gravitational unit is our solar system. However, our sun, is in a group of stars in our neighborhood. Our sun is one star in the orbiting mass of stars in the Milky Way Galaxy which has about 100 billion stars (1 x ). (The universe is estimated to have about 100 billion galaxies in it.) The local collection of galaxies that are gravitationally connected is called the Local Group. Compare the distance between stars to the distance between galaxies. Our local group is part of our corner of the Universe - our Supercluster. 3 of 3

4 IB Physics - Astronomy Throughout the night, stars will rotate in a circular pattern with the axis on the north and south poles. Through the seasons, different stars can be visible and the position of other stars will change. Explain the nightly motion of stars and the annual motion of stars. Q1-Q4, 1, 3, 5-6, Stars The source of energy in the sun is nuclear fusion. The energy of the hydrogen that collapsed to form the sun (kinetic energy from the gravitational energy) is enough to initiate nuclear fusion. The simplified reaction is 4 hydrogen nuclei becoming one helium nuclei, two neutrinos and six photons. The energy released per reaction is 26.7 MeV (3.98 x J) The kinetic energy on the particles and energy in the sun generates a radiation pressure that counteracts the gravitational pressure contracting the sun. A star that is in an equilibrium state between gravity and radiation pressure is a main sequence star. Larger stars will be at a hotter temperature and consume their nuclear fuel faster at equilibrium. The more nuclear fuel a star has, the shorter its time in the main sequence. 4 of H! 24 He + 2" + 6#

5 The luminosity of a star is the amount of energy radiated by a star per second. As a star is an excellent example of a black body its luminosity depends only on its temperature and surface area. L =! AT 4 This is the Stefan-Boltzmann relationship. The apparent brightness of a star depends on its luminosity and the distance from the star to the detector. The energy released by the star is spread over the surface of a sphere at the distance of the detector. For a unit area detector: d is distance not diameter. b = L 4!d 2 Combining luminosity and apparent brightness gives: Example 1: Star B is twice the radius and half the temperature of star A. What is the difference in apparent brightness of these stars. How must they situated to have the same apparent brightness from earth? b =! AT 4 4"d 2 The colour of a star depends on its temperature as described by Wien s Law.! max (meters) = 2.90x10"3 T (kelvin) λ max is the wavelength of the peak. The light from stars shows an absorption spectrum from the atoms that are on the outer atmosphere of the star. 5 of 5

6 The light from a star can be too dim to determine the λ max. As most stars have a similar chemical composition, the presence or absence of certain lines can give information about temperature. We will also see how the Doppler Effect can be applied to the spectrum to determine the relative velocity of the star. Stars are separated in to spectral classes. Oh, Be A Fine Girl (Guy), Kiss Me. p. 496, Q1-Q6, 1-11, 14 Stars can be divided into a myriad of types and classifications. The best tool to describe the primary categories is the Hertzsprung-Russell Diagram. This graph compares absolute magnitude and/or luminosity with surface temperature. Note that neither of the scales are linear. Note the correlation between radii, mass and position for Main Sequence. 6 of 6

7 Main Sequence stars are getting their energy from fusion. Size, temperature, luminosity, life expectancy, fate, position on H- R diagram all determined by mass of the star. White dwarfs and red giants are no longer getting energy from fusion. They are not in the Main Sequence. Red giant About 1% of stars High luminosity due to very large size Relatively cool Hot core surrounded by low density gas Super giants can be 10 6 times larger then the sun White Dwarf Hot core left after red giant Small to medium sized stars end as white dwarfs Very small size gives very low luminosity - hard to see Gravity counteracted by the physical size of atoms - density ~ 10 6 that of earth A binary star is a system of two stars that orbit each other. Visual binaries can be viewed as separate stars through a telescope. Information about period and distance can give valuable information about the mass of the stars. An eclipsing binary occurs if the orbiting stars block out each other periodically as they orbit. The resulting pattern gives information about the light from each star and the period. A spectroscopic binary depends on the spectroscopic observation of the Doppler effect on the light from the star. Light from an approaching star will have its wavelength shortened (blue-shift) Light from an receding star will have its wavelength shortened (red-shift) Astronomy - Star Types A Spectroscopic binary will show an alternating red shift and blue shift as the stars move towards and away from the earth. 7 of 7

8 An important type of variable star is a Cepheid Variable that shows a periodic variability in its luminosity by expansion and contraction. The non-main Sequence stars have a strong correlation between period of variability and luminosity. Q7-9, 12, 13, (note the formula for binaries in the chapter) Stellar Distances Distances to stars that are relatively close to us (<100 ly) can be determined by their relative movement or parallax. (Up to 500 ly for space based measurements.) The distance to the star: sin p = 1AU d! p If the angle is small and in radians: d = 1.5x1011 m p Notes 1AU (radius of earth orbit = 1.5x10 11 m) p radians = (2π/360) Ø degrees A parsec is the distance a star must be so that is experiences a parallax of 1 arc second. One arc second is 1/3600 of a degree. d (in parsecs) = 1 p (in arcseconds) Ex 1: Show that one parsec is 3.26 ly. 8 of 8

9 Ancient astronomers devised a relative brightness scale from 1-6 where the 6 was 100 times dimmer than 1. Modern assignments of magnitude are based on this with a reference brightness of b 0 = 2.52 x 10-8 Wm -2 b b 0 = 100! m 5 m =! 5 2 log b b 0 To determine a reference point for comparison, the absolute magnitude (M) of a star is defined as the apparent magnitude (m) it would have if it were 10 pc from earth. The absolute magnitude (M) can also be calculated from the luminosity of a star. The absolute brightness is: L B = 4!(10 pc) 2 The difference between absolute and apparent magnitude is related to distance: " m! M = 5 log d % # \$ 10& ' d is measured in parsecs (pc). d = 10 (m! M )/5 x 10pc Ex 1 Two stars have the same luminosity. One is a magnitude 12, the other a magnitude of 9.5. What is their relative distances from the earth? How much brighter does the one appear? Q1,2; of 9

10 Stellar Distances Spectroscopic Parallax uses information from the light from the star to determine the distance to the star. The relationship between luminosity and apparent brightness can be used to estimate the distance to a star. This can be used up to about 10Mpc. Ex 1 A star has a peak wavelength at 3.5x10-7 m. Its apparent brightness is 2.5x10-10 W m -2 What is the distance to the star? b = L 4!d 2 d = L 4!b A Cepheid variable star can be used to estimate distances for stars that are very far away, even in different galaxies. A Cepheid variable is a non-main Sequence star that is undergoing an expansion and contraction. A relationship was found between the period of the change and the peak absolute magnitude. Ex 2 A Cepheid is identified in a different galaxy with a period of 2 days. Its peak apparent magnitude is -27 Estimate its distance from the earth. Q3, of 10

11 Cosmology At the time of Isaac Newton, the Universe was assumed to be infinite, uniform and static. Based on the arrangement of matter in the galaxy we can see that this is not true. In the 19 th century it was realized that an infinite uniform universe would produce a bright sky at night. If the average density of stars is n, and the apparent brightness of a star at distance d is: b = L 4!d 2 Then the number of stars in a thin shell of thickness t, d distance from the earth is: The energy from these stars is the number of stars times the apparent brightness of each one: density x volume = 4!d 2 nt L 4!d 2 x 4!d2 nt = Lnt The distance to the shell does not mater. Because there are an infinite number of thin shells, there must be an infinite amount of energy reaching the earth. Olbers Paradox. The resolution of Olbers Paradox involves all three of Newton s assumptions: The universe is not infinite (finite number of stars with a finite lifetime in a finite amount of space). The universe is not uniform. The universe is expanding (time and space) Once it was realized that there were other galaxies that were very distant from us, Edwin Hubble discovered that the red shift of the light from these galaxies was correlated to the distance of the galaxy from the earth. 11 of 11

12 The conclusion drawn was that the Universe is expanding. Like the points on the outside of a balloon, each part of the Universe is expanding away from each other point. The Universe is NOT expanding into pre-existing empty space. It is stretching our Universe as it expands. All parts of our Universe are expanding together. The conclusion that is a direct consequence of the expansion is that the Universe must have originated at a Point start: The Big Bang. Time and space were created at this time. The Big Bang happened everywhere in the Universe The energy from the very early Universe is still present today. However, it has expanded along with the Universe and now has a much longer wavelength. In 1964, two radio-astronomers, Penzias and Wilson were finding that there was microwave radiation in every direction they looked. After eliminating all other sources (including pigeon poop) they solved the problem with scientists from Princeton. 12 of 12

13 The radiation corresponds to an average temperature of 2.7K according to Wien s Law. This temperature and the very fine level of isotropy of this radiation has lead to interesting discoveries about the early Universe. The evidence for the Big Bang is overwhelming and theories about the early Universe continue to be refined. 1, 3, 4, 6, 7, 10, 14 Fate of the universe The universe is currently expanding, but the gravitational pull of the matter and energy of the universe is slowing it down. What is the fate of the Universe? We must consider an open (coasting), closed (re-collapsing) and flat (critical, asymptote) Universe. They imply an different fate and a different age of the Universe. The critical density (mass and energy of all types) of the Universe will result in a Universe that will slowly slow its expanding until it reaches a steady state (at time = infinity) A closed universe does not have an edge and will eventually result in a collapse. 13 of 13

14 An open Universe will go on forever. The current theory has a Universe that is Expanding at an increasing rate. The problem with determining the density of the Universe is that much of it does not interact with light - dark matter. WIMPS - non-baryonic, weakly interacting massive particles - do not interact with light, but do have mass. MACHOS - massive compact halo objects - like black holes and brown dwarfs. Measurements of the gravitational rotation of galaxies imply that the visible mass is only a small percentage of the mass that must be present. Models of the Big Bang also make predictions about the anisotropies of the background microwave radiation that indicate that op to 85% of all matter is dark matter. There also appears to be a dark energy that is inherent in the Universe that produce a vacuum pressure that is increasing the expansion of the universe. The studies of the microwave radiation also indicate that up to 73% of the energy of the Universe is dark energy. Only 4 % of the total energy of the Universe may be the matter that we see around us. 2, 5, 8, 9, 11-13, of 14

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