MSci Physics and Astrophysics Lecture Notes - Part 21a

 Please note: this site is not an official course Website.  The Physics Lecture notes and other material are for reference purposes only.



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 MT1 Mathematical Techniques 1 (QMUL):  additional material

 MT1 Exams 2007:

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 Dynamical Systems (Cambridge):

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 PHY206 Atomic Spectra notes (Sheffield):

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 Cosmology Lecture notes 2010  (Imperial): 

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 Gamma Functions - reminder (Cambridge):  see also Beta functions

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 Dimensional Analysis Introduction (Cambridge):

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 The Once and Future Cosmos (2002): gives an accessible overview of some current theories

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 WMAP 1st Year Cosmological Parameters 2003 (ApJ):

 Determination of the Cosmological Parameters from the WMAP 1st Year observations (ApJ):

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 Physical Constants and Formulae:

  or as a Word.DOC

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  More Constants, Quantities and Units (rough uncorrected draft):

 Quick summary reference

  e- rest mass, m_e= 8.18 x 10^-14 J

  Electron volt: 1 eV = 1.602 × 10^-19 J
  Erg: 1 erg = 10^-7 J

  Solar Luminosity, Lsun = 3.90 × 10^26 W (= J/s)

  Typical energy released (Joules):
  1 Ton TNT = 4.2 x 10^9 J
  Typical atomic bomb = 1.5 x 10^14 J
  Powerful H-bomb = 1 x 10^17 J
  Krakatoa eruption = 5 x 10^17 J
  Lake Toba volcanic eruption Sumatra = 5 x 10^19 J
  Shoemaker-Levy fragment G impact on Jupiter = 2.5 x 10^22 J
  K-T 10 km meteor impact on Earth = 4 x 10^23 J
  Typical GRB = 1 x 10^45 J

  Type II SN photon energy = 3 x 10^44 J
  Type II SN neutrino energy = 3 x 10^46 J

  Temperatures:
  Tnuc (max) = 1 x 10^9 K
  T* (5 Msun) = 2.7 x 10^7 K
  Tsun (center) = 1.46 x 10^7 K
  Tsun (surface) = 5780 K
  Solar Luminosity, Lsun = 3.827x10^26 W

  Tdec = 3000 K
  CMB present day temperature, T₀ = 2.73 K (t₀ = 13.7 Gyr)

  Zirconium melt point, Tmelt = 1854+273 K = 2127 K
  Carbon steel = 1540+273 K = 1813 K
  Iron Tmelt point = 1811 K
  Stainless steel = 1510+273 K = 1783 K
  Gold 24K pure Tmelt = 1063 +273 K = 1336 K

  Mass:
  atomic mass unit 1 amu = 1.661 × 10^-27 kg
  proton rest mass mp = 1.673 × 10^-27 kg = 938 MeV
  neutron rest mass mn = 1.675 × 10^-27 kg (mn-mp = 1.29MeV) = 939 MeV
  electron rest mass me = 9.109 × 10^-31 kg (mp/me = 1836) = 0.511 MeV

classical electron radius, re = 2.818 × 10^-15 m
Bohr radius, a0 = 5.292 × 10^-11 m

  M_sun = 1.998 x 10^30 kg
  M_jup = 1.8987 x 10^27 kg
  M_earth = 5.976 x 10^24 kg

  P_sun = 2.7 x 10^16 N m^-2
  P_earth (center) = 5 x 10^11 N m^-2
  P_jupiter (center) = 4 x 10^12 N m^-2

  Typical large spiral galaxy mass, eg. Milky Way = 10^11 Msun
  Typical dwarf galaxy mass 10^5 to 10^6 Msun
  Approximate mass of the visible Universe, Mvis ~ 10^52 kg (excluding Dark Matter contribution)

  Peak current in lightning bolt, I = 1 x 10^4 A
  Typical voltage across Lightning bolt, V = 3 x 10^8 V

 Velocities:
  v_esc (Moon) = 2380 ms-1
  v_esc (Earth) = 11000 ms-1
  v_esc (Sun) = 6.2 x 10^5 m/s
  v_esc (Neutron star) = 2 x 10^8 m/s

  Speed of Light in vacuum, c = 2.998 x 10^8 m/s
  Speed of sound in air, c_s in air = 330 m/s

  R_Earth = 6.371 x 10^6 m
  R_Jup = 7.1 x 10^7 m
  R_Sun = 6.96 x 10^8 m

  Earth-Moon distance = 3:8 x 10^8 meters
  Earth-Sun distance, 1 AU mean = 1.5 x 10^11 m
  Pluto-Sun distance = 5.91 x 10^12 m

  Some useful Physical Constants and conversion factors:
  Gravitational constant G = 6.67 x 10^-11 m3 kg-1 s-2
  Reduced Planck's constant (h-bar) = 1.05 x 10^-34 J s
  Boltzmann constant (k) = 1.38 x 10^-23 J/K
  Radiation constant (alpha) = 7.565 x 10^-16 Jm^-3 K^-4

  1 year (365.25 days) = 3.156 x 10^7 s
  1 ly = 9.461 x 10^15 m = 0.31 pc
  1 pc = 3.086 x 10^16 m = 3.26 ly
  4 x 10^16 meters = Nearest Extrasolar star to Earth

  1 keV as unit of temperature = 1.1605 x 10^7 K
  Neutron half-life t1/2 = 940 s
  Neutron mass-energy (mc^2) = 939.6 MeV
  Proton mass-energy = 938.3 MeV
  Electron mass-energy = 0.511 MeV
  1 eV = 1.602 x 10^-19 J

  2 x 10^19 meters Characteristic height of the Milky Way main disk
  6 x 10^19 meters Typical dwarf galaxy radius

  2.4 x 10^20 meters = Distance from Sun to Galactic center ~ 8 Kpc
  2 x 10^21 meters = Rough Milky Way dark matter halo radius
  Visible Milky Way disk diameter, d ~ 15 Kpc (100,000 light years across) excluding Dark Matter halo.

  1.9 x 10^22 meters = Distance to M31 galaxy
  3 x 10^22 meters = Radius of the core of the Virgo Cluster of galaxies
  4 x 10^22 meters = Rough Local Group radius
  9.2 x 10^22 meters Cepheid Variable distance determination limit (via ground observations)

  7 x 10^23 meters = Distance to the z = 0:0036 Seyfert 2 NGC 1068
  7 x 10^23 meters = Distance to the center of the Virgo Cluster of galaxies

  4:1 x 10^24 meters = Luminosity distance to the z = 0:022 Coma cluster of galaxies
  3:0 x 10^25 meters = Luminosity distance to the z = 0:158 Quasar 3C273
  5:5 x 10^26 meters = Luminosity distance to the z = 2:286 ultraluminous IRAS galaxy, IRAS   F10214+4724
  1:3 x 10^27 meters = Luminosity distance to the z = 4:897 Quasar PC 1247+3406

  Larger Redshifts, z :

 Redshift at decoupling, z_dec = 1091
 Redshift at Matter-radiation equality, z_eq = 3280

Primordial nucleosynthesis, tnuc ~ 3 min after the Big Bang (stable nuclei form)
Decoupling of the CMB photons, tdec ~ 380,000 years after the Big Bang (stable atoms form)
  Present age of the Universe, t0 = 13.7 Gyr = 13.7x10^9 yr
  Age of the Milky Way galaxy ~ 13 Gyr
  Age of oldest globular clusters ~ 11 to 12 billion years
  Age of the Solar System ~ 5 billion years
  Age of the Earth = 4.5 billion years
First appearance of life on Earth ~ 3.5 billion years ago (i.e. 1 billion years after the Earth's formation)
  KT Event impact ~ 65 million years ago
  First appearance of proto-humans? ~ 1.5 million years ago?
  First migrations of homo sapiens ~ 160,000 years ago?
  First migrations of homo sapiens into Europe ~ 40,000 years ago
  Lascaux cave paintings (France) ~ 35,000 years ago
  Last Ice Age ~ 14,000 years ago
  First migrations of humans into the Americas ~ 13,000 years ago
Oldest known human settlement at the transition from hunter-gatherer to agricultural farming (Anatolia) ~ 12,000 years ago (oldest known man-made stone monuments).
  Oldest inhabited city (Jericho) ~ 9000 years old
  End of the western Roman Empire (476 AD) = 1536 years ago as of 2012

Milky Way - Andromeda interactions including initial close passes occur ~ 2-5 billions years from now Sun Main Sequence total lifetime ~ 10-11 billion years (currently half-way through)
Sun red giant phase ~ a further 2 billion years before envelope ejection
Sun white dwarf core cooling phase > the following 30 billion years after formation of the planetary nebula?

  Time since the Big Bang (Cosmic Milestones from Krauss, Scherrer):
  10^-30 s Inflation occurs
  100 s D and He are created
  10^5 yrs Formation of the CMB
  10^9 yrs Accelerated expansion begins
  10^10 yrs Present age of the universe
  20 billion yrs Milky Way and Andromeda collide
  100 billion yrs Far away galaxies have moved beyond the horizon
  1 trillion years Primordial isotopes are lost or diluted
  100 trillion years Last star burns out

  Triple point of Water:
The single combination of pressure and temperature at which liquid water, solid ice, and water vapor can coexist in a stable equilibrium occurs at exactly 273.16 K (0.01 °C) and a partial vapor pressure of 611.73 pascals (ca. 6.1173 millibars, 0.0060373 atm).

  Temperature conversions:

  Fahrenheit => Celsius: C = (5/9 - 32) F

  Celsius => Kelvin: K = C + 273.16

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 Keywords: physics, astronomy, astrophysics, cosmology, general relativity, quantum mechanics, MSc degree, MSci degree, university degree, lecture notes, mathematical sciences, physical sciences

Main Lecture Notes index : 2B22 Quantum Physics (slides), 2B28 (2228) Statistical Thermodynamics (UCL), Condensed Matter Physics 1 (QMUL), Past Exam papers, etc.

Degree Modules Section 1 : Stellar Structure and Evolution (Penn State), ASTM115 Astrophysical Fluid Dynamics (QMUL), MTH6123 Mathematical Aspects of Cosmology 1-20, ASTM003 Angular Momentum and Accretion in Astrophysics 1-10, etc.

Part 1 : More RWFQ and GR lecture notes (UCL), ASTM001 Solar System dynamics, MAS347 Mathematical Aspects of Cosmology cont., C6 M.Phys option Theoretical Physics (Oxford), Quantum Field Theory extra notes, etc.

PART 2 : Waves and Modern Physics, Fields and Waves, etc. (Main Waves Section)

Part 2a

Part 6 : More Condensed Matter Physics, 3C25 Solid State Physics (UCL), Electromagnetic Fields (EMF), Thermal and Kinetic Physics (QMUL), Physical Dynamics, Electro-Optics notes, Statistical Mechanics, Quantum Mechanics and Symmetry, Mechanics, etc.

Part 7 : More RG and Cosmology notes, MAS347 Mathematical Aspects of Cosmology cont. (QMUL), Cosmology Pt II of 3 Structure Formation (Cambridge), Stellar Structure and Evolution cont. (U Colorado), 4C15 High Energy Astrophysics cont. (UCL), misc. Tables of Physical Constants, Units  and Quantities, Hydrodynamics notes, extra Quantum Mechanics notes, and MSci Degree info, etc.

PART 13 : 3C17 Solar System Science, C3 Condensed Matter Physics option Pt. 1 (Oxford) cont., 380 Plasmas (U. Texas), ASTR 4C15 High Energy Astrophysics cont. (UCL), Elements of Astrophysics (U. Hawaii), Planetary Systems (U. Colorado), 2B72 Mathematical Methods II (UCL).

PART 14 : 4C65 Space Plasmas and Magnetospheric Physics section 2 (UCL), 4C15 High Energy Astrophysics slides cont., Holographic Principle, etc.

PART 15 : 2B70 Lab Practicals, C3 Condensed Matter Physics Pt. 1 cont (Oxford), MT4510 Solar Physics (St Andrews), 3C24 Nuclear and Particle Physics (UCL), Misc Astrophysics short notes (Oxford), etc.

PART 19 : MTH6123 Mathematical Aspects of Cosmology 2010 notes (QMUL), short notes on Tensors (Swarthmore College), Mathematical Physics (Imperial), Statistical Mechanics IV (Univ. of Heidelberg), 3C36 Cosmology and Extragalactic Astronomy (UCL), 3C35 Stellar Structure and Astrophysical Processes (UCL), PHY319 Quantum Mechanics A (QMUL), ASTM002 The Galaxy revision notes (QMUL), 1B02 Physics of the Universe partial notes (UCL), ASTM116 Solar Wind properties, etc.

PART 20a

PART 21 : RWQF part 2/3 cont (QMUL), Electricity and Magnetism (UVic), Statistical Mechanics (Temple Univ), Geometric Optics (UVic), MTH4100 Calculus I cont. (QMUL).

 Part 21a - this Site

Part 26a - Cambridge Lecture Notes, IB Mathematical Methods 1-3, IA Dynamics, Quantum Mechanics, Waves, IA Vector Calculus, Symmetries and Particles, Advanced Quantum Field Theory (Cambridge), Stellar Structure and Evolution - intermediate (Sheffield University), Tevatron Kinematics Primer (Glasgow University), Experiment E5 (UCL), The Celestial Sphere (Sheffield University), Short summary recap on Tensors for GR (Warwick University), ASTM109 Stellar Structure and Evolution - redone as PDFs (QMUL), PHY101 Electricity and Magnetism (Sheffield), etc.

PART 27 : Extra sample MSci Physics degree problems - 1B28 Thermal Physics slides 23-30/30 cont. (UCL), ASTM041 Relativistic Astrophysics (QMUL), 3C43 Lasers and Modern Optics, EM Fields, MTH6132 Relativity, 2B27 Environmental Physics, EPP Glossary, PHY215 QP, 2B22 Quantum Physics (UCL), PHY319 Quantum Mechanics A (QMUL).

Part 27a : 4C26 Advanced Quantum Theory Problems, Atomic and Laser Physics (Sheffield), General Relativity  (Warwick), Principles of Thermal Physics short notes (KCL), etc.

PART 30 : MSci Physics and Astrophysics sample Past Exam Papers

Main Cosmology Section : 3C74 Topics in Modern Cosmology, C358 Cosmology, ASTM108 Advanced Cosmology (QMUL), C348 Mathematics for General Relativity (UCL), Introduction to Tensor Calculus (KCL), ASTM041 Relativistic Astrophysics (QMUL), etc.