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 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, me= 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

  Msun = 1.998 x 10^30 kg
  Mjup = 1.8987 x 10^27 kg
  Mearth = 5.976 x 10^24 kg

  Psun = 2.7 x 10^16 N m^-2
  Pearth (center) = 5 x 10^11 N m^-2
  Pjupiter (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:
  vesc (Moon) = 2380 ms-1
  vesc (Earth) = 11000 ms-1
  vesc (Sun) = 6.2 x 10^5 m/s
  vesc (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, cs in air = 330 m/s

  REarth = 6.371 x 10^6 m
  RJup = 7.1 x 10^7 m
  RSun = 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, zdec = 1091
 Redshift at Matter-radiation equality, zeq = 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