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D.3 Cosmology

The expanding universe


The wavelength of the light measured upon arrival is longer than the wavelength at emission

Doppler effect:

Moving sources $$ f'=f(\frac{v}{v\pm u_s}) $$ 但是在天体物理中不用多普勒效应解释

表象:波长增加,doppler effect

本质:The space between galaxies is stretching out(expands)

$$ z=\frac{\Delta\lambda}{\lambda_0}=\frac{\lambda-\lambda_0}{\lambda_0}\simeq\frac{v}{c} $$ V: Recessuibak soeed if galaxies

$\lambda_0$: wavelength on emission

$\lambda$: wavelength observed on Earth

R: Cosmtic scale factor


(v<0.2C z<0.2


z: absorption spectra

Hubble's law

The velocity of recession of galaxies is directly proportional to the distance

$$ v=H_0d $$ Recessional velocity-> Measured redshift of star $z=\frac{\Delta\lambda}{\lambda_0}$

Milky way: Star (Sun) + 8 plants (made of rock or gas)

Asteroid: Made of rock (Mostly carbon)

The Hot Big Bang Model: the creation of space and time

A definite biggining

(Enourmous temperature, infinitesmimally small size)

The space was created

the universe is not expending into empty space



  1. Made of ice (Frozen gas)
  2. As they draw near to the sun, the gases in the comet are vaporized, forming the distinctive tail
  3. Sharply elliptical orbit around the sun

Stellar system-> cluster

globular cluster

  1. Starts positioned closely enough to be held by gravity
  2. Formed at the same time from the same nebula

Constellation (星座): A pattern formed by stars that are in the same general direction

  1. Star Not at the same time

Locating areas of the sky

Uniform distribution of matter, every part of the universe looks the same

Stellar Evolution

Protostart (Nebula): contration of H gases and dust

Gravitational potential energy -> Thermal energy

要有Strong Nucler force才能聚


Energy in

Low mass star 双层shell

higher 有很多shell

  • core被撕裂,电子被迫压倒质子,变中子


  • Core collapse/contracts -> burning helium in core

Burning hydrogen in shell around the core

^4^~2~He -> 12C8 + Some 18O9

  • Expand, bigeer, cooler, more luminous


只剩下C和一部分的O 被吹走,变成了planetary nebula

  • C blowed away outer layer

内核还会继续收缩,Gravitational pressure 和 Electron degeneracy pressure 相互 Balance,最后保持 Constant radius 变成dwaft

Pauli Exclusion Principle:

No two electron may occupy the same quantum state



Larger Stars

red supergiant phase:

  • 从里到外


Multiple shell burning

  • Very hot in the core -> nuclei are ripped apart into protons and neutrons(可以直接拆成proton和neutron)
  • Electrons combine with protons to form neutron
  • 1e- -1+1p1+1n0+0ve)

Neutron degeneracy pressure 负责接着和gravitation balance

  • The outer layer of the star rush in towards the core, but the core bounce off it in a huge explosion -> Supernova (Much more violence)

Core 的归宿

If the core is more massive than the Chandrasekhar limit but less than the Oppenheimer–Volkoff limit of about 2–3 solar masses, the core will collapse further until electrons are driven into protons, forming neutrons. Neutron pressure now keeps the star from collapsing further, and the star becomes a neutron star.


Based on a constant rate of expansion equal to the present rate

Actual = 13.8 Billion years, 这个理论高估了年龄 估算:14.4 By(因为一开始的扩张实际上非常快)

Two edidence

In support of Big Bang

  • The observation of an expanding universe
  • The cosmic microwave background radiation (CMB)

1964年 CMB

  • A spectrum corresponding to blackbody radiation at a temperature of 2.76K
  • Peak radiation in the microwave region
  • Isotropic(各向同性) radiation with no apparent source


The accelerating universe

CMB was the afterglow of the enormous temperatures that existed in the very early universe, as the universe has expanded, the temperature has fallen to 2.76K

Dark energy?


Type 1a Supernovae

  • All have the same peak luminosity
    • Standard candle => a start of known luminosity
    • 然后用apparent brightness的公式

companion star - 双星里的另一个星

Type 1a supernova 吸red gaint的hydrogen(一吸就燃) -> Mass超过那个太阳质量->变成high mass start?->

Occur at a certain mass