Difference between revisions of "Hubble's Law and Scale Factors"

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(Created page with '===Short Topical Videos=== * [https://www.youtube.com/watch?v=1V9wVmO0Tfg Hubble's Law (Khan Academy)] * [http://study.com/academy/lesson/hubbles-law-hubbles-constant.html Hubble…')
 
 
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===Reference Material===
 
===Reference Material===
 
* [https://en.wikipedia.org/wiki/Hubble%27s_law Hubble's Law (Wikipedia)]
 
* [https://en.wikipedia.org/wiki/Hubble%27s_law Hubble's Law (Wikipedia)]
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* [https://en.wikipedia.org/wiki/Scale_factor_(cosmology) The Scale Factor (Wikipedia)]
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* [http://timtrott.co.uk/scale-factor/ Cosmic Scale Factor (Tim Trott)]
  
 
<latex>
 
<latex>
\documentclass[]{article}
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\documentstyle[11pt]{article}
\usepackage[top=1in,bottom=1in,left=1in,right=1in]{geometry}
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\def\:{\ddot }
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\def\.{\dot }
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\def\^{\hat }
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\def\_{\bar }
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\def\~{\tilde }
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\def\hf{\frac12}
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\def\imply{\Rightarrow}
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\def\inv#1{{1\over #1}}
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\def\ddt{{d\over dt}}
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\def\aa{{\dot a \over a}}
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\def\adda{{\ddot a \over a}}
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\def\thnot{\theta_0}
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\def\etot{\Omega_0}
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\def\econs{\Omega_{0,\Lambda}}
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\def\emat{\Omega_{0,M}}
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\def\econs{\Omega_{0,\Lambda}}
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\def\p{^\prime}
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\def\iff{\Leftrightarrow}
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\def\xv{{\vec x}}
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\def\pv{{\vec p}}
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\def\vv{{\vec v}}
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\def\ppt{{\partial\over\partial t}}
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\def\ddt{\frac{d}{dt}}
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\def\epot{{8\pi \over 3}}
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\usepackage{fullpage}
 
\usepackage{amsmath}
 
\usepackage{amsmath}
\usepackage{graphicx}
 
\usepackage{natbib}
 
 
\usepackage{eufrak}
 
\usepackage{eufrak}
  
 
\begin{document}
 
\begin{document}
\section{Hubble's Law}
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\section*{ Hubble's Law (1929) }
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Hubble's Law is an empirical law stating that, on large scales, recessional
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velocity is proportional to distance from observer.
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$$\boxed{v=Hr}$$
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where $H$, the Hubble parameter, is not constant, but can
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vary slowly with time.  By convention, $H$ is often expressed as
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$H=100\cdot h{km\over s\cdot Mpc}$, where 1 parsec (pc) $\approx3\cdot10^{18}cm
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=3.26ly$, is the distance at which 1 AU appears as 1 arcsec on the sky. 
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The Hubble Space Telescope Key Project (Freedman et al. ApJ 553, 47, 2001)
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measured the present day value of Hubble Constant
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$H_0=72\pm 8{km\over s\cdot Mpc}$, giving us that the current timescale for
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the expansion of the universe is
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$H_0^{-1}\approx{h\over 10^{11}}yrs\approx 9.778h^{-1}Gyrs$.
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\section*{ The Scale Factor, $a(t)$ }
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$a(t)$ relates physical ($r$) and {\it comoving} ($x$) coordinates in an
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expanding universe:
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$$\begin{align}
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r&=a(t)x\\
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\dot r&=\dot ax+a\dot x=\underbrace{\aa}_{\equiv H}r+\underbrace{a\dot x}_{\equiv v_p}\\
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\end{align}$$
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Thus, the two components of physical velocity are $H$ (the Hubble expansion
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parameter) and $v_p$ (the peculiar velocity, or motion relative to expansion)
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By convention, $t_0 \equiv$ today and $a(t_0)=1$.
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\end{document}
 
\end{document}
<\latex>
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</latex>

Latest revision as of 13:43, 17 January 2017

Short Topical Videos[edit]


Reference Material[edit]

Hubble’s Law (1929)

Hubble’s Law is an empirical law stating that, on large scales, recessional velocity is proportional to distance from observer.

where , the Hubble parameter, is not constant, but can vary slowly with time. By convention, is often expressed as , where 1 parsec (pc) , is the distance at which 1 AU appears as 1 arcsec on the sky. The Hubble Space Telescope Key Project (Freedman et al. ApJ 553, 47, 2001) measured the present day value of Hubble Constant , giving us that the current timescale for the expansion of the universe is .

The Scale Factor,

relates physical () and comoving () coordinates in an expanding universe:

Thus, the two components of physical velocity are (the Hubble expansion parameter) and (the peculiar velocity, or motion relative to expansion) By convention, today and .