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

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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)] | ||

+ | * [https://en.wikipedia.org/wiki/Scale_factor_(cosmology) The Scale Factor (Wikipedia)] | ||

+ | * [http://timtrott.co.uk/scale-factor/ Cosmic Scale Factor (Tim Trott)] | ||

<latex> | <latex> | ||

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the expansion of the universe is | the expansion of the universe is | ||

$H_0^{-1}\approx{h\over 10^{11}}yrs\approx 9.778h^{-1}Gyrs$. | $H_0^{-1}\approx{h\over 10^{11}}yrs\approx 9.778h^{-1}Gyrs$. | ||

+ | |||

+ | \section*{ The Scale Factor, $a(t)$ } | ||

+ | |||

+ | $a(t)$ relates physical ($r$) and {\it comoving} ($x$) coordinates in an | ||

+ | expanding universe: | ||

+ | $$\begin{align} | ||

+ | r&=a(t)x\\ | ||

+ | \dot r&=\dot ax+a\dot x=\underbrace{\aa}_{\equiv H}r+\underbrace{a\dot x}_{\equiv v_p}\\ | ||

+ | \end{align}$$ | ||

+ | Thus, the two components of physical velocity are $H$ (the Hubble expansion | ||

+ | parameter) and $v_p$ (the peculiar velocity, or motion relative to expansion) | ||

+ | By convention, $t_0 \equiv$ today and $a(t_0)=1$. | ||

\end{document} | \end{document} | ||

</latex> | </latex> |

## Revision as of 13:42, 17 January 2017

### Short Topical Videos

### Reference Material

## 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 .