AST-01

Hubble law

Local expansion.

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AstroHubble

Governing equation

v=H_0 d

$d \in \left[1, 4000\right]$

where

H_0: H0 (km/s/Mpc)
d: Distance (Mpc)
v: Recession (km/s)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

v=H_0 d

$d \in \left[1, 4000\right]$

$d = 1$ $v = 70$

Along the curve

②

Domain of the variable — blue

d_{\min} = 1,\quad d_{\max} = 4000

$d \in \left[1, 4000\right]$

$d = 1$ $d = 1$

Along the curve

③

Response curve — green

v=H_0 d

$d \in \left[1, 4000\right]$

$d = 1$ $v = 70$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}v}{\mathrm{d}d}

$d \in \left[1, 4000\right]$

$d = 26.15$ $v^{\prime} = 70$

Along the curve

Lecture brief

Historical brief

Hubble expansion, Jeans collapse, Eddington luminosity, Bondi accretion and Stefan–Boltzmann stars are the first astrophysical budgets. The sheets scale a star, a cloud and a horizon. This sheet (AST-01 — Hubble law) is the form associated with Hubble. Working symbols: $H_0$ , $d$ $\rightarrow$ $v$ . Local expansion.

Purpose

Purpose: compute

v

from

H_0

d

in Astrophysics via

v=H_0 d

Local expansion. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

H_0 = 70.000\,\mathrm{km/s/Mpc}

d = 100.000\,\mathrm{Mpc}

, the governing relation

v=H_0 d

yields

v = 7000.0\,\mathrm{km/s}

. Local expansion. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

H0 H_070 km/s/MpcDistance d100 Mpc

Outputs

Recession v7000.0 km/s

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Narration of this film

Local expansion.

Reading speed

Watch on YouTube