AST-30

Parallax distance

Parsec definition.

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Astroparallax

Governing equation

d=1/\varpi

$\varpi \in \left[0.001, 1\right]$

where

\varpi: Parallax (arcsec)
d: Distance (pc)

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

d=1/\varpi

$\varpi \in \left[0.001, 1\right]$

$\varpi = 0.001$ $d = 1000$

Along the curve

②

Domain of the variable — blue

\varpi_{\min} = 0.001,\quad \varpi_{\max} = 1

$\varpi \in \left[0.001, 1\right]$

$\varpi = 0.001$ $\varpi = 0.001$

Along the curve

③

Response curve — green

d=1/\varpi

$\varpi \in \left[0.001, 1\right]$

$\varpi = 0.001$ $d = 1000$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}d}{\mathrm{d}\varpi}

$\varpi \in \left[0.001, 1\right]$

$\varpi = 0.007$ $d^{\prime} = -73713.5$

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-30 — Parallax distance) is the form associated with parallax. Working symbols: $\varpi$ $\rightarrow$ $d$ . Parsec definition.

Purpose

Purpose: compute

d

from

\varpi

in Astrophysics via

d=1/\varpi

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

Live realistic example

In symbols

Live case. Given

\varpi = 0.100\,\mathrm{arcsec}

, the governing relation

d=1/\varpi

yields

d = 10.00\,\mathrm{pc}

. Parsec definition. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Parallax \varpi0.1 arcsec

Outputs

Distance d10.00 pc

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Narration of this film

Parsec definition.

Reading speed

Watch on YouTube