AST-26

Surface gravity

g = G M / R². Surface acceleration of a spherical body.

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GravitySurface gravity

Governing equation

g=GM/R^2

$M \in \left[0.08, 40\right]$

where

M: Mass (M_\odot)
R: Radius (R_\odot)
g: Gravity (m/s²)
\log g: log g (cgs)

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

g=GM/R^2

$M \in \left[0.08, 40\right]$

$M = 0.08$ $g = 21.94$

Along the curve

②

Domain of the variable — blue

M_{\min} = 0.08,\quad M_{\max} = 40

$M \in \left[0.08, 40\right]$

$M = 0.08$ $M = 0.08$

Along the curve

③

Response curve — green

g=GM/R^2

$M \in \left[0.08, 40\right]$

$M = 0.08$ $g = 21.94$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}g}{\mathrm{d}M}

$M \in \left[0.08, 40\right]$

$M = 0.331$ $g^{\prime} = 274.2$

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-26 — Surface gravity) is the form associated with Surface gravity. Working symbols: $M$ , $R$ $\rightarrow$ $g$ , $\log g$ . log g in cgs is the stellar-atmosphere parameter. White dwarfs have log g ~ 8.

Purpose

Purpose: compute

g

\log g

from

M

R

in Astrophysics via

g=GM/R^2

g = G M / R². Surface acceleration of a spherical body. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

M = 1.000\,\mathrm{M_odot}

R = 1.000\,\mathrm{R_odot}

, the governing relation

g=GM/R^2

yields

g = 274.208\,\mathrm{m/s^{2}}

\log g = 4.438\,\mathrm{cgs}

. A world, a falling test mass. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass M1 M_\odotRadius R1 R_\odot

Outputs

Gravity g274.208 m/s²
log g \log g4.438 cgs

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Narration of this film

A world, a falling test mass.

log g in cgs is the stellar-atmosphere parameter. White dwarfs have log g ~ 8.

Reading speed

Watch on YouTube