AST-28

Schwarzschild radius

2.95 km per solar mass.

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AstroSchwarzschild

Governing equation

r_s=2GM/c^2

where

M: M (M_\odot)
r_s: rs (km)

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-28 — Schwarzschild radius) is the form associated with Schwarzschild. Working symbols: $M$ $\rightarrow$ $r_s$ . 2.95 km per solar mass.

Purpose

Purpose: compute

r_s

from

M

in Astrophysics via

r_s=2GM/c^2

2.95 km per solar mass. 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 = 10.000\,\mathrm{M_odot}

, the governing relation

r_s=2GM/c^2

yields

r_s = 29.50\,\mathrm{km}

. 2.95 km per solar mass. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

M M10 M_\odot

Outputs

rs r_s29.50 km

Reading speed

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Narration of this film

2.95 km per solar mass.

Reading speed

Watch on YouTube