Published equation contexts

$1.8\times10^6\,\mathrm{km}$

Why this formula appears here

To make this concrete rather than asymptotic, take the mass of Sagittarius A* as measured by the Event Horizon Telescope, M $\approx$ 4 $\times$ 10^6\, $M_\odot$ , giving a Schwarzschild radius $r_s$ $\approx$ 1.18 $\times$ 10^{10}\, $\mathrm m$ and a horizon-scale acceleration factor GM/ $r_s^2$ $\approx$ 3.80 $\times$ 10^{6}\, $\mathrm{m\,s^{-2}}$ [ 14 ] . At a clearance of just one kilometer above the horizon — a distance smaller than a millionth of the horizon’s own radius — f $\approx$ 8.46 $\times$ 10^{-8} and the required proper acceleration is already a $\approx$ 1.3 $\times$ 10^{10}\, $\mathrm{m\,s^{-2}}$ , more than a billion Earth gravities. Even at a clearance of 1.8 $\times$ 10^6\, $\mathrm{km}$ — about fifteen percent of the horizon’s own…

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Research cited beside this formula

[14] First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way ↗

Published contexts (1)

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1.8\times10^6\,\mathrm{km}

Equation 69 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

To make this concrete rather than asymptotic, take the mass of Sagittarius A* as measured by the Event Horizon Telescope, M $\approx$ 4 $\times$ 10^6\, $M_\odot$ , giving a Schwarzschild radius $r_s$ $\approx$ 1.18 $\times$ 10^{10}\, $\mathrm m$ and a horizon-scale acceleration factor GM/ $r_s^2$ $\approx$ 3.80 $\times$ 10^{6}\, $\mathrm{m\,s^{-2}}$ [ 14 ] . At a clearance of just one kilometer above the horizon — a distance smaller than a millionth of the horizon’s own radius — f $\approx$ 8.46 $\times$ 10^{-8} and the required proper acceleration is already a $\approx$ 1.3 $\times$ 10^{10}\, $\mathrm{m\,s^{-2}}$ , more than a billion Earth gravities. Even at a clearance of 1.8 $\times$ 10^6\, $\mathrm{km}$ — about fifteen percent of the horizon’s own…

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