REL-32

Mercury perihelion (scale)

GR perihelion advance.

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GoverningMercury perihelion (scale)

Governing equation

\Delta\phi=6\pi GM/(c^2 a(1-e^2))

$e \in \left[0, 0.6\right]$

where

M: M (Msun)
a: a (AU)
e: e (—)
dphi: Mercury perihelion (scale) (arcsec/rev)

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

\Delta\phi=6\pi GM/(c^2 a(1-e^2))

$e \in \left[0, 0.6\right]$

$e = 0$ $dphi = 0.099$

Along the curve

②

Domain of the variable — blue

e_{\min} = 0,\quad e_{\max} = 0.6

$e \in \left[0, 0.6\right]$

$e = 0$ $e = 0$

Along the curve

③

Response curve — green

\Delta\phi=6\pi GM/(c^2 a(1-e^2))

$e \in \left[0, 0.6\right]$

$e = 0$ $dphi = 0.099$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}dphi}{\mathrm{d}e}

$e \in \left[0, 0.6\right]$

$e = 0.004$ $dphi^{\prime} = 7.47\times 10^{-4}$

Along the curve

Lecture brief

Historical brief

Einstein’s 1905 Lorentz kinematics and 1915 field equation, then Schwarzschild (1916) and Hawking temperature, recast time, mass and gravity. The lab computes dilation, E=mc² and horizon scales. This sheet (REL-32 — Mercury perihelion (scale)) is the form associated with Mercury perihelion (scale). Working symbols: $M$ , $a$ , $e$ $\rightarrow$ $dphi$ . GR perihelion advance. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

dphi

from

M

a

e

in Relativity via

\Delta\phi=6\pi GM/(c^2 a(1-e^2))

GR perihelion advance. Use it when a real relativity question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

M = 1.000\,\mathrm{Msun}

a = 0.387\,\mathrm{AU}

e = 0.206\,\mathrm{—}

, the governing relation

\Delta\phi=6\pi GM/(c^2 a(1-e^2))

yields

dphi = 0.103\,\mathrm{arcsec/rev}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

M M1 Msuna a0.387 AUe e0.206 —

Outputs

Mercury perihelion (scale) dphi0.103 arcsec/rev

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

GR perihelion advance. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube