Mercury’s Perihelion
A dent slightly steeper close to the Sun closes it. Make the Sun’s dent deeper than −GM/r by an extra amount falling as 1/r² — 7.65 parts in 100 million at Mercury — and Mercury gains 42.96 arcseconds a century.
That one number, sized on Mercury, then gives the other planets unaided: Venus 8.60 against 8.62, the Earth 3.89 against 3.84, Mars 1.35 against 1.35.
What this memo does and does not do
It runs the Sun and all eight planets as summed dents, the method of 1.12 and 5.20, and measures what the dents give Mercury.
It then finds the one extra steepness near the Sun that the remainder requires, and tests it on three other planets. What produces that steepness in the Aether is set out as open in section 7.
1. The Problem Le Verrier Left
A planet round a lone Sun traces the same ellipse forever. Mercury’s does not close: its perihelion — the nearest point to the Sun — creeps forward every orbit.
In 1846 Le Verrier summed the pulls of the known planets on Uranus and predicted Neptune, found where he said. In 1859 he did the same for Mercury and came up short: the planets explained most of Mercury’s turning, not all. He proposed an unseen planet, Vulcan. It was never found. Simon Newcomb refined the gap in 1882 to 43 arcseconds a century.
2. Every Planet’s Dent
The Sun and the eight planets were run as nine dents that add, for a thousand years, from their standard positions at the start of 2000. Mercury’s perihelion was read off the run. Each planet was also run alone with the Sun and Mercury, to see its share.
| Planet | From its dent, arcseconds a century | Published (Clemence 1947) |
|---|---|---|
| Venus | 275.7 | 277.9 |
| Jupiter | 152.8 | 153.6 |
| Earth and Moon | 90.1 | 90.0 |
| Saturn | 7.3 | 7.3 |
| Mars | 2.5 | 2.5 |
| Uranus | 0.14 | 0.14 |
| Neptune | 0.04 | 0.04 |
| All together | 528.8 | 531.6 |
The run sits half a per cent under the published sum. How much turning a run shows depends slightly on how the perihelion is defined and how long it is fitted over; one numerical study finds 532.1 for thousand-year fits. The difference does not touch the gap.
3. What Is Left Over
| Arcseconds a century | |
|---|---|
| Measured turning of Mercury’s perihelion (MESSENGER ranging, 2017) | 575.31 |
| From every planet’s dent | 529 to 532 |
| Left over | about 43 |
Summing dents gives the 531. The 43 needs something the plain sum does not have.
4. A Steeper Dent Close In
In a dent that is exactly −GM/r, every orbit closes on itself, whatever its shape. Any extra steepness that falls away faster than 1/r breaks that, and the perihelion turns. The simplest extra is a small addition to the Sun’s depth falling as 1/r²:
depth = − GM / r − β / r²
It turns the perihelion by 2πβ / (GM a (1 − e²)) each orbit. For 43 arcseconds a century on Mercury that fixes β = 5.88 × 1023.
| Where | Extra depth, J/kg | As a share of the dent |
|---|---|---|
| Sun’s surface | 1,215,224 | 6.4 parts per million |
| Mercury | 175.4 | 7.65 parts in 100 million |
| Venus | 50.2 | 4.10 parts in 100 million |
| Earth | 26.3 | 2.96 parts in 100 million |
| Mars | 11.3 | 1.94 parts in 100 million |
5. One Number, Four Planets
The same run, all nine dents, with the Sun’s dent made steeper by that one β:
| Planet | Extra turning from the steeper dent | Excess required by the measurements |
|---|---|---|
| Mercury | 42.96″ | 42.98″ |
| Venus | 8.60″ | 8.62″ |
| Earth | 3.89″ | 3.84″ |
| Mars | 1.35″ | 1.35″ |
ResultOne steepness, four planets
β was set on Mercury alone. Venus, the Earth and Mars were not used, and each comes out within a per cent or two. A single steepening of the Sun’s dent, falling as 1/r², accounts for the extra turning of all four.
6. Mercury’s Stretch
Mercury’s orbit is the most stretched of the planets, eccentricity 0.21. At its nearest it is 46.0 million km from the Sun and at its farthest 69.8 million; the gradient it feels changes 2.3 times round each orbit, and the Sun’s dent at Mercury is 6.7 times steeper than at the Earth.
A steep dent does not by itself stretch an orbit: in a dent of exactly −GM/r any stretch holds forever. The stretch is changed by the other planets. In the run it grows by 0.0000201 a century, against the published 0.0000191. Over about a million years it swings between roughly 0.1 and 0.3, and over billions it has ranged from near zero to about 0.4.
The extra steepness near the Sun protects it. Long-term runs that leave out the extra turning give Mercury more than a 60 % chance of passing an eccentricity of 0.7 within five billion years; with it, about 1 %. The extra steepness moves Mercury’s perihelion out of step with Jupiter’s, and that keeps the stretch in bounds.
7. What This Settles, And What It Does Not
SettledThe requirement
The Sun’s dent must be deeper than −GM/r close in, by β/r² with β = 5.88 × 1023. One number accounts for the extra turning of Mercury, Venus, the Earth and Mars.
Open
What makes the Aether deeper close in. The author proposes the flow of the Aether near the Sun (T.7). Flow or density, it has to come out at this β.
The same number as relativity. The β found here equals the correction general relativity gives for planetary orbits, so the perihelion measurements alone do not separate the two. They are separated where the numbers differ.
Starlight. This steepening bends starlight by only a few millionths of Newton’s 0.87 arcseconds. The measured 1.75 needs its own account — E.2 Eddington 1919.
8. The Numbers
- Mercury’s perihelion from every planet’s dent: 528.8″ a century; published sum 531.6.
- Measured: 575.31″ (MESSENGER, 2017). Left over: about 43″.
- Extra steepness needed: β = 5.88 × 1023; 7.65 parts in 100 million of the dent at Mercury, 6.4 per million at the Sun’s surface.
- From that one number: Mercury 42.96″, Venus 8.60″, Earth 3.89″, Mars 1.35″.
- Mercury’s eccentricity: 0.2056, growing 0.0000201 a century in the run (published 0.0000191).
- The Sun’s gradient at Mercury: 6.7 times that at the Earth.
Terms Used Here
| Word | What it means |
|---|---|
| Dent | The lowered pressure a mass makes in the Aether around it. |
| Gradient | How fast the depth of a dent changes with distance. |
| Perihelion | A planet’s nearest point to the Sun. |
| Eccentricity | How stretched an orbit is: 0 is a circle. |
| β | The size of the extra depth near the Sun, falling as 1/r². |
Sources
- U. Le Verrier (1859); S. Newcomb (1882, 1895). Carried as reported.
- G. M. Clemence, “The Relativity Effect in Planetary Motions”, Reviews of Modern Physics 19 (1947): planet-by-planet contributions and the 531.6 sum. Venus about 278, Jupiter 153–154, Earth 90, checked against published summaries, 21 September 2026.
- E. M. Standish, Keplerian Elements for Approximate Positions of the Major Planets (JPL): starting positions for 2000, and the rate of change of Mercury’s eccentricity. Carried as reported.
- J. Laskar (1988, 2008); J. Laskar and M. Gastineau (2009): Mercury’s eccentricity over millions to billions of years, and the effect of the extra turning on its stability. Checked against published summaries, 21 September 2026.
- R. S. Park et al., “Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft”, Astronomical Journal 153 (2017): total 575.3100 ± 0.0015 arcseconds a century. Value checked against a citing paper, 21 September 2026.
- A numerical N-body study of Mercury’s perihelion: the rate depends on the perihelion definition and fitting interval, converging to 532.1 over about a thousand years. Checked 21 September 2026.
- The dent run: the Sun and eight planets as summed dents, integrated to thirteen-figure accuracy over a thousand years. The script, mercury-dent-proof.py, reproduces every figure here.
Where this sits in the series
The Experiments: each measurement examined on its own terms.
- 5.20 — The Moon From the Dents Alone — Three bodies, every classical term.
- E.4 — Mercury’s Perihelion — This memo.
- E.2 — Eddington 1919 — Starlight: the next test.