The Actions of the Aether

MemoTOE 1.12 — The Actions of the Aether
AuthorBrett Murrell
Versionv1.0
DateSeptember 2026
SeriesTOE — Theory of Everything
Categorieslife-science
A mass makes a dent in the Aether, and the dent does not push. The gradient does. A body sits across two depths — one at its inside face, one at its outside face — and the pressure difference between them is the force. The Earth sits 887 million J/kg deep in the Sun’s dent, and what holds it in orbit is the 75,578 J/kg between one face and the other.

Put two masses together and each shadows the other. The shadow raises the dent between them. That gives two pushes on each body: inward, from the other body’s dent, and outward, from its own dent made lopsided. Nothing pulls. Everything is pushed.

The answer is the same at every scale. Two Aetherons, two protons, two red giants — at four radii apart the outward push is 6.351 % of the inward push for every one of them. Mass cancels, size cancels, and only geometry, distance and mass remain.

What this memo does and does not do

Section 1 separates the measured law from the proposed mechanism. Sections 3 to 9 are arithmetic on the measured law of gravity and can be checked directly.

Sections 10 to 19 set out shadowing, a proposed mechanism, not an established result. Every assumption it makes is numbered in section 12. Nothing in it is fitted. Section 20 states what it does not yet settle.

PressureSpace does not curve. Gravity is the pressure of the Aether
PushNothing pulls. Bodies are pushed down the gradient
GradientFalls as 1/r² from the surface out, r counted from the centre. The gradient, not the depth, is the force
DensitySets how deep and steep a dent is close in. Far out, only mass and distance

Published for scrutiny rather than as a settled result.

The model behind the figures — dents in three dimensions, cross-sections, gradients and orbits — is built as an interactive tool, and the gravity figures reproduce in it.

1. Gravity: The Measurement And The Mechanism

Two questions are easy to run together. How strong is gravity? That is a measurement. What does the pushing? That is a mechanism. This memo accepts the first answer as it stands and proposes a different answer to the second.

SettledNewton’s law is correct

In 1687 Newton published the law: the force between two masses is GMm/r². Every figure in this memo is calculated with it, unchanged. It gives the Moon’s acceleration from its measured period to within 0.008 %. This memo does not challenge Newton’s calculations. It reproduces them.

Newton did not say what causes it. In 1713 he wrote that he would frame no hypotheses about the cause. In a 1693 letter to Richard Bentley he went further: one body acting on another across empty space, with nothing between them to carry the action, he called an absurdity. Newton left the mechanism open and thought a medium was needed.

In 1717 he proposed one. In Query 21 of his Opticks he asked whether the medium filling space is thinner inside and near the Sun and planets, growing denser with distance — so that every body is pushed from the denser parts toward the thinner. That is the dent this memo sets out. Newton put it as a question and never ruled it out.

The people and their breakthroughs

YearWhoBreakthrough
c. 330 BCAristotleHeavy things fall to their natural place, the centre of the world.
1543CopernicusThe Sun, not the Earth, at the centre of the planets.
1609–1619KeplerFrom Tycho Brahe’s observations: planets move in ellipses, by three fixed laws.
1638GalileoFalling bodies speed up alike, whatever their weight.
1644DescartesPlanets carried round by vortices in a fluid filling space.
1679HookeSuggests to Newton an attraction falling as the inverse square of distance.
1687NewtonThe law of universal gravitation, GMm/r². Cause left open.
1717NewtonOpticks, Query 21: a medium thinner near the Sun and planets, denser with distance, pushing bodies toward the thinner parts.
1748Le SageBodies pushed by particles arriving from every direction, each shadowing the other.
1798CavendishWeighs the Earth with a torsion balance — the first laboratory measurement of the force between masses.
1801SoldnerNewton’s law applied to light: starlight should bend 0.87 arcseconds at the Sun’s edge.
1846Le Verrier, AdamsFrom the wobble of Uranus, predict an unseen planet. Neptune is found where predicted.
1859Le VerrierMercury’s orbit turns faster than the other planets explain. Proposes a planet, Vulcan. Never found.
1865MaxwellLight as a wave of the electromagnetic field, taken to travel in an aether.
1887Michelson, MorleyLook for the Earth’s motion through the aether. Find none.
1905EinsteinSpecial relativity: light explained with no aether.
1915EinsteinGeneral relativity: gravity as the curvature of spacetime by mass. Gives Mercury’s extra turning exactly.
1916SchwarzschildThe first exact solution: the field around a single round mass.
1919Eddington, DysonEclipse measurement of starlight bending at the Sun: 1.75 arcseconds, twice Soldner’s figure.
1920EinsteinAt Leiden: space in general relativity has physical properties, and in that sense an aether exists.
1959Pound, RebkaClocks lower in a dent run slower — measured up a 22.5 m tower.
1974Hulse, TaylorA pair of neutron stars losing orbit exactly as gravitational waves predict.
2015LIGOGravitational waves detected directly.
2019Event Horizon TelescopeAn image of the dark centre of the black hole in the galaxy M87.
2026This seriesThe dent and the flow of the Aether. Bodies pushed down its gradient. Space does not curve.

Mapping every body — what it already gives

Summing the force from every body is Le Verrier’s method, and the method this memo reproduces. It found Neptune. Applied to Mercury, the forces from all the planets turn its orbit about 531 arcseconds a century. The measured turning is about 574. 43 arcseconds a century are left over. A map of every body’s dent gives the 531. The author proposes the 43 come from the flow of the Aether — motion of the medium itself, beyond the static sum of dents. Mercury’s orbit is the most stretched of the planets (eccentricity 0.21) and the most tilted (7° to the Earth’s orbit). A full model of every body, and the flow between them, is the test.

How the ephemerides are calculated today

NASA’s Jet Propulsion Laboratory computes the positions of the planets (the DE440 ephemeris) by integrating every planet, the Moon, hundreds of asteroids and a ring of outer bodies, with each body’s field mapped from its shape. That part is the dent and its gradient — the method of this memo. The equations of motion also carry relativistic correction terms, and the quantity used is energy per kilogram. No pressure appears in the calculation.

ProposedA dent in the Aether

This series proposes a different mechanism from Einstein’s. Space is filled with the Aether at a deep-space pressure. A mass lowers that pressure around itself — the dent — and bodies are pushed down its gradient. Nothing pulls. The arithmetic of the dent is Newton’s arithmetic, which is why sections 3 to 9 reproduce his law exactly.

The author’s position: space does not curve. Gravity is the pressure of the Aether — its dents and its flow. This is the premise of the Aether model: an alternative explanation to the curvature of space. The full case is set out in T.1 — Space Is the Void.

What the mechanism still has to answer

General relativity has passed measurements that Newton’s law alone does not explain. A mechanism offered in its place must account for each:

The dent as set out in this memo gives Newton’s results. Each measurement above has its response in the series, listed with it. The Experiments set, E.1 to E.15, examines each on its own terms — what was measured, what was assumed in reducing it, and whether the same data reduce differently under the Aether model.

2. The Rules

Everything that follows rests on these. Rules 1, 2 and 4 to 7 are the measured law of gravity in this series’ terms. Rule 3 is the series’ reading of it, set out in T.5.1. Rule 8 belongs to the proposal that starts in section 10.

Rule 1A mass makes a dent

depth = −GM/r. Deepest at the mass, rising toward the deep-space level, never reaching it.

Rule 2A dent does not push. A gradient does.

Depth on its own does nothing. The centre of the Earth is the deepest point and has no force at it.

Rule 3Nothing pulls

Every force is a push. A body moves toward another because its outside face is pushed harder than its inside face.

Rule 4The gradient acts on the whole mass

It acts on every Aetheron in the volume, not on the surface. force = M × gradient.

Rule 5A body is moved only by another body’s dent

Its own dent is the same all round and cancels — unless something makes it lopsided.

Rule 6At a distance, only mass and distance count

Outside a body the gradient is GM/r². Its radius and its density do not enter.

Rule 7At the surface and inside, density counts

Two bodies, both of mass 10. One has radius 10, the other radius 100, so the small one is 1,000 times denser. Depth and gradient in units of GM:

Distance from centreR = 10 depthgradientR = 100 depthgradient
0−0.1500−0.0150
10−0.1001.0 × 10−2−0.014951.0 × 10−5
50−0.0204.0 × 10−4−0.013755.0 × 10−5
100−0.0101.0 × 10−4−0.0101.0 × 10−4
200−0.0052.5 × 10−5−0.0052.5 × 10−5
1000−0.0011.0 × 10−6−0.0011.0 × 10−6

The dense body’s dent goes ten times deeper at its centre and is a thousand times steeper at radius 10. Outside radius 100 the two dents are identical. Inside a body the gradient is (4/3)πGρ per metre from the centre — density alone.

Two measures of steepness at a surface. The gradient there is (4/3)πGρR — density times size. How fast it changes with distance there is density alone: it rises at (4/3)πGρ per metre just inside, and falls away at (8/3)πGρ per metre just outside. Going to small scales, size shrinks the first and leaves the second untouched. A proton is denser than a neutron star (6.74 × 1017 against 2.75 × 1017 kg/m³), so its gradient falls away faster just outside its surface — 3.77 × 108 against 1.54 × 108 per second squared — though the gradient itself is 1019 times smaller.

What sets steepness close inInside each body the gradient rises in a straight line whose slope is density alone; the peak at the surface is slope times radius. Large, density ρ Small, density ρ Small, 4 × density gentle rise, high peak same rise, low peak 4 × the rise, same peak Shaded: inside the body. How fast the line rises is set by density alone. The peak is the surface. Its height is rate of rise × radius — density times size. Gradient up, distance from centre across, same scales in all three. Dashed line: equal peaks.
Figure 2.1 — What sets steepness close in. The rate of rise inside is density; the peak at the surface is density times size.

The same mass at three densities. One solar mass, packed tighter each time:

Density ×1Density ×8Density ×27
Radius696,340 km348,170 km (½)232,113 km (⅓)
Density, kg/m³1,40611,25137,970
Rate of rise inside, per s²3.93 × 10−73.15 × 10−6 (×8)1.06 × 10−5 (×27)
Peak gradient at surface273.81,095 (×4)2,464 (×9)
Dent depth at surface, J/kg1.91 × 10113.81 × 1011 (×2)5.72 × 1011 (×3)
Dent depth at centre, J/kg2.86 × 10115.72 × 10118.58 × 1011
Gradient at 1 AU0.0059310.0059310.005931

At the same mass, raising the density by k raises the rate of rise inside by k, the peak gradient at the surface by k and the dent depth by k. Far out, nothing changes.

One mass at three densitiesOne mass packed to three densities. Each rises in a straight line inside, steeper for denser bodies, and meets one shared 1/r squared curve at its own surface. 27 × density, radius ⅓ — peak ×9 8 × density, radius ½ — peak ×4 density ×1, radius R One shared 1/r² curve from each surface out Same mass throughout. Shading marks the inside of each body. Inside, the rate of rise grows with density: ×1, ×8, ×27. The peak at the surface rises ×1, ×4, ×9. Gradient up, distance from centre across.
Figure 2.2 — One mass at three densities. Each climbs the same 1/r² curve further in before its surface stops it.

Rule 8The shadow is geometry

How much one body shadows another is set by its size and its distance. A denser body of the same mass is smaller and casts less shadow.

Geometry, distance and mass — and density, where a body’s own surface and interior are concerned. At every scale.

3. What A Mass Does To The Aether

A mass lowers the pressure of the Aether around it. That lowered region is the dent. Its depth at distance r from the centre is

depth = − G M / r

Deepest at the mass, rising back toward the deep-space level with distance, never quite reaching it — which is why gravity has no edge.

A mass, its dent, and the gradientTop: the depth of the dent below deep space, deepest at the centre of the mass. Bottom: the gradient, zero at the centre, peaking at the surface and falling away as one over r squared outside. Arrows show the push on one kilogram toward the centre. Deep space level the mass The dent depth −GM/r outside, deepest at the centre R2R3R4R centre The gradient zero at the centre, peak at the surface outside: 1 at R, ¼ at 2R, 1/9 at 3R, 1/16 at 4R — 1/r² The push on 1 kg, toward the centre, falling away with distance Shading marks the mass. Schematic; r counted from the centre.
Figure 3.1 — A mass and its dent. The dent is deepest at the centre; the gradient peaks at the surface and falls away as 1/r².

One fact. The rest of the memo is what follows from it.

4. A Dent Does Not Push. A Gradient Does.

How fast the depth changes with distance is the gradient:

gradient = G M / r²

At the bottom of a valley nothing moves you. On the side of one you roll. The bottom of a dent is the same: at the centre of the Earth the depth is greatest and there is no difference in any direction, so there is no force at all. All the depth in the world, and nothing pushing.

Depth does nothing, the gradient pushesA dent in cross-section. A body at the bottom has no difference across it and feels no force. A body on the wall sits across a change in depth and is pushed toward the centre. Deep space level On the wall: the depth changes across it — pushed toward the centre At the bottom: deepest point, no force no difference across it in any direction — the centre of the Earth
Figure 4.1 — Depth does nothing. The gradient pushes.

The depth does not act. The gradient acts.

What the gradient acts on

The gradient acts on every Aetheron in the body — the whole volume of its mass, not its surface. The force is the gradient times the mass it acts on:

force = M × gradient

The body’s radius does not enter. A wider body spans a larger difference in depth, but over a wider width, and the two cancel. The Earth at double its radius and the same mass:

Earth radiusDifference across itGradientForce
6,371 km75,578 J/kg5.931408 × 10−33.5422 × 1022 N
12,742 km151,156 J/kg5.931408 × 10−33.5422 × 1022 N

Radius enters in two places only: inside a body, where its own dent’s gradient is GMa/R³ (section 13), and in the shadow, where how large one body looks from the other sets q (section 11).

5. A Body Has Two Faces

A body is not a point. It has an inside face, toward the other mass, and an outside face, away from it. The dent has one depth at each, and the pressure difference between them is the force.

The ruleThe difference across a body is the force

The Earth in the Sun’s dent. Radius 6,371 km, distance 149.6 million km.

WhereDepth of the Sun’s dent, J/kg
Earth’s inside face−887,376,427
Earth’s outside face−887,300,849
difference across the Earth75,578

The inside face is deeper, so the pressure there is lower, so the outside face is pushed harder. Divided by the Earth’s width and multiplied by its mass: 3.54 × 1022 N, toward the Sun.

Two facesThe Earth in the Sun's dent. The outside face sits at higher pressure than the inside face, so it is pushed harder, and the net push is toward the Sun. Sun Earth Inside face −887,376,427 J/kg deeper — lower pressure Outside face −887,300,849 J/kg shallower — higher pressure Net push toward the Sun: 3.54 × 10²² N from a difference of 75,578 J/kg across the Earth Arrow lengths exaggerated: the difference is 0.0085 % of the depth.
Figure 5.1 — Two faces. The outside face sits at higher pressure and is pushed harder.
The gradient across the EarthTop: the Sun's dent from the Sun out past the Earth. Bottom: a zoom on the Earth. Its inside face sits deeper in the dent than its outside face; the difference over the Earth's width is the gradient, and times the Earth's mass it is the force. Deep space level Sun the Sun’s dent Earth, 1 AU Earth Inside face, toward the Sun −887,376,427 J/kg Outside face −887,300,849 J/kg difference 75,578 J/kg width 12,742 km Gradient = 75,578 J/kg ÷ 12,742 km = 5.931 × 10⁻³ per metre × the Earth’s mass = 3.54 × 10²² N, toward the Sun Zoomed and exaggerated: across the Earth the difference is 0.0085 % of the depth.
Figure 5.2 — The gradient across the Earth: the difference between its two faces, over its width.

6. Why Its Own Dent Does Nothing

The Earth makes its own dent — 62.6 million J/kg deep at its surface. It is the same depth all round the Earth’s centre. Every push it makes in one direction is matched by an equal push in the opposite direction, and it cancels.

A body's own dentAlone, a body's own dent pushes it equally in every direction and the pushes cancel. With a neighbour shadowing one side, the inside face is raised, pushed harder, and the body is pushed outward. Alone its own dent the same all round Shadowed on one side a neighbour to the left pushed equally every way — cancels inside face raised, pushed harder — net outward Arrows: the push from the body's own dent on each part of its surface. Schematic.
Figure 6.1 — A body’s own dent: equal all round and cancelling, until a shadow makes it lopsided (section 12).

A body is moved only by another body’s dent. Section 12 is about the one thing that changes that.

7. Adding It Up Inside

Nothing is watertight to the Aether. The pressure difference acts on every Aetheron in the body, not on its skin. The force is summed through the whole volume, and that is why mass and not size decides it.

Every Aetheron, not the skinWrong: the push drawn acting only on a body's surface, as on a hull in water. Right: the push acting on every Aetheron through the whole volume, which is why mass, not size, decides the force. Not on the skin as water pushes a hull — wrong here On every Aetheron nothing is watertight to the Aether force set by surface area force set by the Aetherons inside — the mass The faces read the gradient. The volume carries the force. Arrows point toward the other body. Schematic.
Figure 7.1 — The push acts on every Aetheron in the body, not on its skin.

The faces are how the gradient is read, not where the force acts

“Inside face” and “outside face” describe the gradient across the body. The force itself lands throughout the interior. For the outward push in section 13, taking it at the surface instead gives an answer eight times too large.

The check: with no shadowing, summing through the volume reproduces Newton’s law exactly — 1.0000 at 4, 10 and 40 radii.

This is Archimedes in form and Newton in result. A floating body is pushed on its skin because water is kept out. Nothing keeps the Aether out, so there is no displaced volume and no buoyancy — only mass.

8. Same Mass, Any Size

Two bodies of the same mass, one large and thin, one small and dense, placed at the same spot in the Sun’s dent. The large one spans more of the dent, so the difference across its faces is larger — but over a wider width. The gradient comes out the same, and so does the force.

Same mass, two sizes, in the Sun's dentA large low-density body and a small high-density body of the same mass sit at the same place in the Sun's dent. The large one spans a bigger depth difference across a bigger width, so the gradient and the force are the same. Large, low density radius 63,710 km Small, high density radius 6,371 km difference 755,780 J/kg across 127,420 km difference 75,578 J/kg across 12,742 km Same gradient, 5.931 × 10⁻³ — same force, 3.5422 × 10²² N Earth's mass at 1 AU. The Sun is off to the left; the dent deepens toward it. Schematic.
Figure 8.1 — Same mass, two sizes, in the Sun’s dent.
Earth’s mass at 1 AU, radiusDensity, kg/m³Difference across faces, J/kgForce
637 km5.5 × 1067,5583.5422 × 1022 N
6,371 km5,51375,5783.5422 × 1022 N
63,710 km5.5755,7803.5422 × 1022 N
637,100 km0.00557,557,9403.5422 × 1022 N

Close in, the two faces stop telling the whole story. Near the Sun the dent curves across a large body: its near side is pushed much harder than its far side. Summed through every Aetheron, the round body comes out at exactly the push at its centre.

Pushed harder on the near sideA large body close to the Sun, cut into strips. Near strips are pushed hard, far strips lightly. Averaged through the whole round body, the push equals the push at its centre, the same as for a small body at the same place. Large, low density radius 637,100 km, 2 Sun radii from its centre Small, high density radius 6,371 km, same place every part pushed alike Averaged through the body: 68.4, the push at its centre 68.4 — the same Per kilogram: near side 185, centre 68.4, far side 35.3. The Sun lies to the left. Whole-body force the same for both: 4.087 × 10²⁶ N. Arrow lengths to scale.
Figure 8.2 — Pushed harder on the near side, less on the far side, and the same in total.
Earth’s mass, 2 Sun radii from its centre, radiusTwo-face reading ÷ NewtonVolume sum ÷ Newton
6,371 km1.000021.00000
63,710 km1.002101.00000
637,100 km1.264661.00000

In another body’s dent, force = mass × the gradient at the body’s centre, for any round body, whatever its size or density. The faces read the gradient; the volume carries the force.

9. Two Dents, One Medium

Put a second mass nearby and the two dents add. Between them the two gradients oppose, and at one point they cancel exactly:

PairGradients cancel atShare of the separation
Earth and Moon346,000 km from Earth90.019 %
Sun and Earth259,000 km from Earth99.827 %
two matched bodiesthe midpoint50.000 %
Two dents, one mediumThe Earth's dent and the Moon's dent along the line between them, and their sum. The sum is shallowest where the two gradients cancel, 346,000 km from the Earth. Deep space level gradients cancel: 346,000 km Earth Moon Both dents run off the bottom of the chart: the Earth's to −6.26 × 10⁷ J/kg at its surface Earth's dent Moon's dent The two added
Figure 9.1 — Two dents, one medium: the Earth’s, the Moon’s, and the two added.

Each body still feels only the other body’s dent. The combined curve shows where the gradients cancel. It does not show the force on either body.

10. One Body Shadows The Other

From here the memo sets out a proposal. Everything above is arithmetic on measured gravity. What follows is not.

The dent is held in place by the Aether pressing in from every direction. A second body standing nearby blocks part of that from the side it stands on. That blocking is the shadow, and it raises the dent in the region between the two bodies.

body 1 body 2 shadowed
The Aether presses in from every direction. Between the two bodies each blocks part of what reaches the other.

11. What The Shadow Blocks

How much one body blocks is geometry and nothing else. Seen from one body, the other covers an angle θ with

sin θ = R / d   ·   blocked fraction f = (1 − cos θ) / 2   ·   shadow factor q = 2f

q is the blocked fraction as a share of the inside half — the half facing the other body.

Separationθfq
4 radii14.478°1.5877 %0.031754
What the shadow blocksSeen from body 1, body 2 of radius R at distance d covers an angle theta, with sin theta equal to R over d. The covered part of body 1's surroundings is the blocked fraction. body 1 body 2 R d θ blocked part of body 1's surroundings sin θ = R / d · blocked fraction f = (1 − cos θ) / 2 · shadow factor q = 2f Drawn at 4 radii: θ = 14.478°, f = 1.5877 %, q = 0.031754. Size and distance only.
Figure 11.1 — What the shadow blocks: geometry only.

No mass, no depth, nothing about what the bodies are made of. Only size and distance.

12. The Shadow Working, Step By Step

Assumptions — stated, not yet shown

A1. Something maintains the dent.

A2. Whatever maintains it can be blocked by another body.

A3. The amount blocked scales with the covered fraction, q.

A4. The shadow raises a body’s own dent at its inside face by the fraction q.

A5. A body responds to its own dent once that dent is no longer the same all round.

Two protons, four radii apart. Each shadows the other.

Step 1Proton 2’s dent, across proton 1

Proton 1’s faceDepth of proton 2’s dent, J/kgPressure
inside−4.429793 × 10−23lower
outside−2.657876 × 10−23higher

Higher pressure on the outside face. Pushed inward.

Step 2Proton 1’s own dent, shadowed by proton 2

Proton 1’s faceDepth of its own dent, J/kgPressure
inside — raised by q−1.286739 × 10−22higher
outside — unshadowed−1.328938 × 10−22lower

Before proton 2 arrived these two were equal. Now the inside face is higher. Pushed outward.

Step 3The dent between them

The region between the pair is raised 3.175 % at the midpoint and 0.794 % two radii outside it.

The shadow raises the depth at the inside face, which changes the difference across the body, which changes the push. Both pushes come from shadowing.

13. How Big The Outward Push Is

Inside a body its own dent has gradient GMa/R³ at distance a from the centre. The unshadowed part cancels by symmetry. What remains, summed over the inside half, is πR⁴/6. Divided through the volume:

outward push = G M² q / (8 R²)

Far apart, q approaches R²/2d², so for two matched bodies

outward push = G M² / 16 d²   ·   inward push = G M² / d²

Both fall as 1/d². Their ratio never changes with distance.

14. Two Pushes, Opposite Ways

Nothing pulls. Each body is pushed twice: inward by the other body’s dent, outward by its own. For the two protons:

At 4 radii
inward push1.6539 × 10−35 N
outward push1.0503 × 10−36 N
outward ÷ inward6.351 %
Two pushes, opposite waysTwo protons four radii apart. Each is pushed inward by the other's dent and outward by its own shadowed dent. The outward push is 6.351 percent of the inward push, drawn to scale. proton 1 proton 2 inward push 1.6539 × 10⁻³⁵ N outward push 1.0503 × 10⁻³⁶ N inward push, from proton 1’s dent outward push, own dent Outward ÷ inward = 6.351 %. Net: pushed together. Arrow lengths to scale. Four radii apart; the same ratio at every scale.
Figure 14.1 — Two pushes on each proton, drawn to scale.

What repulsion would require

Between two matched bodies, with q as geometry gives it, the inward push is larger at every distance. For them to be pushed apart, the outward push must exceed the inward one, which requires the shadow to be 16 times the geometric value — q = 0.5 at four radii. q cannot exceed 1, so closer than 2.83 radii no shadow of any strength reaches it. And because the ratio is the same at every scale (section 15), the factor that separated two protons would separate the Earth and the Moon by the same share. Between unequal bodies one of the two can be pushed away — section 19. Where repulsion comes from is set out as open in section 20.

15. The Same Answer At Every Size

Outward ÷ inward is q·d²/(8R²), and q depends only on R/d. The mass cancels and the size cancels.

Separation, radiiqOutward ÷ inward
2 (touching)0.13397466.6987 %
40.03175426.3508 %
1005.0001 × 10−56.2502 %
The same answer at every sizeOutward push as a share of inward push for two matched bodies, against separation in radii. It falls from 6.699 percent touching to 6.250 percent far apart, and the curve is the same for every pair. 2461015206.3%6.5%6.7% touching: 6.699 % 4 radii: 6.351 % far apart: 6.250 % — one sixteenth Separation, in radii One curve for two Aetherons, two protons, two grains of sand and two red giants alike.
Figure 15.1 — The same answer at every size.

Two protons and two 1,000 kg spheres, both at four radii, both give 6.351 %. The forces differ by 1031.

16. Nothing About It Changes With Size

Geometry, distance and mass decide the answer, at every scale. No new force appears as bodies get larger or smaller, and nothing is re-tuned from one scale to the next.

Pair, four radii apartOutward ÷ inward
two Aetherons6.3508 %
two protons6.3508 %
two grains of sand6.3508 %
two Earths6.3508 %
two red giants6.3508 %

What does not stay the same

The forces. They span about 1070 N across that table. What holds is the ratio and the form of the law, not its size.

The floor. The Aetheron has one fixed radius. Near that size the blocked region stops being a smooth disc in a continuous medium, and f = (1 − cos θ)/2 no longer applies. “Every scale” means every scale above the Aetheron.

17. Bodies That Match

Two matched bodies see the same blocked fraction and receive the same outward push. Everything is symmetric, and the forces on the pair sum to zero. One curve describes every matched pair in the universe.

18. The Large And The Small

Each body is shadowed by how large the other looks, but feels that shadow through its own dent. For unequal bodies those are different things.

PairOutward ÷ inward, larger bodyOutward ÷ inward, smaller body
Sun and Earth174.569 %0.224 %
Earth and Moon37.790 %1.034 %

A large body’s own dent is deep, so shadowing it slightly produces a large outward push. A small body’s own dent is shallow, so the same shadow does little. The matched case is the exception. Every pair doing real work in the universe is unequal.

For a proton and an electron, both are pushed inward only if the electron’s radius lies between 0.583 % and 9.335 % of the proton’s. Outside that window one of the two is pushed away.

19. Dense And Diffuse

Start with the dent itself. Sirius B, a white dwarf, holds about one solar mass in a radius of 5,850 km — 119 times smaller than the Sun and 1.69 million times denser.

Same mass, two densitiesThe Sun beside Sirius B, same mass. A dashed circle around Sirius B marks where the Sun's surface would be; the ring between is the near zone. Sun radius 696,340 km Sirius B Near zone outside Sirius B, inside where the Sun would be 1 solar mass, spread out 1 solar mass, packed tight Sirius B radius 5,850 km — drawn larger than true scale (119 times smaller than the Sun)
Figure 19.1 — Same mass, two densities. The near zone is outside Sirius B but inside the radius the Sun would have.

Outside the Sun’s surface the two dents are one curve. Inside it they separate: the Sun’s flattens into a shallow bowl, and Sirius B’s keeps following the same curve down into a narrow, deep hole. Sirius B is the Sun’s mass packed inward. Where that mass went, the dent deepened. Beyond the Sun’s radius no mass moved, so nothing changed.

The two dents in cross-sectionOutside the Sun's surface the two dents are one curve. Inside it the Sun's dent is a shallow bowl and Sirius B's is a narrow, deep hole. Deep space level Sun's surface Sun's surface Sun: shallow bowl Sirius B: deep, narrow hole Same dent for both, from the Sun's surface out The rounded bottom of the hole is the inside of Sirius B Sun Sirius B Near zone Not to scale — the real Sirius B hole is 24 times narrower again, and far deeper
Figure 19.2 — The two dents in cross-section. Schematic.

Density makes the dent deeper. The same two dents drawn to true scale:

Dent depth to true scaleThe Sun's dent and Sirius B's dent to the same true vertical scale. The Sun's is a barely visible dip; Sirius B's is a needle 119 times deeper. Deep space level 1×10¹³ 2×10¹³ 3×10¹³ Sun: 2.9×10¹¹ at the bottom — the thin dip along the top Sirius B's surface: 2.3×10¹³ Sirius B's bottom: 3.4×10¹³ 119 times deeper than the Sun's True scale, J/kg, one solar mass each. A neutron star's would go about 490 times deeper again.
Figure 19.3 — Dent depth to true scale. The Sun’s whole dent is the thin dip along the top.
Depth, J/kgBottom of the dentAt the surfaceAt 1 AU
Sun−2.86 × 1011−1.91 × 1011−8.87 × 108
Sirius B−3.40 × 1013−2.27 × 1013−8.87 × 108
Neutron star−1.66 × 1016−1.11 × 1016−8.87 × 108

Same mass, same depth far out. At the surface the depth is GM/R, so packing the mass into a smaller radius deepens it: 119 times for Sirius B, 58,000 times for a neutron star. The bottom, at the centre, is one and a half times the surface depth.

Distance from centreSun, N/kgSirius B, N/kgNeutron star, N/kg
6 km0.0024 inside3,978 inside4.61 × 1011 inside
12 km0.0047 inside7,957 inside9.22 × 1011 surface
1,000 km0.39 inside663,100 inside1.33 × 108
5,850 km2.30 inside3,879,000 surface3,879,000
100,000 km39.3 inside13,27013,270
696,340 km273.8 surface273.8273.8
1 AU0.00590.00590.0059

One solar mass each. Densities 1,406, 2.37 × 109 and 2.75 × 1017 kg/m³, taken as uniform. The neutron-star column carries −GM/r to its limit; measurements near a neutron star’s surface depart from it.

Apply the face rule to a 1 kg object 2 km wide. Close in, its two faces sit at nearly the same depth in the Sun’s bowl and at very different depths on Sirius B’s wall. Far out they sit at the same two depths whichever body made the dent.

The face rule, close in and far outClose in, the Sun's dent is nearly flat under the object and Sirius B's is steep. Far out, both give the same slope and the same push. Close in — 100,000 km inside the Sun, outside Sirius B Far out — 1,000,000 km outside both Sun 39 N Sirius B 13,275 N Sun 133 N Sirius B 133 N Line: the dent's slope under the object. Dots: its inside and outside faces. Arrow: the push toward the centre, which lies to the left. 1 kg object, 2 km wide, one solar mass. Slopes and arrow lengths not to scale.
Figure 19.4 — The face rule, close in and far out.

The ruleDensity decides how deep and how close

A denser body of the same mass has a deeper dent. It also lets you stand, outside it, nearer its centre, and the gradient keeps climbing as 1/r² all the way down to that surface. Surface gradient is (4/3)πGρR — density times size. Beyond the less dense body’s radius the dents even out: mass and distance alone, which is why an orbit weighs a star without telling its size.

The same density that deepens the dent carries into the outward push.

Mass alone does not decide how a body is treated. Rule 7 showed that at the same mass a denser body has a deeper, steeper dent at and inside its surface. Its outward push comes from that dent, so density carries straight into the push. Far apart, for body i facing body j:

outward ÷ inward = (Mi / Mj) × (Rj / Ri)² ÷ 16

The same two bodies as rule 7, both of mass 10:

PairOutward ÷ inward
both radius 10 — dense and dense6.251 %
both radius 100 — diffuse and diffuse6.351 %
radius 10 facing radius 100 — the dense body626.6 %
radius 10 facing radius 100 — the diffuse body0.0625 %

Matched pairs give the same small share whatever their density. Put a dense body beside a diffuse one of the same mass and the dense one is pushed away: its own dent is deep, and the diffuse body is wide enough to shadow a large share of it.

Other body’s radius ÷ own radius, equal massOutward ÷ inward
225.00 %
356.25 %
4100.00 %
10625.00 %

This is repulsion, and it comes from density, not a stronger shadow. It acts on one body of the pair. The diffuse body is still pushed inward, so the pair is not driven apart and the forces on it do not balance — section 20.

20. Where The Argument Stops

OpenThe third law

Matched pairs are balanced. Unequal pairs are not, because each body’s outward push goes with its own M²/R². Earth and Moon: 7.279 × 1019 N left over, 1.204 × 10−5 m/s² of self-acceleration on the pair — 0.2 % of Earth’s acceleration about the Sun, 5.931 × 10−3 m/s². The fault lies in the M²/R² scaling of the outward push, not in the dent.

OpenWhat maintains the dent

A1 and A2 are assumed. A standing field can be shadowed — a Faraday cage does it — but the series has not yet said what maintains the dent.

OpenRepulsion

Between matched bodies (section 14) the inward push wins at every distance and every scale. Repulsion there needs a shadow 16 times the geometric value, unreachable closer than 2.83 radii, and by scale invariance it would apply to every matched pair at once.

Between unequal bodies (section 19) a body is pushed away when (Mi/Mj)(Rj/Ri)² exceeds 16. The other body is still pushed in, so the pair is not driven apart as a pair.

TestThe laboratory

If the shadow is real, a measurement of G depends on the apparatus. For two spheres of equal density the correction on the test mass is Rtest/(16 Rsource).

Rtest / RsourceG measured low by
0.053,581 ppm
0.2013,095 ppm
0.3321,741 ppm
0.7548,255 ppm

CODATA 2022: G = 6.67430(15) × 10−11 m³ kg−1 s−2, relative uncertainty 22 ppm. Experiments disagree with each other by about 550 ppm, and that disagreement has not been shown to follow apparatus geometry. The predicted effect is 6.5 to 88 times the whole spread. This is where the mechanism is tested first. Response: E.1 Measuring G (planned).

ClosedIt is not charge

Two protonsN·m²
electric, k e²2.3071 × 10−28
gravity, G mp²1.8672 × 10−64
outward push, G mp²/161.1670 × 10−65

Short by 1.977 × 1037 — sixteen times the gravity-to-electricity gap of 1.2356 × 1036. Held by the dent alone, a hydrogen atom would be 1.20 × 1029 m across. Charge has two signs, is the same on bodies of different mass, cancels in a neutral atom, and comes in one fixed unit; a shadow does none of these. Electromagnetism is T.5.2.

21. Why The Apple Falls

In 1726 Newton told William Stukeley that the idea of gravity first came to him when an apple fell, at his mother’s farm at Woolsthorpe in the plague years of 1665–66. He asked why it went straight down — not sideways, not up, but always toward the centre of the Earth.

In the Aether model the answer is the rules of this memo, applied to an apple. The Earth’s mass lowers the pressure of the Aether around it: at the ground the dent is 62.6 million J/kg deep, deeper below and shallower above. An apple 8 cm across has its top face 0.79 J/kg shallower than its bottom face. The top is pushed harder than the bottom. While the stem holds, the stem takes the push. When it lets go, nothing does, and the apple falls — one metre in 0.45 seconds.

Why the apple falls, and why you feel heavyAn apple falling from a tree, pushed down because its top face sits shallower in the Earth's dent than its bottom face. A person standing, pushed down through every part of the body; what they feel is the floor pushing back. Toward deep space: higher pressure Earth’s surface — the dent deepens below pushed down, 0.98 N 1 m in 0.45 s head, outside face −62,560,221 J/kg 17.7 J/kg deeper at the feet feet, inside face −62,560,239 J/kg the floor pushes back: 687 N that is the weight you feel Arrows in the body: the push on every part. Schematic.
Figure 21.1 — Why the apple falls, and why you feel heavy.

The same is happening to you now. Standing 1.8 m tall, your feet sit 17.7 J/kg deeper in the Earth’s dent than the top of your head — three ten-millionths of the depth. That difference, acting on every Aetheron in a 70 kg body, is 687 N, pushing you toward the Earth’s centre.

What you feel is the floor. The push acts through the whole body at once, on every part alike, so it cannot be felt on its own. What you feel is the floor stopping you, pressing back on your feet with 687 N. Take the floor away and the feeling goes. On the space station, 400 km up, the gradient is still 89 % of what it is at the ground; the crew feel nothing because nothing stops them — they are falling around the Earth.

And the same dent holds the Moon. This was Newton’s next step. The Moon is about 60 Earth radii away, so by 1/r² the gradient there is 60 × 60 = 3,600 times weaker:

Distance from Earth’s centreGradient, m/s²
The apple1 Earth radius9.82
The Moon, by 1/r²60 Earth radii9.82 ÷ 3,600 = 0.00273
The Moon, measured from its orbit60.4 Earth radii0.00273

The apple and the Moon are pushed by the same dent. One falls to the ground; the other is moving sideways fast enough that it keeps falling around the Earth instead.

The weight you feel sitting here is the Aether of deep space pressing on every part of you — a little harder on the side away from the Earth than on the side toward it.

22. The Numbers

Terms Used Here

WordWhat it means
AetherThe proposed substance filling all space, made of one kind of particle.
AetheronThe proposed single particle the Aether is made of. One size, one mass.
DentThe lowered pressure a mass makes in the Aether around it.
DepthHow far down the dent goes at a point, in J/kg.
GradientHow fast depth changes with distance.
DifferenceThe gap in depth between a body’s two faces.
Inside face / outside faceThe side of a body toward the other mass, and the side away from it.
Inward pushThe push from the other body’s dent, toward the other body.
Outward pushThe push from a body’s own dent once shadowing makes it lopsided.
Near zoneThe region outside a dense body but inside the radius a less dense body of the same mass would have. Where density shows.
ShadowThe proposed blocking of what maintains a dent, by a second body.
Blocked fraction, fThe share of all directions one body covers, seen from another.
Shadow factor, qThe blocked fraction as a share of the inside half. q = 2f.

Every term used across the series is on the terms page.

Sources

Reference codes read source.work.passage and resolve on the Master Source Register.

  1. I. Newton. Philosophiæ Naturalis Principia Mathematica (1687). The inverse-square law and the shell theorem. Carried as reported; the original has not been consulted.
  2. G.-L. Le Sage. Lucrèce Newtonien (1784). The earliest shadowing account of gravity. Carried as reported; not verified.
  3. I. Newton. Opticks, 2nd edition (1717), Query 21. Carried as reported; to be checked against the original text before publication.
  4. I. Newton. General Scholium, Principia, 2nd edition (1713), and letter to R. Bentley (25 February 1692/3). Carried as reported; not consulted in the original.
  5. A. A. Michelson and E. W. Morley (1887); A. Einstein (1905, 1915); A. Einstein, “Ether and the Theory of Relativity”, Leiden (1920). Carried as reported.
  6. Tests of general relativity: Mercury’s perihelion; the 1919 eclipse; Pound and Rebka (1959); Cassini (2003); LIGO (2015). Standard results, carried as reported; figures to be checked against the original papers before publication.
  7. U. Le Verrier (1859); S. Newcomb (1882, 1895): Mercury’s perihelion and the 43 arcsecond residual. C. M. Will, “The Confrontation between General Relativity and Experiment”, Living Reviews in Relativity. Residual and planetary sum checked against published summaries 21 September 2026.
  8. R. S. Park et al., “The JPL Planetary and Lunar Ephemerides DE440 and DE441”, Astronomical Journal 161 (2021). Method description checked 21 September 2026.
  9. J. G. von Soldner (1801); Aristotle; Copernicus (1543); Kepler (1609, 1619); Galileo (1638); Descartes (1644); Hooke to Newton (1679); Cavendish (1798); Maxwell (1865); Schwarzschild (1916); Dyson, Eddington and Davidson (1920); Hulse and Taylor (1975); LIGO (2016); Event Horizon Telescope (2019). Standard history, carried as reported.
  10. W. Stukeley, Memoirs of Sir Isaac Newton’s Life (1752): the 1726 conversation and the apple. Carried as reported.
  11. CODATA 2022 recommended values of the fundamental physical constants: G = 6.67430(15) × 10−11 m³ kg−1 s−2, relative standard uncertainty 22 ppm; disagreement between input measurements about 550 ppm; expansion factor 3.9 applied. Verified against published summaries 21 September 2026.
  12. Masses, radii and distances for the Sun, Earth and Moon; proton and electron masses; elementary charge; Coulomb constant; Bohr radius. Standard reference figures; not individually sourced.

Verification register: sections 3 to 9 are arithmetic on standard figures. Sections 10 to 19 are a proposed mechanism, its assumptions listed in section 12. The laboratory comparison in section 20 is load-bearing as a test.

Where this sits in the series

What the Aether does when there is more than one mass in it — and the proposal that each mass shadows the other.