◄ WORLD V · SONNY 5DART 560 · a helldive down the well

THE TIDAL FORCE gravity's difference, not its strength

Tides are not about how hard gravity pulls — they are about how differently it pulls across a body. The near side feels more than the far side, and that difference stretches you: Δg ≈ 2GM·r/d³, falling off as 1/d³, far faster than gravity’s 1/d². The Moon raises Earth’s oceans; close enough (see the Roche limit) the same difference tears moons apart.

THE TECHNIQUE Δg ≈ 2GM r / d³

The demo computes the tidal gradient 2GM·r/d³ across a body (illustrative μ): live demo







  
HISTORY & CREDIT Newton · the two-bulge tide

  
“There is one tidal bulge, on the Moon’s side.” — there are two: the far side bulges too, because it is pulled less than the Earth’s center. cited

  
the difference · near side pulled more than far side → a stretch, two bulges.
the falloff · Δg ∝ 1/d³ — steeper than gravity itself.
Newton · explained the tides from the differential 1/r² pull (Principia).

  
The gradient, not the pull, moves oceans. physics






  
RECOMMEND FOR I-13 the gradient, on the compiler

  
On i-13, the tidal gradient 2μr/d³ across a body (illustrative μ) is a tiny stretch:

  
$ i13 run gw_tidal.i13   # 2*mu*r / d^3
RUN OK · 20 step(s)
d3 = 5.68e25
dg = 0.00008942   -- differential acceleration (2*mu*r/d^3)

  
Recommend as a NULL — a theorem (B39). The tidal gradient is the exact spatial derivative of the 1/r² field; a pinned function of M, r, d. NULL — gravity’s difference, not its strength.