Phase 2: measuring gravity on the ground and in tests of the equivalence principle #3

Activity

1. dan-garden

   added this to the Cross-domain frontiers milestone on Oct 25, 2026
2. dan-garden

   added

   enhancementNew feature or requestNew feature or request

   on Oct 25, 2026
3. dan-garden commented on Oct 25, 2026

   

   dan-garden

   on Oct 25, 2026

   CollaboratorAuthor

   More actions

   Phase 2 is in #16, with item 14 in FusionVault/geo5d#1. These are the findings beyond the report.

   Tides (items 9–11)

   • LongmanTide's vector reproduces to 3×10⁻¹¹ mGal. longman takes a Julian epoch, which holds the time to about 4 µs, and that sets the residual.
   • Averaged over the 18.61-year nodal cycle, Longman's tide is δ₂ times the permanent tide. The match with Mäkinen's −g_T is 0.1% at the equator and poles (0.19 µGal worst, at 45°). This checks the time-domain tide against the spectral M0S0 average independently; it is the non-zero mean Honkasalo (1964) pointed out.
   • Two quirks in Longman as coded:
     • The degree-2 factor 1.1575 also scales the degree-3 lunar term, whose own δ₃ is 1.07.
     • His cgs masses make the lunar tide 0.09% and the solar 0.2% larger than today's GMs.
     • Both are kept so the vector holds, and the docs say so.
   • The permanent tide is exact at any height in Cartesian form, W_T = (A/3a²)(2z² − p²).
     • It matches Mäkinen's Eqs. 19–21 to their printed digits.
     • Eq. 19's height factor 1 + 2h/a is good to 4×10⁻⁶ at 1 km.
     • A = −2.9166 follows from IERS H₀ = −0.31460 m via his Eq. 16 (−2.91663).
   • Defect, now documented: a mean-tide C̄20 gives the wrong gravity. TideSystem::MeanTide puts W_T into the Earth's own field, falling as r⁻³ instead of growing as r². That is right only on r = R ("there is no mean-tide C20", Mäkinen). Its gravity is +45.7 µGal at the equator against −30.49, a factor −3/2, and a test pins it.
   • Small offsets in the C̄20 conventions.
     • The EGM direct term −3.11080×10⁻⁸/√5 differs from IERS's A₀H₀ = −1.39141×10⁻⁸ by 1.7×10⁻⁴.
     • TN36 quotes the −4.1736×10⁻⁹ offset for EGM2008. Its own Eq. 6.14 with k₂₀ = 0.30190 gives −4.2007×10⁻⁹.

   Gradiometer (item 12)

   • The tunnel signal comes out close to Stray's. Over the example's tunnel the 1 m-baseline difference is 152 E and 17.7 mrad, against Stray's 150 E and 17.5 mrad.
   • Over a line mass the baseline difference is exactly the point gradient at the geometric-mean depth √(z₁z₂).
   • Averaging time: at the 466 E/√Hz reached outdoors, a 10:1 detection takes 937 s per station; at the projection limit it takes 9 s.

   Equivalence (item 13)

   • Fayet doesn't print the Earth's charges per mass, but Eq. 7's coefficients give them:
     • (B − L)/A_r = 0.5138 and L/A_r = 0.4870, which sum to 1.0008 nucleons per u.
     • B's coefficient has only three digits and Δ(B/A_r) only two, so its value of 1.010 is good to 1%.
   • All six bounds reproduce. The bounds for B, L and B − L at both spins match his Eqs. 24–25. For B − L they match note 40's unrounded 1.07 and 1.28×10⁻²⁵, which differ by exactly √(6.5/4.5).
   • The form factor matches Fayet's tables, through the existing functions. φ(x) matches Table IV to its printed digits. Eq. 80's five shells, with yukawa_factor and boson_mass_ev, reproduce Table V's F and G at 710 km for m = 10⁻¹⁴ to 2×10⁻¹³ eV.
   • The closed-form φ(x) fails near zero. It returns −4.96 at x = 10⁻⁸ and loses 8 digits at 10⁻⁴, so it is summed as a series below x = 1.
   • The registry isn't ordered by uncertainty. MICROSCOPE's Pt–Pt control has a smaller combined error (2.55×10⁻¹⁵) than Ti–Pt (2.75×10⁻¹⁵).

   geo5d (item 14)

   • Mercury: JPL's J2000 elements give 42.980″ per century against Will's 42.98″ (Eq. 65).
   • S2: with GRAVITY 2020's own Table E.1 it is 12.16′ against their 12.1′. The 12.21′ above used later GRAVITY elements.
   • Cassini: the exact round trip is 262.42 µs, 0.5% under Will's Eq. 63 shorthand (263.84).
   • The solar redshift paper has a sign slip. González Hernández et al. call the Earth-distance correction "+4 cm s⁻¹", but their 633.10 m/s is 633.35 − 0.04 − 0.21. The correction lowers the value.
4. dan-garden

   closed this as completedin #16on Oct 25, 2026
5. dan-garden

   added a commit that references this issue on Oct 25, 2026

   Merge pull request #16 from FusionVault/issue-3-ground-gravity-and-eq…

   ...

   c80dac0
6. dan-garden commented on Oct 25, 2026

   

   dan-garden

   on Oct 25, 2026

   CollaboratorAuthor

   More actions

   Released 2026-10-25 as compatible z-bumps: geopotential 0.3.5, gravimetry 0.7.1, gravitics 0.5.5 and physica 0.3.4 (tagged <crate>-vX.Y.Z), plus geo5d 0.5.2 (v0.5.2) for item 14. All are confirmed on crates.io.