Testing gravity with interstellar precursor missions
Pith reviewed 2026-05-25 13:36 UTC · model grok-4.3
The pith
MOND gravity would reduce a spacecraft's radial velocity by 3 cm/s and shift its sky position by 0.2 mas after 20 years beyond 7000 AU.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Beyond approximately 7000 AU, the Sun's gravity is 50 percent stronger in MOND than in Newtonian dynamics, causing an anomalous deceleration that lowers a spacecraft's radial velocity by about 3 cm/s and shortens two-way light travel time by 0.1 seconds after 20 years at 0.01c. The external field from the Galaxy makes the Sun's pull non-radial, producing a sky-position deviation reaching 0.2 mas that always lies in the plane defined by the spacecraft trajectory and the Galactic Centre direction.
What carries the argument
The Sun's MOND radius of 7000 AU, at which solar gravity strengthens by 50 percent while the Galactic external field introduces a non-radial component through the non-linear MOND equations.
If this is right
- Spacecraft would experience a 3 cm/s reduction in radial velocity after 20 years.
- Two-way radio signal travel time would shorten by 0.1 seconds after 20 years.
- Sky position would shift by up to 0.2 mas in the plane containing the trajectory and Galactic Centre.
- Launches in varied directions would reveal the expected angular pattern.
- An onboard accelerometer could isolate gravitational effects from drag or other forces.
Where Pith is reading between the lines
- The same trajectory data could also constrain the strength of the external field effect at Solar-System scales.
- Repeated measurements over longer baselines would amplify the timing and angular signals proportionally.
- A Cavendish-style experiment placed beyond 7000 AU could provide an independent local test of the same non-linear gravity.
- If the directional deviation pattern is absent, the result would tighten bounds on any MOND-like modification at these distances.
Load-bearing premise
The standard MOND equations hold with the Galactic external field included self-consistently and the Sun's transition distance set near 7000 AU.
What would settle it
A spacecraft launched at 0.01c showing neither a 3 cm/s radial-velocity deficit nor a 0.2 mas sky deviation aligned with the Galactic Centre plane after 20 years would contradict the MOND trajectory predictions.
read the original abstract
We consider how the trajectory of an interstellar precursor mission would be affected by the gravity of the Sun in Newtonian and Milgromian dynamics (MOND). The Solar gravity is ${\approx 50\%}$ stronger in MOND beyond a distance of ${\approx 7000}$ astronomical units, the MOND radius of the Sun. A spacecraft travelling at $0.01 \, c$ reaches this distance after 11.1 years. We show that the extra gravity in MOND causes an anomalous deceleration that reduces its radial velocity by ${\approx 3}$ cm/s and the two-way light travel time from the inner Solar System by ${\approx 0.1}$ seconds after 20 years. A distinctive signature of MOND is that the gravity from the Sun is not directly towards it. This is due to the non-linear nature of MOND and the external gravitational field from the rest of the Galaxy, which we self-consistently include in our calculations. As a result, the sky position of the spacecraft would deviate by up to 0.2 mas over 20 years. This deviation is always in the plane containing the spacecraft trajectory and the direction towards the Galactic Centre. By launching spacecraft in different directions, it is possible to test the characteristic pattern of angular deviations expected in MOND. This would minimize the chance that any detected anomalies are caused by other processes like drag from the interstellar medium. Such confounding factors could also be mitigated using an onboard accelerometer to measure non-gravitational forces. We briefly discuss how the gravity theories could be conclusively distinguished using a Cavendish-style active gravitational experiment beyond the Sun's MOND radius.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript proposes using trajectories of interstellar precursor spacecraft (at 0.01c) to test Milgromian dynamics (MOND) against Newtonian gravity. It predicts that beyond the Sun's MOND radius (~7000 AU, reached after 11.1 years), the ~50% stronger gravity produces an anomalous deceleration reducing radial velocity by ~3 cm/s and two-way light travel time by ~0.1 s after 20 years. A distinctive non-radial gravitational component arising from the nonlinear MOND field equation plus the Galactic external field effect is claimed to produce sky-position deviations up to 0.2 mas, always lying in the plane containing the spacecraft trajectory and the Galactic Centre direction; launching in multiple directions could confirm the pattern.
Significance. If the central predictions hold, the work supplies concrete, falsifiable numerical targets and a directional signature that could distinguish MOND from Newtonian gravity (or other perturbations) with future missions, while mitigating confounders via directionality or onboard accelerometers. The self-consistent EFE treatment and emphasis on the characteristic angular pattern are strengths that elevate the proposal beyond generic anomaly searches.
major comments (2)
- [non-radial gravity / EFE calculations] The section describing the non-radial gravitational component and resulting 0.2 mas sky deviation: the claim that this deviation is always confined to the spacecraft-Galactic Centre plane and reaches the quoted amplitude rests on a self-consistent MOND+EFE solution, yet the manuscript provides no explicit statement of the interpolating function employed nor any sensitivity test to its choice. Literature shows the transverse acceleration near the transition regime is sensitive to the form of μ(x), which would scale the angular prediction without altering the radial-velocity shift; this is load-bearing for the 'distinctive signature' used to discriminate against other effects.
- [trajectory and timing results] The paragraphs presenting the numerical predictions (~3 cm/s velocity reduction, ~0.1 s light-travel-time difference, 0.2 mas deviation): these values are stated without accompanying integration details, error budgets, or the precise numerical treatment of the transition across the MOND radius, rendering it impossible to verify that the quoted figures follow from the stated assumptions (standard MOND framework, Sun's MOND radius ~7000 AU). This directly affects in the central forward predictions.
minor comments (1)
- [abstract/introduction] The abstract and introduction would benefit from an explicit statement of the value of a0 adopted and the spacecraft launch direction(s) assumed for the quoted numbers.
Simulated Author's Rebuttal
We thank the referee for the constructive comments and positive assessment of the work's significance. We address each major comment below.
read point-by-point responses
-
Referee: The section describing the non-radial gravitational component and resulting 0.2 mas sky deviation: the claim that this deviation is always confined to the spacecraft-Galactic Centre plane and reaches the quoted amplitude rests on a self-consistent MOND+EFE solution, yet the manuscript provides no explicit statement of the interpolating function employed nor any sensitivity test to its choice. Literature shows the transverse acceleration near the transition regime is sensitive to the form of μ(x), which would scale the angular prediction without altering the radial-velocity shift; this is load-bearing for the 'distinctive signature' used to discriminate against other effects.
Authors: We agree an explicit statement of the interpolating function is required. Our calculations used the standard simple form μ(x) = x/(1+x). We will add this to the revised manuscript. The planar confinement of the deviation follows from the vector structure of the MOND field equation plus EFE and holds independently of the specific μ(x); the amplitude may vary. We will clarify this distinction. A full quantitative sensitivity analysis requires further numerical work beyond the present scope and is noted as a limitation. revision: partial
-
Referee: The paragraphs presenting the numerical predictions (~3 cm/s velocity reduction, ~0.1 s light-travel-time difference, 0.2 mas deviation): these values are stated without accompanying integration details, error budgets, or the precise numerical treatment of the transition across the MOND radius, rendering it impossible to verify that the quoted figures follow from the stated assumptions (standard MOND framework, Sun's MOND radius ~7000 AU). This directly affects in the central forward predictions.
Authors: The quoted values were obtained via numerical integration of the spacecraft trajectory under the full nonlinear MOND field including self-consistent EFE. The transition at the MOND radius was treated by solving the complete MOND equations. We will add a methods subsection (or appendix) detailing the integration scheme, time-stepping, transition handling, and an error budget tied to the standard MOND assumptions. This will enable verification of the ~3 cm/s, ~0.1 s and 0.2 mas results. revision: yes
Circularity Check
No significant circularity; predictions follow from external MOND equations applied to new scenario
full rationale
The paper applies the established MOND framework (including self-consistent EFE treatment) to compute spacecraft trajectories, radial velocity shifts, light travel times, and angular deviations. These quantities are obtained by solving the MOND field equations with the Sun's gravity plus the Galactic external field at distances beyond the MOND radius; no equation or result is shown to reduce by construction to a parameter fitted inside this work or to a self-citation whose content is itself unverified. The central claims remain independent calculations on top of the pre-existing theory.
Axiom & Free-Parameter Ledger
free parameters (1)
- a0 =
~1.2e-10 m/s^2
axioms (2)
- domain assumption Milgromian dynamics equations with external field effect hold at low accelerations
- domain assumption The Galactic external gravitational field can be included self-consistently in the spacecraft trajectory integration
Lean theorems connected to this paper
-
IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
the gravity from the Sun is not directly towards it... due to the non-linear nature of MOND and the external gravitational field... self-consistently include... sky position... deviate by up to 0.2 mas... always in the plane containing the spacecraft trajectory and the direction towards the Galactic Centre
-
IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
QUMOND... ν(y) = ½ + √(¼ + 1/y)... simple interpolating function
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.