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arxiv: 2606.05344 · v1 · pith:D2KOWQWMnew · submitted 2026-06-03 · 🌌 astro-ph.EP · astro-ph.GA· astro-ph.IM

Sky-Plane Velocity Distributions of Interstellar Objects and Implications for Their Detection

Pith reviewed 2026-06-28 03:56 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.GAastro-ph.IM
keywords interstellar objectssky-plane velocitydetection biassynthetic populationsanalytic motion formulavelocity distributions1I
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The pith

Interstellar objects can move across the sky faster than surveys link, suggesting many dim ones remain undetected.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an analytic formula for the apparent sky motion of an object on any orbit viewed from any location and applies it to three synthetic populations of roughly 100,000 interstellar objects placed inside heliocentric spheres of 1.2, 3.0, and 5.0 AU. These populations are assigned absolute-magnitude distributions appropriate for asteroids and for comets, then evaluated at a range of limiting magnitudes to produce sky-velocity distributions. The resulting distributions show that brighter objects and active comets reach detection thresholds at lower speeds than fainter objects, while the high-velocity tails extend beyond the discovery motion of 1I. This pattern implies that linking difficulties for fast-moving, intrinsically dim interstellar objects could leave a larger population undetected as it crosses the Solar System.

Core claim

The sky motions of the three known interstellar objects are typical for populations of similar absolute magnitude; brighter objects and active comets reach observable magnitudes at lower speeds than dimmer ones; and the velocity distributions possess tails extending to speeds faster than the discovery motion of 1I, indicating that detection and linking challenges may leave additional interstellar objects unobserved.

What carries the argument

Analytic solution for the apparent sky motion of an arbitrary orbit observed at an arbitrary location, applied to evaluate sky motions within three synthetic populations of interstellar objects.

If this is right

  • The sky motions of the three known interstellar objects fall within the characteristic range for populations of comparable absolute magnitude.
  • Intrinsically brighter objects reach detection magnitude thresholds at lower speeds than dimmer objects.
  • Active comets reach detection thresholds at lower speeds than asteroids for the same apparent magnitude.
  • The velocity distributions possess tails that extend to speeds faster than the discovery motion of 1I.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Survey linking algorithms tuned only to slower motions would systematically miss the high-velocity tail of the interstellar-object population.
  • Revised population estimates that incorporate the missed fast movers would be higher than current counts based on detected objects alone.
  • The same analytic motion formula could be reused to assess detection biases for other classes of fast-moving solar-system bodies.
  • Improved cadence or software for high-speed object linking would constitute a direct test of whether the undetected fraction is large.

Load-bearing premise

The three synthetic populations of approximately 10^5 interstellar objects placed within heliocentric spheres of 1.2, 3.0, and 5.0 AU radii together with the assumed absolute-magnitude distributions for asteroids and comets are representative of the true underlying population.

What would settle it

A dedicated search either detects or fails to detect interstellar objects with sky-plane speeds substantially higher than the tails of the computed distributions at the rates those tails predict.

Figures

Figures reproduced from arXiv: 2606.05344 by Cassidy E. Walker, Darryl Z. Seligman.

Figure 1
Figure 1. Figure 1: Sky motion over time for 1I/‘Oumuamua (top) and 2I/Borisov (bottom), using JPL Horizons ephemerides data, overplotted with values from 3D calculation in Equation A2. Object Discovery Date 𝑚𝑉 Sky Motion [◦ /d] 1I 19 Oct 2017 19.705 6.6433 2I 29 Aug 2019 18.815 0.4684 3I 01 Jul 2025 18.170 0.4850 Object Fastest Date 𝑚𝑉 Max. Motion [◦ /d] 1I 15 Oct 2017 19.958 12.2088 2I 08 Dec 2019 16.663 0.8654 3I 26 Dec 20… view at source ↗
Figure 2
Figure 2. Figure 2: The apparent sky motion as a function of perihelion distance and orbital inclination. We set remaining parameters of interstellar object eccentricity, argument of periastron, and longitude of ascending node, to be 𝑒 = 1.9, 𝜔 = 3.4 rad, and Ω = 3.1 rad based on the spread of values for these elements in the synthetic population generated in section 3.1. The true anomaly values of the interstellar object and… view at source ↗
Figure 3
Figure 3. Figure 3: Apparent sky motion for given values of the true anomaly of the Earth and the interstellar object orbital inclination. We set the remaining parameters of interstellar object semimajor axis, eccentricity, true anomaly, argument of periastron, and longitude of ascending node, to be 𝑎 = −2.0 AU, 𝑒 = 1.9, 𝑓 = 0.0 rad, 𝜔 = 3.4 rad, and Ω = 3.1 rad based on the spread of values for these elements in the syntheti… view at source ↗
Figure 4
Figure 4. Figure 4: (Top row) Distributions of sky motions for asteroid-like objects, calculated using the 3D approximation in Equation A2 for 106,398 interstellar objects within a heliocentric model sphere of radius 1.2 AU when they reach apparent v-band magnitudes of 17.0, 19.0, 22.0, and 25.0. The red dotted lines mark the apparent sky motion of 1I/‘Oumuamua at discovery (6.6433 deg/day), and the black dotted lines represe… view at source ↗
Figure 5
Figure 5. Figure 5: Summary statistics showing the median, 1-sigma, and 2-sigma quartiles for distributions of sky motions shown in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

In the past decade, three macroscopic-scale interstellar objects have been discovered, implying that a larger galactic population exists. In this paper, we investigate the possibility that the rapid sky-plane velocities of interstellar objects may preclude their discovery. We provide an analytic solution for the apparent sky motion of an object on an arbitrary orbit observed at an arbitrary location which (i) is more efficient and (ii) requires less overhead than the numerical approach. This formula is applied to evaluate the typical sky motion of an interstellar object as a function of its orbit and limiting magnitude/distance. We generate three synthetic populations of $\sim10^5$ interstellar objects within heliocentric spheres of radii 1.2, 3.0, and 5.0 AU, and calculate the sky motion for these objects when they reach a range of limiting magnitudes for multiple populations of interstellar asteroids and comets. The sky motions of the three known interstellar objects are broadly characteristic of populations with similar absolute magnitudes. Moreover, the intrinsically brighter objects reach detection magnitude thresholds at lower speeds than the dim objects, and active comets at even lower speeds for the same apparent magnitudes. The tails of these distributions extend to speeds faster than the discovery motion of 1I. Therefore, the difficulties associated with linking rapidly moving interstellar objects, especially those with intrinsically dim properties, could imply that more exist undetected traversing the Solar System.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper derives an analytic expression for the sky-plane angular velocity of an object on an arbitrary orbit viewed from an arbitrary location, then applies it to three synthetic populations of ~10^5 interstellar objects placed inside heliocentric spheres of radii 1.2, 3.0 and 5.0 AU. Using assumed absolute-magnitude distributions for interstellar asteroids and comets, it computes sky-motion distributions at various limiting magnitudes and concludes that the high-velocity tails exceed the discovery motion of 1I, implying that many (especially faint) ISOs remain undetected because of rapid apparent motion.

Significance. If the synthetic populations are representative, the work supplies a quantitative framework for assessing ISO detection biases and motivates targeted search strategies for high proper-motion objects. The provision of a closed-form sky-motion formula rather than a purely numerical approach is a clear methodological strength that reduces computational overhead for population studies.

major comments (2)
  1. [synthetic population generation (abstract and methods)] The central implication that high-speed tails imply many undetected ISOs rests on the representativeness of the three ~10^5-object populations placed inside fixed heliocentric spheres together with the adopted absolute-magnitude distributions. The manuscript provides no explicit description of how galactic velocity vectors, impact parameters, or hyperbolic excess speeds are sampled; if these differ from the true encounter distribution, the tails (and therefore the detection-bias conclusion) can shift without altering the analytic formula itself.
  2. [results and discussion of sky-motion distributions] No quantitative validation, error analysis, or direct comparison of the computed sky-motion distributions against the three known ISOs (beyond the qualitative statement that they are “broadly characteristic”) is presented. This leaves the strength of the claim that the tails extend beyond 1I’s discovery motion dependent on untested assumptions about the underlying orbital and magnitude distributions.
minor comments (2)
  1. [abstract] The abstract would benefit from a brief quantitative statement (e.g., fraction or percentile) of objects exceeding the sky motion of 1I at each limiting magnitude.
  2. [analytic derivation] Notation for the analytic sky-motion formula should be defined once in a dedicated subsection before its application to the populations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for highlighting the utility of the analytic sky-motion formula. We address the two major comments point by point below, indicating where revisions will be made to improve clarity and strengthen the supporting evidence.

read point-by-point responses
  1. Referee: The central implication that high-speed tails imply many undetected ISOs rests on the representativeness of the three ~10^5-object populations placed inside fixed heliocentric spheres together with the adopted absolute-magnitude distributions. The manuscript provides no explicit description of how galactic velocity vectors, impact parameters, or hyperbolic excess speeds are sampled; if these differ from the true encounter distribution, the tails (and therefore the detection-bias conclusion) can shift without altering the analytic formula itself.

    Authors: We agree that the sampling procedure requires explicit documentation. In the revised manuscript we will expand the methods section to detail the sampling of galactic velocity vectors (drawn from a Maxwellian distribution consistent with local stellar kinematics), impact parameters (uniform within the heliocentric sphere), and hyperbolic excess speeds (drawn from a distribution informed by prior ISO encounter models). These choices will be justified with references to the literature. The analytic formula remains independent of the specific population model, but the added description will allow readers to evaluate how changes in the encounter distribution would affect the high-velocity tails. revision: yes

  2. Referee: No quantitative validation, error analysis, or direct comparison of the computed sky-motion distributions against the three known ISOs (beyond the qualitative statement that they are “broadly characteristic”) is presented. This leaves the strength of the claim that the tails extend beyond 1I’s discovery motion dependent on untested assumptions about the underlying orbital and magnitude distributions.

    Authors: We acknowledge the absence of quantitative validation. In revision we will add a new figure and accompanying text that directly compares the sky-motion distributions for synthetic objects with absolute magnitudes matching those of the three known ISOs against their reported discovery motions, including median and percentile statistics. We will also include a brief sensitivity analysis showing how the high-velocity tail changes with modest variations in the adopted magnitude distributions. A full statistical error analysis is limited by the small number of known objects, but the added quantitative metrics will better support the claim that the tails exceed 1I’s motion. revision: partial

Circularity Check

0 steps flagged

Analytic sky-motion formula is independent of synthetic population inputs

full rationale

The paper derives an analytic expression for sky-plane motion of an arbitrary orbit observed at an arbitrary location from first principles; this formula is then applied to three synthetic populations of ~10^5 objects placed in fixed heliocentric spheres together with separately assumed absolute-magnitude distributions. No equation reduces to a self-definition, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on a self-citation chain. The central claim about high-speed tails follows directly from applying the independent formula to the external synthetic inputs, making the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are identified.

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discussion (0)

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Reference graph

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