🔭 astrophysics

Inferring the mass and size of 3I/ATLAS from its non-gravitational acceleration

By analyzing the non-gravitational acceleration of interstellar object 3I/ATLAS, this study estimates a smaller nucleus radius of approximately 0.42 km and a mass of $1.6\times10^{11}$ kg under a CO $_2$ -dominated sublimation model, suggesting that water sublimation primarily occurs in the coma rather than on the surface.

Original authors: Valentin Thoss, Abraham Loeb, Andreas Burkert

Published 2026-03-18

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CC BY 4.0

Original authors: Valentin Thoss, Abraham Loeb, Andreas Burkert

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a cosmic traveler named 3I/ATLAS. It's not a planet or a star, but a wandering "interstellar comet"—a chunk of ice and rock that came from deep space, far beyond our solar system, and is currently zooming past our Sun.

Scientists have been watching this traveler closely. They noticed something strange: as it got closer to the Sun, it didn't just get brighter; it started spewing out massive clouds of gas and dust. This outgassing acted like a tiny, natural rocket engine, pushing the comet slightly off its expected path.

This paper is essentially a detective story. The authors, V. Thoss, A. Loeb, and A. Burkert, are trying to figure out how heavy and how big this cosmic traveler actually is. They can't weigh it on a scale, so they have to use the "rocket push" (the non-gravitational acceleration) to do the math.

Here is the story of their investigation, broken down into simple concepts:

1. The Mystery of the "Rocket Push"

Imagine you are standing on a skateboard holding a heavy bag of sand. If you suddenly throw the sand out behind you, the skateboard will shoot forward. The harder you throw the sand, the faster you go.

The Sand: The gas and dust spewing off the comet.
The Skateboard: The comet's solid core (the nucleus).
The Push: The force that changes the comet's orbit.

The scientists know how much "sand" (gas) is being thrown off. They can also measure how much the "skateboard" (the comet's path) is being pushed. The missing piece of the puzzle is the weight of the skateboard.

If the skateboard is heavy (a massive comet), it takes a lot of sand to push it.
If the skateboard is light (a small, fluffy comet), even a little bit of sand will push it far.

2. The Confusing Clues: Water vs. Carbon Dioxide

The team looked at the gas coming off the comet and found two main suspects: Water vapor and Carbon Dioxide (CO2).

The Water Problem: Some telescopes saw huge amounts of water. But here's the catch: The water wasn't just coming from the solid rock core. A lot of it was coming from icy dust grains floating in the cloud around the comet.
- Analogy: Imagine a campfire. If you throw a bucket of water on the fire, the steam pushes the fire. But if the steam is coming from wet leaves floating in the smoke above the fire, that steam doesn't push the fire itself.
- The Lesson: Only gas coming directly off the solid rock pushes the comet. Gas from the floating dust cloud does nothing to the comet's weight or path.
The CO2 Clue: The data suggested that Carbon Dioxide was the main driver coming directly off the rock. CO2 is heavier than water and sublimates (turns to gas) at lower temperatures.

3. The Two Theories

The authors built two main models to solve the mystery:

Theory A (The "Big Water" Model): They assumed a lot of the water was coming off the rock. This would mean the comet is pushing itself hard, so to keep the orbit consistent, the comet must be very heavy and large (about the size of a small town, ~1.1 km wide).
Theory B (The "CO2 King" Model): They assumed most of the water was just floating dust, and only CO2 was pushing the rock. This means the comet is being pushed gently. To match the observed path, the comet must be light and small (about the size of a large mountain, ~0.4 km wide).

4. The "Active Surface" Test

To decide which theory was right, the authors used a clever trick called the "Active Surface" test.

Imagine you have a tiny campfire (the comet) and you need to burn enough wood to create a specific amount of smoke.

If the fire is tiny, it can't possibly burn enough wood to make that much smoke unless the wood is burning incredibly fast.
If the fire is huge, it can easily make that smoke.

The scientists calculated: "How big does the comet's surface need to be to produce the gas we see?"

The Result: The "Big Water" theory required the comet to be so big that its surface area would have to be larger than the comet itself! It was like saying a tiny pebble is somehow burning enough wood to smoke out a stadium. It didn't make sense.
The "CO2 King" theory, however, fit perfectly. A small, fluffy comet could easily produce the amount of CO2 needed.

5. The Conclusion: A Small, Light Traveler

The evidence points to Theory B.

Size: The comet is likely only about 0.42 kilometers (0.26 miles) in radius. That's much smaller than previous photos suggested (which guessed it was over 1 km).
Weight: It is very light, likely made of fluffy, porous ice and rock, rather than a dense, solid rock.
The Twist: The huge clouds of water we see are mostly coming from the "fog" around the comet, not the comet itself. The comet is mostly pushing itself with Carbon Dioxide.

Why Does This Matter?

This discovery changes how we think about interstellar visitors.

They might be lighter than we thought: If these travelers are small and fluffy, it's easier for them to survive the journey across the galaxy.
They might come from "metal-poor" places: A lighter, fluffier comet fits the idea that this object came from a part of the universe with fewer heavy elements (metals), which is a hot topic in astronomy right now.
We need better photos: The previous estimate of the comet's size (1.3 km) was likely wrong because the bright cloud of dust hid the small, dark core. It's like trying to guess the size of a person standing inside a giant, bright fog machine.

In a nutshell: 3I/ATLAS is a small, lightweight, fluffy snowball from another star system. It's not the giant boulder we thought it was; it's more like a cosmic dandelion seed, pushed along by a gentle breeze of carbon dioxide, while a massive cloud of water vapor floats around it, tricking our telescopes.

1. Problem Statement

The interstellar object 3I/ATLAS (discovered as C/2025 N1) exhibits significant cometary activity, including rapid brightening and strong gas/dust production near perihelion. This outgassing generates a non-gravitational acceleration ( $a_{ng}$ ) due to the rocket effect (momentum conservation).

The Challenge: The coma (gas and dust cloud) dominates the object's brightness, making direct photometric determination of the nucleus size ( $R_{3I}$ ) difficult and uncertain. Previous estimates range widely ($0.16$ km to $2.8$ km), with a recent photometric claim of $1.3 \pm 0.2$ km.
The Goal: To constrain the mass ( $M_{3I}$ ) and radius ( $R_{3I}$ ) of the nucleus by modeling the non-gravitational acceleration derived from astrometric data, while accounting for the uncertainty in the mass loss rate ( $\dot{M}$ ) and the composition of the outgassing (Water vs. Carbon Dioxide).

2. Methodology

A. Modeling Mass Loss Rates ( $\dot{M}$ )

The authors synthesized observational data from various telescopes (HST, JWST, VLT, SOHO, etc.) regarding the production rates of $H_2O$ , $CO_2$ , and $OH$.

Key Observation: $CO_2$ dominates production at large heliocentric distances ( $r \gtrsim 3$ AU). Near perihelion, water production increases, but evidence suggests a significant fraction of this water sublimates from icy grains in the coma rather than the nucleus surface. Only surface sublimation contributes to the rocket effect.
Three Models for Total Mass Loss:
1. Model A (High Water): Combines a $CO_2$ model with a high-end power-law fit for $H_2O$ (based on large-aperture observations).
2. Model B (Low Water): Combines the $CO_2$ model with a low-end power-law fit for $H_2O$ (based on small-aperture observations, assuming less coma contribution).
3. $CO_2$ -Only Model: Assumes the rocket effect is driven purely by $CO_2$ sublimation following a $1/r^2$ scaling (energy-limited sublimation).

B. Orbital Fitting and Non-Gravitational Acceleration

Equation of Motion: The non-gravitational acceleration is modeled as $M_{3I} a_{ng} = \zeta \dot{M} v_{gas}$ , where $\zeta$ is the asymmetry factor (collimation) and $v_{gas}$ is the outflow velocity.
Integration: The authors used the ASSIST code (an extension of REBOUND) to integrate the orbit of 3I/ATLAS, incorporating the Sun, planets, massive asteroids, and relativistic corrections.
Data: 8,086 astrometric observations from the Minor Planet Center (MPC) spanning May 2025 to March 2026.
Sensitivity Analysis: To address systematic uncertainties (noted as $\sim 0.5$ $\sim 0.5$ arcsec biases in some data), four different weighting schemes were applied:
1. Uniform weighting.
2. High-fidelity telescopes weighted at $\sigma=0.1''$ , others at $1''$ .
3. Weighting based on reported seeing conditions.
4. High-fidelity only: Using only data from major telescopes (HST, VLT, etc.) and interplanetary spacecraft (Lucy, Psyche, TGO).

C. Parameter Inference

The magnitude of the non-gravitational acceleration ( $A$ ) was inferred by fitting the models to the astrometric residuals. The mass was then derived using $M_{3I} = \zeta \dot{M} v_{gas} / A$ .

3. Key Contributions

Decoupling Coma vs. Nucleus Sublimation: The paper rigorously argues that observed high water production rates likely include a massive contribution from coma grains, which do not exert a rocket force on the nucleus. This distinction is critical for accurate mass estimation.
Robustness of Acceleration Magnitude: Despite systematic errors in the astrometric data, the magnitude of the non-gravitational acceleration ( $A$ ) is found to be robust (varying by only ~5% across weighting schemes).
Scaling Law Preference: The orbital fit shows a subtle but consistent preference for a $1/r^2$ scaling of the non-gravitational acceleration, particularly when high-fidelity data is used. This scaling is characteristic of energy-limited $CO_2$ sublimation, whereas water sublimation often follows steeper laws.
Active Surface Constraint: The authors introduce a physical consistency check: the surface area required to sustain the observed sublimation rate ( $R_{active}$ ) must not exceed the physical radius derived from the rocket effect ( $R_{ng}$ ).

4. Key Results

A. Mass and Radius Estimates

Assuming a density $\rho = 0.5 \text{ g cm}^{-3}$ and asymmetry factor $\zeta = 0.5$ :

Model	Assumption	Mass ( $M_{3I}$ )	Radius ( $R_{3I}$ )
$CO_2$ -Only	Pure $CO_2$ sublimation ( $1/r^2$ )	$1.6 \times 10^{11}$ kg	0.42 km
Model B	Low water production	$8.5 \times 10^{11}$ kg	0.74 km
Model A	High water production	$3.2 \times 10^{12}$ kg	1.15 km

B. Consistency Checks

The Tension: Models A and B (significant water sublimation) require a nucleus radius ( $R_{ng}$ ) that is smaller than the minimum radius required to sustain the observed sublimation flux ( $R_{active}$ ). This implies the surface area needed to produce that much water is larger than the object itself, which is physically impossible unless the object is extremely porous or the assumptions are wrong.
The Resolution: The $CO_2$ -Only model is the only scenario where $R_{ng} \geq R_{active}$ , making it the physically consistent solution.
Comparison to Photometry: The derived radius of 0.42 km is significantly smaller than the recent photometric estimate of $1.3 \pm 0.2$ km (Hui et al. 2026). The authors suggest the photometric estimate may be unreliable due to strong extinction around the nucleus or that the $CO_2$ production was underestimated.

C. Orbital Parameters

The non-gravitational parameters $A_1, A_2, A_3$ were derived. The magnitude $A$ is robustly estimated at $\approx 6.4 \times 10^{-8} \text{ AU d}^{-2}$ (for Model A) and $\approx 5.2 \times 10^{-8} \text{ AU d}^{-2}$ (for $CO_2$ -only).
The data slightly favors $A_1 > A_2 > A_3$ , with $A_1/A_2 \approx 1.5-2$ , differing from some previous JPL solutions but consistent with the preference for a $1/r^2$ scaling.

5. Significance and Implications

Nature of 3I/ATLAS: The results strongly suggest that 3I/ATLAS is a smaller, lighter object ( $R \approx 0.42$ km) than previously thought, with its non-gravitational acceleration dominated by $CO_2$ sublimation rather than water.
Coma Physics: The study provides strong evidence that a large fraction of the observed water production in interstellar comets occurs in the coma (from icy grains) rather than the nucleus, a crucial distinction for interpreting future interstellar object data.
Origin Constraints: A lighter nucleus ( $M \sim 10^{11}$ kg) reduces the mass budget required for interstellar objects, potentially alleviating tensions with theories suggesting 3I/ATLAS originated from a metal-poor environment.
Methodological Impact: The paper demonstrates that combining astrometric orbital fitting with physical constraints (active surface area) is a powerful tool for resolving ambiguities in cometary properties when direct imaging is impossible.

Conclusion: The most plausible physical model for 3I/ATLAS is a small nucleus ( $R \approx 0.42$ km) driven by $CO_2$ outgassing, with water sublimation occurring primarily in the coma. This challenges recent photometric size estimates and highlights the need for better constraints on $CO_2$ production rates and comet densities.