A census of visitors is a census of the survey

In October 2017 a survey telescope in Hawaii found a small object moving far too fast to be bound to the Sun. Its orbit had no period: an eccentricity of 1.2 and a speed at infinity of 26 kilometres a second, which meant it had come from another star and would leave for good. It was named ʻOumuamua and it was the first. The second, Borisov, an active comet, was found in 2019 by an amateur astronomer with a sixty-five-centimetre telescope. The third, found in July 2025 by a survey in Chile, arrived at 58 kilometres a second, faster than either.

Three detections are not much data, but they answer a question that had been open for decades: how common are bodies ejected from other planetary systems? Theories of planet formation predict that most of the solid material in a young system is thrown out by its giant planets, and that interstellar space should therefore be full of comets and asteroids. Before 2017, the absence of any detected visitor was used to put upper limits on their number. Afterwards, the count could be turned into a number density — with a caveat that is the subject of this essay. A count becomes a density only when divided by the volume searched, and the volume searched by a survey for interstellar objects depends on the objects themselves.

From a count to a rate to a density #

The logic is a flux calculation. If interstellar objects fill space with a number density $n$ and move relative to the Sun at a speed $v_\infty$, the number passing within a distance $q$ of the Sun each year is $n$ times the cross-section times the speed. Without gravity the cross-section would be $\pi q^2$. With it, the cross-section is larger.

A count of detections in a span of years, divided by that rate per unit density, gives the density — provided the survey saw every passage within $q$. It did not, so a further factor enters: the efficiency, the fraction of passages within $q$ that the survey actually caught.

The opening figure draws the result for one detection in eight years. The answer depends on two things that are not properties of the visitors: the distance inside which the survey could have seen an object of that size, and the fraction of those passages it caught. Assume a hundred-metre body can be seen inside half an astronomical unit and a tenth of such passages are caught, and there are about five per hundred cubic astronomical units. Assume it can be seen inside two astronomical units and every passage is caught, and there are a hundred times fewer.

The published estimate after ʻOumuamua — about 0.2 such bodies per cubic astronomical unit, so that one is passing inside the Earth’s orbit at any moment — came from a careful model of what the survey had actually been able to see. Everything about that number rests on the model, and the rest of this essay is about what goes into it.

The Sun gathers slow visitors #

The cross-section is the first correction, and it is the only one that is pure orbital mechanics.

A body approaching on a straight line that would miss the Sun by an impact parameter $b$ is bent inward by the Sun’s gravity and passes closer. On the hyperbola it actually follows, its closest approach $q$ and its impact parameter are related by conservation of energy and angular momentum:

$$b^2 = q^2\left(1 + \frac{v_{\rm esc}(q)^2}{v_\infty^2}\right),$$

with $v_{\rm esc}(q)$ the escape speed at distance $q$, 42.1 kilometres a second at the Earth’s distance. Every body whose straight path would have come within $b$ actually comes within $q$, so the number passing inside $q$ is enhanced by the factor in brackets: gravitational focusing.

The factor depends strongly on speed. For a body arriving at ten kilometres a second, the Sun gathers nearly nineteen times as many inside the Earth’s orbit as it would without gravity, and nearly two hundred times as many inside a tenth of an astronomical unit. For ʻOumuamua’s 26 kilometres a second the factors are three and a half and twenty-seven; for 3I’s 58, one and a half and six.

Two consequences follow. A survey looking near the Sun sees an enhanced density of visitors, and the enhancement must be removed before a density in interstellar space can be quoted. And the enhancement is larger for slow visitors, so a census made near the Sun is weighted towards them; a population with a broad range of speeds is seen through a filter that favours its slow end — counteracted, partly, by the fact that fast bodies arrive more often.

How far each size can be seen #

The second correction is the survey’s reach, and it depends on how big the visitor is.

A small body shines by reflected sunlight, so its brightness falls as the square of its distance from the Sun and again as the square of its distance from the Earth. Its intrinsic brightness, the absolute magnitude, depends on its diameter and on how reflective its surface is. A hundred-metre body with a typical asteroid-like reflectivity of a tenth is so faint that a survey reaching magnitude 21.5 — the depth of the survey that found ʻOumuamua — can see it only when it is within about 1.35 astronomical units of the Sun and close to the Earth. A survey four times deeper, reaching 24.5, extends that to about two.

A kilometre-sized body is a hundred times brighter and is visible out to three to five astronomical units. The volume a survey searches therefore grows steeply with the size of the object, as roughly the cube of the reach. A census of small visitors samples a tiny region around the Earth; a census of large ones samples the inner solar system.

That is why a density must always be quoted for a size. The count of ʻOumuamua-sized bodies says something about a few cubic astronomical units around the Earth; the count of comet-sized bodies like Borisov, whose activity made them brighter still, says something about a much larger volume and a much rarer class.

The weeks in which a visitor can be seen #

Being inside the reach is not enough; the visitor must be inside it while the survey is looking at the right part of the sky.

A visitor passes through the inner solar system quickly. On ʻOumuamua’s orbit, a hundred-metre body spends about ninety days within 1.35 astronomical units of the Sun and about 140 within two. Half of that time is before its closest approach, when nobody yet knows it exists, and during all of it the body is visible only if the survey happens to point at the part of the sky where it is, on a clear night, and if the body is not lost in the Sun’s glare or the plane of the Galaxy.

ʻOumuamua was found forty days after its closest approach to the Sun, five days after its closest approach to the Earth, when it was at its brightest as seen from here. It was followed for about eighty days before it faded beyond reach. A visitor of the same size passing on the other side of the Sun, or a few weeks earlier in a cloudy season, would have gone unseen, and there is no way to know how many did.

The efficiency in the opening figure is the product of all of this: the fraction of the sky covered, the weather, the time of year, the geometry of each passage. It is computed by simulating a population of synthetic visitors and passing each through a model of the survey’s actual pointing history, and it is the largest uncertainty in every density published.

One detection fixes a product #

There is a structural point hidden in the density figure. A detection rate is the number density times the rate per unit density times the efficiency, and only the product of the first and last is constrained by a count. A survey that saw one body could be one with a high efficiency looking at a sparse population or a low efficiency looking at a dense one, and nothing in the detection distinguishes them.

The degeneracy is broken only by modelling the survey independently — which is possible, because its pointing history is known — and by comparing surveys of different depth and coverage. Two surveys with different efficiencies looking at the same population should find visitors at rates whose ratio depends only on their efficiencies and reaches, not on the density. The deep survey that began operating in 2025, imaging the whole southern sky every few nights to a limiting magnitude near 24.5, is the first with the depth and coverage to make that comparison, and its rate over its first few years will measure whether the density inferred from three detections is right.

That rate is also sensitive to something the three detections cannot measure: how the number of visitors changes with size. Small bodies are more numerous and can only be seen nearby; large ones are rarer and can be seen further out. A deep survey sees smaller bodies than a shallow one, and how many more visitors it finds is a direct measurement of the size distribution — which is, in turn, a measurement of how planetary systems grind up and eject their solid material.

A visitor’s speed is a clock #

The speeds of the three visitors carry information independent of their number, and it points at where they came from.

A body ejected from a planetary system leaves at a few kilometres a second relative to its star, much less than the spread of stellar velocities in the Galaxy. Its speed relative to the Sun is therefore essentially its parent star’s speed relative to the Sun, and the speeds of stars are correlated with their ages. Young stars move nearly in step with the gas they formed from, with random speeds of ten to twenty kilometres a second; over billions of years, encounters with molecular clouds and spiral arms stir them, and old stars have random speeds two or three times larger. The thick disc, the Galaxy’s oldest disc population, is hotter still.

The figure draws the speed distribution of visitors passing within an astronomical unit of the Sun for three populations, weighting each speed by how often bodies of that speed arrive — proportional to the speed — and by the focusing, which favours slow ones. ʻOumuamua’s 26 kilometres a second and Borisov’s 32 are typical of young-disc visitors. ʻOumuamua’s arrival direction and speed were close to the average motion of the stars around the Sun, consistent with a young parent system. 3I/ATLAS’s 58 kilometres a second is faster than about 96 per cent of young-disc passages and slower than almost nine in ten from the thick disc, and its speed was read, within weeks of its discovery, as evidence of an old parent star — perhaps older than the Sun.

That reading is a likelihood, not a measurement: one object at a speed found in every population, more often in some than in others. But it is a probe nothing else offers. A cometary nucleus from a planetary system several billion years older than the Sun is a sample of planet formation from an earlier epoch of the Galaxy, and its composition — measured by spectroscopy as it outgassed near the Sun — is a direct comparison with the comets formed here.

The mass the count implies #

A density of interstellar bodies is also a mass budget, and the budget is where the census meets planet formation.

Stars near the Sun number about a tenth per cubic parsec, and a cubic parsec is about $10^{16}$ cubic astronomical units, so a density of a tenth of a hundred-metre body per cubic astronomical unit means of order $10^{16}$ such bodies for every star. A hundred-metre body of icy rock weighs about a billion kilograms, so that is of order an Earth mass of hundred-metre bodies per star. With a size distribution rising steeply towards small sizes, as collisional grinding produces, most of the mass is in the largest bodies, and the total ejected mass per star implied by the census is several Earth masses or more.

That is a lot, but not absurd. The solar system’s giant planets are thought to have ejected most of the solid material that was once between and beyond them — the same scattering that populated the Oort cloud sent far more material out of the system altogether, and each ejection is a gravity assist in which the planet pays a little of its orbital energy. Estimates of the mass the young solar system lost this way run to tens of Earth masses. If every star with giant planets did the same, interstellar space would be well stocked.

The tension, when it appears, is in the small sizes. The census of ʻOumuamua-sized bodies implies more of them than a simple extrapolation from the comets of the solar system predicts, and either planetary systems produce small fragments more efficiently than the solar system seems to have, or ʻOumuamua was a lucky detection from a sparser population — a statement about one count, whose uncertainty is a factor of several in each direction. The deeper survey’s count of small visitors will decide which. Its result will also constrain how often giant planets wander through their own systems scattering material as they go, because a system whose giants migrated ejects much more than one whose giants stayed put.

What was actually measured #

1I/ʻOumuamua, found by Pan-STARRS in October 2017, on an orbit of eccentricity 1.20 with a closest approach of 0.26 astronomical units. No coma was ever seen; its brightness varied by a factor of about ten over seven or eight hours, implying an extremely elongated or flattened shape, and its size, from its brightness and an assumed reflectivity, is a hundred to a few hundred metres. It accelerated slightly as it left, by an amount a comet’s outgassing would produce, though no gas was detected.

2I/Borisov, found in August 2019, on an orbit of eccentricity 3.36, an unmistakable comet with a coma and tail. Its gas was rich in carbon monoxide compared with most solar-system comets, and its nucleus was well under a kilometre across.

3I/ATLAS, found in July 2025 by the ATLAS survey, on an orbit of eccentricity about six with a closest approach of 1.36 astronomical units, an active comet whose nucleus is between a few hundred metres and a few kilometres across. Its pre-discovery images in the survey’s own archive extended its observed arc back by weeks.

The density. Analyses of the surveys that found ʻOumuamua give about 0.1 to 0.2 bodies of its size per cubic astronomical unit, with uncertainties of a factor of several dominated by the size, the reflectivity and the survey efficiency. Borisov and 3I, larger and active, imply a lower density of larger bodies, consistent with a size distribution that rises steeply towards small sizes.

Where the estimates stop #

Opposition only. The reach is computed for a body directly opposite the Sun, at its brightest, with no allowance for the darkening at larger phase angles. Real detections happen at other geometries, and every reach drawn is the best case.

Representative sizes and reflectivities. The diameters of the three visitors are uncertain by factors of a few, and so are their reflectivities. A darker surface makes a body smaller for the same brightness and shrinks the reach.

One speed per population. The focusing figure uses fixed speeds; the population figure uses representative dispersions for each stellar population, taken from the motions of stars near the Sun, and assumes visitors share their parents’ kinematics exactly. Bodies ejected long ago have had time to be stirred like their parent stars, so the assumption is reasonable, and it is still an assumption.

A straight-line window. The detection window is computed for one orbit. Faster visitors spend less time in the inner solar system and slower ones more, so the efficiency depends on speed as well, adding to the focusing’s weighting.

A count divided by the wrong volume #

The general shape is that a census is never only of the thing counted. It is of the thing counted through an instrument, and the instrument’s response depends on the thing: on its size, its speed, its brightness, its path. Dividing a count by a volume that ignores that dependence gives a number that is precise and wrong, and the error is largest exactly where the count is smallest.

Every rate measured near a massive body has passed through a focusing it must be corrected for, and every count has passed through a detection volume that depends on what is being counted. Both corrections are larger for some members of the population than for others, so the corrected census differs from the raw one not only in its total but in its composition — the same lesson as every survey of planets, and of comets arriving from the Oort cloud, whose distribution of energies is shaped by which ones the planets let through.

The other reading is about how little is needed. Three objects, observed for weeks each, have turned the existence of interstellar bodies from a prediction into a measurement, given a density good to a factor of a few, and offered a first hint of the ages of the systems they came from. That is possible because each one was followed precisely enough for its orbit — and therefore its arrival speed and direction — to be known exactly. The orbit is the one thing about a visitor that is not uncertain.

Still open: the visitors that are slow enough to stay #

Gravitational focusing concentrates slow visitors near the Sun, and the slowest of all raise a possibility the three fast ones do not: capture. A visitor arriving at a few hundred metres a second, passing close to Jupiter, could lose enough energy to be left on a bound orbit, an interstellar body living among the solar system’s own. A handful of objects on unusual orbits — retrograde, highly inclined, or co-orbital with Jupiter — have been proposed as captured visitors, and the proposals are contested, because every capture needs a planet to remove the energy and every such encounter is rare. How many captured visitors the solar system should hold, and whether the invariant a planet cannot change in one encounter forbids most of them, is a question about the same orbits run in the other direction.