Twenty hours' notice: near-Earth objects and interstellar visitors

At 06:39:51 UTC on 6 October 2008, Richard Kowalski, observing with the Mt. Lemmon Survey’s 1.5 m reflector in Arizona, measured a faint moving point of light at magnitude $V=18.9$. Over the next hours the sequence of Mt. Lemmon positions was joined by measurements from Sabino Canyon, Moorook in Australia and Siding Spring. The orbit computed from them did not miss the Earth. The object, designated 2008 TC3, entered the atmosphere over northern Sudan at 02:45:44 UTC on 7 October, about 20.1 hours after it was first seen. Fragments were later recovered from the desert and named Almahata Sitta. The telescope had classified the asteroid spectroscopically before it hit, and the laboratory then confirmed the class on the meteorites (MPC 2008; CNEOS pre-impact table; Solin & Granvik 2018).

The asteroid was 3.8 to 4.4 m across. It was found by a telescope built to look for kilometre-sized bodies. It was confirmed in time only because a chain of people and programs, each of which had to work, carried a handful of positions from Arizona to the Minor Planet Center (MPC), out to other observatories and back, and into an orbit calculation. Five years later the same observer found 2014 AA, also about 20 hours before entry. That time only seven positions were obtained, spanning about 70 minutes, before the object entered the atmosphere (Farnocchia et al. 2015).

The two events frame this chapter. A near-Earth object (NEO) survey is not a telescope. It is a distributed inference system. A camera supplies images. Software turns them into candidate moving sources. A short-arc classifier decides which of them deserve scarce follow-up. Observations from other sites constrain their orbits, and impact monitors decide which of the remaining uncertainties matter. Each link has its own threshold and its own blind spot. Interstellar objects, the fastest visitors of all, pass through the same chain, and the three found so far each passed through it differently.

What is being searched for

A near-Earth asteroid (NEA) is an asteroid with perihelion distance $q<1.3$ au. Near-Earth objects also include the near-Earth comets, short-period comets ($P<200$ years) with the same perihelion condition. On 16 October 2026 the JPL Center for Near-Earth Object Studies (CNEOS) counted 42,806 NEAs and 125 near-Earth comets (CNEOS totals). Of the NEAs, about 11,687 are larger than roughly 140 m and 884 larger than roughly 1 km. These size classes are inferred from brightness with an assumed albedo, as explained below.

Three thresholds organise the subject, and confusing them is the commonest mistake in writing about it (Keys et al. 2019).

1. A source-detection threshold decides whether a feature in an image enters a catalogue.
2. A linkage threshold decides whether several catalogue entries plausibly belong to one moving body.
3. A priority threshold decides whether a real moving body merits rapid follow-up as a possible NEO.

None of these is an impact probability. A digest2 score of 100, the highest NEO-likeness score the MPC’s classifier can give, means only that the population bins compatible with the observations are dominated by NEOs. It is not a certain impact, and it is not even a calibrated 100% probability of being an NEO.

It is useful to write the probability that a survey discovers an object with orbit and size $x$ as a chain of conditional factors:

The conditioning matters. Weather, brightness, rate of motion, detector gaps and follow-up are all correlated with one another, so the factors cannot be measured on separate samples and multiplied. A linking efficiency of 99% measured on synthetic objects that were already detected is a statement about one factor. It says nothing about the others. Much of the history below is the story of which factor limited discovery at each stage, and the factor was often not the one the engineers were working on.

Building the network, 1980-2026

Spacewatch and the first automated discovery

Tom Gehrels and Robert McMillan founded Spacewatch at the University of Arizona in 1980. Its early camera did not take exposures in the modern sense. It ran in time-delay-integration, or drift-scan, mode: the telescope stayed still, and the CCD clocked its charge across the chip at the sidereal rate, so that each star’s image moved with the charge packet and was read out continuously. This avoided the long readout overhead of early detectors, at the price of a different exposure time at each declination and observation times that vary across the frame. Production drift scanning began in 1984, and automated asteroid-detection software followed in 1985 (Spacewatch history).

The two decisive steps were separate. David Rabinowitz’s CCD discovery of 1989 UP on 27 October 1989 showed that a CCD survey could find NEAs. On 25 September 1990 Jim Scotti, running Rabinowitz’s Moving Object Detection Program, found 1990 SS, the first NEA discovered by software rather than by a human eye (Spacewatch 1990 SS). Spacewatch also met the fast-mover problem early. On 18 January 1991 it found 1991 BA, which left a streak 161 arcseconds long in the discovery scan. The nearest objects are trails, not points, and the history of NEO discovery is partly a history of trail detection (Chapter 11).

LINEAR: surveillance hardware turned on asteroids

The step change in numbers came from the military. In the mid-1990s MIT Lincoln Laboratory replaced the older Ebsicon tube cameras on prototype GEODSS satellite-tracking telescopes at its Experimental Test Site near Socorro, New Mexico, with back-illuminated CCDs. These were faster to read and more sensitive. Asteroid experiments began in 1996, and NASA-sponsored operations of the Lincoln Near-Earth Asteroid Research program (LINEAR) began in 1998. The first month with the advanced system produced more than 151,000 observations (Lincoln Laboratory; Stokes et al. 2000).

LINEAR did not use a new detection principle. Its innovation was operational: a high duty cycle, rapid-readout wide-field detectors, aggressive scheduling of repeated visits and automated reporting, at a scale no one had attempted. CNEOS today credits LINEAR with 256 NEA discoveries in 2000 and 304 in 2004 (CNEOS by survey). The program later moved to Lincoln’s 3.5 m Space Surveillance Telescope, starting in 2013, and submitted 7.2 million observations in 2015. That number is a useful warning. Observations and discoveries are different quantities, and most observations of a mature survey are of known objects.

Catalina and the dedicated follow-up telescope

Steve Larson, Tim Spahr and Carl Hergenrother founded the Catalina Sky Survey (CSS) in 1998 (CSS history). By 2005 it was discovering more NEAs than LINEAR: 314 against 137 that year. Catalina’s current arrangement is a lesson in system design. It runs two discovery telescopes of different depth and width, and a third telescope for confirmation:

The 1.0 m follow-up telescope became operational in 2014. CSS estimates that moving confirmation work off its discovery telescopes increased their survey time by 10-20% (CSS telescopes). This gain came from a change in how instruments were allocated, not from better software: a cheaper telescope took over the confirmation exposures, and the expensive survey footprint stayed intact. CSS observes about 24 nights per lunation, and its observers inspect candidates and submit them in near real time.

Deep, fast and infrared

Three systems from the 2010s define the present network.

Pan-STARRS1 on Haleakalā began asteroid surveying in spring 2010: a 1.8 m telescope with a field of about 7 deg², a 1.4-gigapixel camera and 0.26-arcsecond pixels. Its Moving Object Processing System (MOPS), built by Larry Denneau, Robert Jedicke and colleagues including Andrea Milani and Mikael Granvik, was designed as a complete catalogue-to-orbit system (Denneau et al. 2013). How it met real data is described below.

ATLAS, the Asteroid Terrestrial-impact Last Alert System of John Tonry, Larry Denneau, Ari Heinze and colleagues, was designed to be cheap, replicable and fast. NASA funding began in 2013 and first light was in June 2015. The 2018 system paper describes 0.5 m telescopes with about 29 deg² of usable field, taking 30 s exposures on a 40 s cadence and reaching about magnitude 19.7 at five sigma in the best conditions (Tonry et al. 2018). ATLAS now runs four units, two in Hawaii and one each in Chile and South Africa (ATLAS project). The southern sites matter less for collecting area than for weather independence, declination coverage and longitude: an object that rises after dawn in Hawaii can be seen in the dark from Chile.

NEOWISE reused the WISE infrared satellite. Amy Mainzer’s team restarted minor-planet searches on 23 December 2013, with the first new NEO found six days later, using the 3.4 and 4.6 μm bands left after the cryogen ran out (Mainzer et al. 2014). The survey ended on 31 July 2024, and the spacecraft was decommissioned on 8 August 2024 (NASA). In 2026 NEOWISE is an archive, not an active survey. Its selection was different in kind: thermal emission depends much less on albedo than reflected light does, so it saw dark asteroids that optical surveys under-count (Chapter 24).

The Zwicky Transient Facility (ZTF) at Palomar also discovers NEAs, though the official statistics hide it. CNEOS groups ZTF’s observatory code, I41, with three other codes under “Other-US”, so the 555 Other-US discoveries of 2025 cannot be reported as ZTF’s.

The figure shows the network changing hands. LINEAR dominated until about 2004. Catalina and Pan-STARRS have together supplied most discoveries since 2010, and the two have been roughly level since 2019. ATLAS discovers fewer objects than either because it is shallower, but it was not built for numbers. Its niche is warning time for objects close to the Earth. Discovery counts also say nothing about follow-up value. Spacewatch discovers almost nothing now, but its 0.9 m, 1.8 m and part-time 2.3 m telescopes recover faint candidates that others find, and the project reports that targeted observing increased its NEO observation rate 4.6 times relative to its old survey pattern (Spacewatch). The annual total has stood at about 3,000 to 3,250 NEAs a year since 2020 (3,240 in 2025). These are retrospective credits computed from today’s MPC database, not the numbers reported at the time.

The signal: brightness, motion and trails

How bright, how big

A sunlit asteroid’s apparent magnitude is

where $r$ and $\Delta$ are its distances from the Sun and the observer in au, $\alpha$ is the phase angle (Sun-object-observer), $\Phi$ is a phase function normalised to $\Phi(0)=1$, and $H$, the absolute magnitude, is the magnitude the object would have at $r=\Delta=1$ au and zero phase. Converting $H$ to a diameter needs the geometric albedo $p_V$:

With the albedo of 0.14 that CNEOS adopts for its size bins, $H=22$ gives $D = (1329/0.374)\times10^{-4.4}\approx0.14$ km. That is why "$H<22$" and “larger than 140 m” are used almost interchangeably (Mainzer et al. 2014). Real albedos range over more than a factor of ten, which changes $D$ by more than a factor of three at fixed $H$. Size estimates from optical brightness alone are therefore uncertain by that factor. Chapter 2 develops these relations.

For the nearest bodies the geometry is extreme. At fixed illumination and a fixed flux threshold, the distance at which an object becomes detectable scales roughly as $\Delta_{\max}\propto D$, because flux goes as $D^2/\Delta^2$ when $r$ is nearly constant. For a body approaching nearly radially at speed $v_{\rm rel}$, the photometric lead time is about $\Delta_{\max}/v_{\rm rel}$. A survey one magnitude deeper therefore sees an incoming impactor $10^{1/5}\approx1.58$ times earlier. This is a scaling estimate under restrictive assumptions. Phase angle, trailing, solar elongation and processing delay can all dominate it.

How fast

Let $\boldsymbol\rho=\mathbf r-\mathbf R$ be the vector from the observatory at $\mathbf R(t)$ to the object at $\mathbf r(t)$, $\rho=|\boldsymbol\rho|$, $\hat{\mathbf u}=\boldsymbol\rho/\rho$, and $\mathbf w=\dot{\mathbf r}-\dot{\mathbf R}$ the relative velocity. The angular velocity on the sky is

Only the transverse part of the relative velocity produces motion, and it is divided by the distance. Two consequences follow. Nearby objects move fast: 1°/day is 1/24 arcsec/s, so a 30 s exposure smears an object by 1.25 arcseconds for each degree per day of motion, and by 12.5 arcseconds at 10°/day. But an object on a collision course has almost no transverse velocity, because it is heading straight at the observer. The most dangerous object need not be the fastest mover. Near arrival, the observer’s own motion, including Earth’s rotation, supplies some curvature, but a collision course is close to stationary on the sky (Walker & Seligman 2026).

The point is not academic. The 2023 digest2 paper discusses 2019 OK, a close-approaching asteroid that was present in earlier Pan-STARRS and ATLAS images but moved too slowly to be flagged by their automated pipelines (Vereš et al. 2023). “Near-Earth means fast” is a population tendency, not a rule a filter can safely enforce.

What a trail costs

For exposure $k$ and pixel $p$, the data are

where $b$ is the background, $F_k$ the source flux, $P_k$ the pixel-integrated point-spread function (PSF), $\boldsymbol\theta$ the trajectory parameters and $h$ the PSF smeared along the path during the exposure, normalised to unit flux. For Gaussian noise with covariance $\mathbf C$, the best linear estimate of the flux and its detection significance are the matched filter of Chapter 1:

Under the null hypothesis, $Z$ is a standard normal variable for each fixed template. The tail probability at five sigma is $2.87\times10^{-7}$, so $10^9$ independent templates would produce about 287 noise peaks above five sigma. Real catalogues are worse than this, because subtraction residuals, cosmic rays and detector defects do not follow a Gaussian tail (Denneau et al. 2013; Masci et al. 2019).

A trail loses signal-to-noise ratio (SNR) in two distinct ways, and only one of them can be fixed in software. The first is physical. A trail of length $L$ spreads the same flux over a noise area of about $Ls$ instead of $s^2$, where $s$ is the PSF width, so even a perfect trail filter has SNR reduced by a factor of roughly $\sqrt{s/L}$ relative to a motion-frozen image. The second loss comes from the detector: if source extraction uses a stellar PSF on a streak, it throws away more. Dorsey et al. fit both effects with one empirical form,

where $\mu$ is the rate of motion in degrees per day, $T_{\rm exp}$ the exposure in seconds, $\theta$ the seeing in arcseconds, and $x$ therefore the trail length in units of the seeing. The coefficients are $(a,b)=(0.67,1.16)$ for the SNR loss alone and $(0.42,0)$ for the total loss of a point-source detector (Dorsey et al. 2025).

Short frames are not free either. If $N$ frames with read variance $R^2$ cover a total time $T$ against a background rate $B$ in the source footprint, the variance includes $BT+NR^2$. Splitting an exposure into many short frames trades trailing loss for read noise. This is the regime of synthetic tracking (Chapter 18), which needs low-noise, fast-readout cameras (Shao et al. 2013).

What a short arc cannot tell you

A tracklet is a few positions from one night. On the tangent plane it is well described by

Over an hour it measures the attributable $\mathcal A=(\alpha,\delta,\dot\alpha,\dot\delta)$, the position and angular velocity, well. It hardly constrains the topocentric range $\rho$ and range rate $\dot\rho$. The heliocentric state is

and every $(\rho,\dot\rho)$ pair gives a different orbit consistent with the same four numbers. A more precise straight-line fit cannot recover the missing two dimensions. They come only from curvature (the $\mathbf a$ term, which near the Earth includes diurnal parallax from the observer’s rotation), from a longer arc, from a second observatory, or from radar (Farnocchia et al. 2015). This single fact explains the architecture of everything downstream. digest2, Scout and Meerkat are all ways of searching the unconstrained $(\rho,\dot\rho)$ plane and asking which orbits survive. Chapter 13 treats the admissible region and orbit determination in depth.

The pipelines

Each survey solved the same four tasks: detect sources, reject stationary ones, link movers into tracklets, and report. Each solved them under different constraints. The differences are instructive because each design choice protects one factor in the discovery chain at the cost of another.

Catalogue differencing: Spacewatch and LINEAR

The classical approach predates modern image subtraction. Calibrate each image, extract sources independently, match the stationary ones across visits, and search what remains for consistent motion. The image is consulted again only to measure or to check a candidate. Stated as an algorithm:

for each repeated sky region:
    calibrate pixels; attach observation times and WCS
    extract sources: positions, fluxes, shapes, uncertainties
    match stationary sources across visits; discard them
    build a spatial index of the unmatched detections
    for each allowed (first, second) detection pair:
        predict positions in the remaining visits
        retrieve candidates inside an uncertainty-aware gate
        fit motion; keep tracklets with enough support
    compare with predictions for known objects
    inspect images of unknown candidates; report astrometry

Calibration is $O(EP)$ for $E$ exposures of $P$ pixels. Enumerating pairs of the $n$ leftover detections in a visit is $O(n^2)$ in the worst case. Spatial indexes and small gates make the real cost output-sensitive, but a dense population of false detections can still dominate. Drift scanning adds a bookkeeping subtlety: each row of the image has its own time, and a frame-midpoint timestamp is wrong for most of the frame. For a moving object, a timing error is a position error along the direction of motion. No published timing model of the historical LINEAR software survives in the sources examined, so its CPU cost cannot be reconstructed honestly.

Pan-STARRS MOPS: what real data did to a near-perfect linker

MOPS ingested detections from the Pan-STARRS image pipeline, formed intra-night tracklets, linked them across nights with kd-trees (Chapter 12), fitted initial orbits, applied differential corrections and maintained a database of derived objects with attribution and precovery. It measured its own efficiency by injecting synthetic objects into the detection catalogues and following them through (Denneau et al. 2013).

In idealised simulations of the planned four-telescope Pan-STARRS4, MOPS produced orbits for more than 99.5% of detectable synthetic objects. For a setup like the real PS1 the figure fell to about 80%, because of processing limits, astrometric quality and the cadence actually achieved. Then the real data arrived and imposed further losses. The focal plane’s effective fill factor was about 75%. Depending on how repeated pointings correlated with an object’s motion, the geometric efficiency for six detections lay somewhere between $f^6$ and $f$, that is, between 26% and 75%, even for bright objects. The false-detection rate was about 8,200 transient detections per square degree above five sigma, and fields near the Galactic plane had 10 to 50 times the statistical expectation. Subtraction residuals and detector behaviour, not Gaussian noise, set the rate.

The response was a series of engineering compromises. From October 2010 PS1 took four exposures of each field, typically 15 minutes apart, giving 45-minute tracklets: three or four detections are far more reliable than pairs. In two-detection processing the team searched two separate speed ranges, 0.3-0.7°/day and 1.2-5°/day, using trail morphology in the faster range, and deliberately left the gap between them unsearched to control confusion. Human “czars” examined postage stamps before anything was reported. The NEO pathway thus used MOPS mainly to make tracklets, and the multi-night orbit machinery served research and simulation. The published MOPS hardware was modest: 32 processing cores, 8 administrative cores and 20 TB of database storage. These are the 2013 paper’s operating choices, not current settings.

ATLAS: a latency budget

ATLAS’s design started from the requirement. Each field is visited four or five times in about an hour, so the processing of one visit must finish before the next one is useful, well within the hour. The pipeline flattens each image, measures bright stars, solves astrometry and photometry, estimates cloud, builds a reference “wallpaper” matched to the exposure, subtracts it with a modified HOTPANTS, detects and classifies residual sources, and runs an adapted MOPS client. Humans check unknown candidates before submission to the MPC. The telescope control system uses Go and Redis, and the processing favours C, bash and ordinary Unix tools (Tonry et al. 2018).

The paper’s timing table is unusually useful. Detection initially goes down to three sigma and is then trimmed to five. The MOPS client completes 1,710 s after the exposure starts. Each site had four summit compute nodes of 12 to 16 cores and 128 GB of memory, plus a 16-node cluster in Honolulu. A normal night produced about 150 GB of compressed raw data. When network bandwidth degrades, more computation moves to the summit, which sends detection tables at once and images later. This keeps latency low without requiring a fast link.

The proportions carry a lesson for anyone hoping to accelerate discovery with a faster linker. In 2018, subtraction and difference-source detection together cost 1,350 CPU-seconds per image, and the moving-object client cost 120. Accelerating the linker alone could not have removed most of the latency. The same survey’s design paper gives an expression for survey speed, background-limited,

where $\Omega/t_{\rm cad}$ is the sky area covered per cadence interval, $A$ the collecting area, $\Omega_0$ the field of view, $\epsilon$ the throughput, $\delta$ the duty cycle, $\omega$ the noise-equivalent PSF area, $\mu$ the sky surface brightness and $m$ the limiting magnitude. Each magnitude of extra depth costs a factor $10^{0.8}\approx6.3$ in area covered per cadence. Computing can shorten the delay and recover photons already collected. It cannot change this trade between collecting area and sky background.

ZTF: stringlets and streaks

ZTF’s image pipeline calibrates each detector quadrant, subtracts references with the ZOGY algorithm (Chapter 10), extracts point sources and streaks, and applies real/bogus classifiers. Its median single-exposure depths are about $g=20.8$ and $r=20.6$ at five sigma in 30 s. The moving-object system, ZMODE, is a separate product that runs after the night on detections from up to four nights. The two latency regimes must not be confused: rapid image alerts and end-of-night multi-night linking are different things (Masci et al. 2019).

ZMODE’s building block is a stringlet of three detections $a,b,c$, not a pair. It computes

and requires the two velocities to agree within a tolerance that depends on the time spans. One pair must span at most 10 hours and the other at most 2.5 days. Stringlets are merged using both their mean velocities and the velocities between their mean positions. Tracks of four or more detections go to orbit fitting with Bill Gray’s find_orb, then to quality cuts, known-object checks, digest2 and human inspection.

select quality-filtered difference detections from the recent nights
for each possible middle detection b:
    retrieve admissible earlier and later neighbours
    keep (a, b, c) where v(a,b) matches v(b,c)
merge stringlets on a coarser velocity grid
deduplicate; require a minimum supported length
fit orbit; reject poor fits; attribute known objects
score with digest2; inspect cutouts; report to the MPC

The idea is to spend work early, on a cheap three-point consistency test, so that false pairs do not propagate into merging and orbit fitting. The worst case is still combinatorial, and no $O(n\log n)$ guarantee for the whole pipeline is claimed. The quoted efficiency above 90% and reliability above 98% near $R\sim20$ come from tests on data from ZTF’s predecessor, PTF. The facility behind it had 66 dual-Xeon nodes with 1,192 physical cores, plus two 768 GB high-memory nodes partly for ZMODE. Routine processing ran only 528 quadrant instances at once, because database and file-system I/O, not CPU, limited useful concurrency. A quadrant took a median of about 290 s with differencing and alerts.

Fast movers take a parallel branch. ZStreak groups contiguous pixels above $1.5\sigma$ in the difference image, keeps groups whose pixels are linear (Pearson correlation above 0.55), and fits a PSF-convolved trail model. For a Gaussian PSF of width $s$ and a uniform trail of length $L$ along $x$,

rotated and translated to the fitted orientation and midpoint (Ye et al. 2019). Through 2018 the streak pipeline yielded 45 confirmed new NEAs in 232 observable nights. A trail measures a position and an unoriented velocity: without a second exposure, its two ends do not say which way the body moved.

The candidate stream is dominated by junk. Between 15 December 2018 and 15 January 2019 ZTF produced about 7 million raw streak candidates. The DeepStreaks ensemble of convolutional networks selected about 33,000 of them, against about 1.7 million passing the earlier random-forest filter, and humans labelled 270 of its selections as real fast-mover streaks (Duev et al. 2019). Of 210 known-NEO streaks that the upstream detector had found, it kept 202, about 96%. Human scanning fell from hours to typically under ten minutes a day. Training ran on an NVIDIA Tesla P100: about 1.5 hours for VGG6, 8 for ResNet50 and 10 for DenseNet121, on about 25,000 images for 300 epochs. This is real GPU evidence, but for training a stamp classifier, not for an end-to-end GPU survey. A 2025 follow-up segmented difference images directly with a TernausNet, reaching completeness of about 0.84 and precision of 0.79-0.85 on its test sample (Irureta-Goyena et al. 2025). Against 317 scanner-selected streaks it recovered 80% and found 697 additional valid ones. More than 80% of the examined streaks appeared to be artificial satellites, so these 697 are streaks, not new asteroids. Chapter 22 returns to these classifiers.

NEOWISE: linking under a spacecraft’s cadence

A spacecraft in a polar orbit scanning the sky cannot choose ground-style quads. NEOWISE’s moving-object system, WMOPS, compared single-exposure catalogues, removed sources coincident within 5 arcseconds, and kept detections with SNR at least 4.5. It linked them with kd-trees, imposing a maximum motion of 5°/day and requiring at least five detections per tracklet. Adjacent overlapping frames only 11 s apart were excluded from initial tuple building. A typical minor planet received 10 to 12 detections over about 36 hours, so arcs were about 1.5 days long, sometimes only 0.4 days (Mainzer et al. 2014).

Two numbers show where the binding constraint lay. The reactivated pipeline ran three times a week and delivered tracklets a mean 2.4 days after their last detection. The requirement was to report within 10 days of the midpoint, which kept the ephemeris uncertainty under about a degree. And optical confirmation commonly needed observations at $V\sim21$-23. Infrared-selected NEOs are often dark and can be at awkward declinations, so the survey’s own discoveries were hard for its confirmation network to observe. A discovery instrument can select objects its follow-up network cannot see.

Synthetic tracking: the smallest objects

At the faint end, Michael Shao, Chengxing Zhai, Bijan Nemati and colleagues at JPL replaced the long exposure with a stack of short frames shifted and added along trial velocities on a GPU (Shao et al. 2013; Zhai et al. 2014). On the Palomar 5 m with the CHIMERA camera, about 500 frames at 16.7 Hz revealed a magnitude-23 object moving at 5.97°/day with SNR about 15 in 30 s. The search covered a $100\times100$ velocity grid on $512\times512$ images, and 1,500 frames spanning 90 s were processed in under 90 s on a Tesla K20c. The authors identified memory bandwidth as the limit. With about $2.6\times10^9$ position-velocity trials, a threshold of $Z=7$ gives an expected 0.34% noise-only false alarms per search. The authors are explicit that their two same-night epochs did not determine an orbit. It was a detection, not a secured discovery. A 2024 system processed a far larger cube, from a 61-megapixel camera with 100 frames and a $100\times100$ velocity bank (24.4 GB in floating point), in about 440 s on a 32 GB V100, for a 500 s acquisition (Zhai et al. 2024). The method itself belongs to Chapter 18.

From tracklet to designation

The NEO Confirmation Page

Surveys send astrometry to the MPC. The MPC attributes what it can to known objects. Unknown candidates that look like possible NEOs go onto the NEO Confirmation Page (NEOCP), with temporary designations and ephemerides. Observers anywhere retrieve the predicted positions, image the fields and send back astrometry, which extends the arc (MPC NEOCP). Candidates leave the page when they are designated, withdrawn or abandoned. Disappearance alone does not show a candidate was false, but some listed objects are indeed artefacts (CNEOS Scout).

The NEOCP is the network’s shared queue, and its capacity is finite. Wagg et al. simulated what the Rubin Observatory’s deeper survey would add to it: about 129 new NEOCP candidates per night under their criteria, of which only 8.3% were NEOs. A predictor of which objects Rubin would itself recover without help cut the list to 64 per night at 8.4% purity (Wagg et al. 2024). These are 2024 forecasts, not measured 2026 rates (Chapter 15), but they show where the next bottleneck sits.

digest2: classifying an orbit you do not have

The gatekeeper is digest2, descended from Rob McNaught’s PANGLOSS work through a FORTRAN lineage involving Robert Jedicke, Carl Hergenrother and Tim Spahr, and later developed by Sonia Keys, Peter Vereš, Matthew Payne and colleagues (Keys et al. 2019). The algorithm does not fit an orbit. It reduces the tracklet to two effective observations, varies them within their uncertainties, explores bound heliocentric orbits over the unconstrained range and range rate, and maps each compatible orbit into bins of perihelion, eccentricity, inclination and absolute magnitude $(q,e,i,H)$. Each bin carries a weight from a synthetic population model. The score for orbital class $c$ is

where $\Sigma_c$ is the summed population weight of compatible bins belonging to class $c$, and $\Sigma_{\rm other}$ that of all other compatible bins. A “raw” score uses the full population. A “no-ID” score first removes known objects bright enough that they would probably already have been identified. The search over bins uses adaptive binary subdivision rather than a posterior-weighted grid. The result is a class score under population assumptions, not a Bayesian probability.

The conventional NEOCP threshold is a score of about 65. The 2019 analysis measured the trade-off: in its test set of real tracklets, 14% of NEO tracklets scored below 65, while 98.5% of non-NEO tracklets did. In a ten-year synthetic experiment, 99.6% of NEOs scored at least 65 at some time. That is not completeness. An object still has to be observed at the favourable moment. Low solar elongations and slow apparent motions are particularly troublesome, which brings us back to 2019 OK.

The 2023 update added per-observation uncertainties from the Astrometry Data Exchange Standard (ADES) format, updated the population model and expanded the table of representative observatory uncertainties to 140 codes (Vereš et al. 2023). It also ran faster:

The tests ran on a 16-core server. The speed-up came from rewritten parsing, arithmetic and uncertainty handling, not from the XML format itself. This is a recurring theme: restructuring the code mattered more than changing the processor.

In 2025 Vereš et al. tried richer triage. They used several digest2 class scores and machine-learning classifiers on 36,046 initial NEOCP tracklets from 2019-2024, trained on earlier years and tested on 2024 (Vereš et al. 2025). Simple class-score filters removed about 20% of non-NEOs with few NEO losses. Their combined approach rejected more than 80% of non-NEOs at the cost of about 5.5% of NEO discovery tracklets. For the selected classifier, 189 of 3,428 NEOs were initially misclassified, and 140 of those were classified correctly once a later follow-up tracklet arrived. The code is public. The apparent residual loss of about 1% needs care, though. Some of those later tracklets exist only because the candidate was posted and followed up. A stricter filter would have prevented some of them, and a delayed classification costs warning time even when the object is eventually recovered. Only a replay of real schedules with the feedback included can measure the operational loss.

Impact monitoring

Systematic ranging and the role of the prior

When a new candidate might be on a collision course, the question cannot wait for a well-determined orbit. Systematic ranging fixes $(\rho,\dot\rho)$ on a grid, refits the attributable at each node, and propagates the resulting orbits to find future sky positions, close approaches and impacts (Farnocchia et al. 2015). With residuals $\boldsymbol\xi$ of covariance $\mathbf C$,

and the impact probability is the posterior weight of grid orbits that enter the atmosphere. The prior $\pi$ matters, and so does the integration measure: a density flat in $\rho$ is not flat in $\log\rho$, in Cartesian volume or in orbital elements. When the likelihood is weak, the prior decides the answer. Farnocchia et al. showed this on the two Kowalski impactors, recomputing the earliest arcs with 0.5-arcsecond astrometric weights:

On four observations over 43 minutes, the computed impact probability for 2008 TC3 ranged from 2% to 63% depending on the prior. With seven observations over 99 minutes, every prior gave certainty. These are retrospective calculations, not the numbers issued at the time. The lesson for algorithm designers is that more information, from a longer arc, removes prior dependence far more effectively than any refinement of the calculation.

JPL’s Scout service runs this analysis on NEOCP objects and updates its summaries every 15 minutes. Its impact rating is undefined for arcs shorter than 20 minutes or with fewer than three observations. Its documentation calls the ratings indicators of interesting objects, not rigorous probabilities (CNEOS Scout). The grid is naturally parallel: with $G$ nodes, $k$ fitting iterations and $n$ measurements the cost is about $O(Gkn)$ plus the numerical propagation.

ESA’s Meerkat Asteroid Guard is the most completely documented operational system of this kind (Drury et al. 2026). It uses a $160\times160$ grid in range and range rate, with range from $10^{-4}$ to $10^2$ au before cropping and range rate within ±100 km/s, three to thirty observations, and up to four fit iterations per node. It propagates for thirty days, defines impact as reaching 50 km above Earth’s equatorial radius, and allows one denser “zoom step” when the confidence region covers less than 2% of the grid. It adds a timing term to each observation’s covariance,

where $\boldsymbol\mu$ is the angular velocity and $\sigma_t$ the timing uncertainty, one second by default. For a fast mover, a one-second clock error is an elongated position error along the track. Ignoring it can manufacture spurious curvature and a false impact corridor. On a 32-core virtual machine Meerkat issues alerts a mean 56 seconds after new data arrive. It is idle an average of 20.5 hours a day, waiting for data. Statistical ranging, as in OpenOrb, samples instead of gridding. Solin and Granvik’s neoranger tests covered 695 NEOCP objects over eight weeks. Ordinary objects stayed below an impact probability of $10^{-7}$, while real and simulated impactors exceeded 10% after their first two tracklets (Solin & Granvik 2018).

Sentry-II: importance sampling the impact region

Long-term monitoring asks a different question: does the uncertainty region of an established orbit contain trajectories that hit the Earth in the next century or so? These trajectories are called virtual impactors. The University of Pisa’s NEODyS (with its CLOMON2 system) and JPL’s original Sentry sample along the line of variations, the one-dimensional curve through the weakest direction of the orbit’s uncertainty. Sentry-II, operational at JPL since 2021, replaces this with a scheme that suits rare-event estimation (Roa et al. 2021).

It first propagates 10,000 virtual asteroids drawn from the orbital uncertainty to find candidate close encounters. For each, it refits the orbit with an extra pseudo-observation that pulls the trajectory towards impact:

where $\mathbf b_s$ is the scaled position on the encounter plane (the b-plane) and $\boldsymbol\epsilon$ a small offset so the target is not the Earth’s centre. The impact is not treated as a measurement. The fit locates an impact-compatible proposal distribution $g$, and importance sampling then estimates the probability under the true orbital uncertainty $p$:

The paper estimates 99% completeness for impact probabilities above $3\times10^{-7}$ and about 80% at $10^{-7}$. Median run times were 41 minutes for Sentry-II against 21 for Sentry. Brute-force propagation of $10^7$ samples for 100 years took about 14 days on the comparison setup, roughly 500 times the Sentry-II median. That factor of 500 came from sampling where the answer is, not from faster hardware. Any GPU port must be compared against Sentry-II, not against naive Monte Carlo.

Three clocks

“Warning time” hides three different intervals:

They can differ completely. In September 2020 a roughly 3 m meteoroid struck over the western Pacific. After the impact, a search of archival images found that ATLAS had captured it as a 0.44° streak in a 30 s exposure, at magnitude 12.5, just 10 minutes before entry (Clark et al. 2022). Its $W_{\rm image}$ was ten minutes. Its $W_{\rm alert}$ was zero. For 2024 UQ, ATLAS images preceded entry, but the candidate reached the NEOCP afterwards, so Meerkat could issue only a retrospective alert (Drury et al. 2026). Simulations usually compute the time at which a discovery criterion is first met, which is none of the three.

The CNEOS table retrieved for this chapter lists thirteen asteroids discovered before impact. Their discovery-to-impact intervals range from 1.8 to 20.8 hours, with a median of 7.4 hours. Six were found with Catalina’s Mt. Lemmon 1.5 m (code G96), and three at station K88 in Hungary. Two entries from 2026, 2026 JN4 and 2026 RW1, are JPL-predicted trajectories whose discovery circulars said no independent report of an atmospheric entry had yet been received (MPC 2026-J143; MPC 2026-R64). The sample is selected twice: by the surveys that found the objects, and by the brightness that let them be found. Every object in it is metre-scale. None was big enough to cause damage.

Interstellar visitors

An interstellar object (ISO) is a body on an unbound orbit that came from outside the Solar System. A large heliocentric speed does not imply a large angular speed. An active ISO can be bright far from the Earth and look at first like an ordinary comet. The three discovered so far passed through three different selection functions.

1I/’Oumuamua (2017)

Pan-STARRS1 recorded the object in October 2017, near its closest approach to the Earth at about 0.4 au. Robert Weryk was among the Pan-STARRS measurers, and Karen Meech led the rapid physical characterisation. The observing literature gives discovery as 18.5 October UT, and NASA’s public account gives 19 October. The first circular called it a comet, C/2017 U1 (PANSTARRS). It was redesignated A/2017 U1, an asteroid, when no coma appeared, and then 1I/2017 U1, the first entry in a new class (MPC 2017; Jewitt et al. 2017). The early orbit had $q\simeq0.254$ au, $e\simeq1.197$ and inclination about 122.6°. Perihelion had already passed on 9 September, when the object was too close to the Sun to be seen. It was intrinsically faint, caught near a favourable brightness peak on its way out, and star-like, so it was the asteroid machinery, not a comet search, that found it. Its large rotational brightness swings make tracklet completeness harder still, since repeated visits need not catch the same phase. Its non-gravitational acceleration belongs to Chapter 27.

2I/Borisov (2019)

Gennady Borisov, an amateur astronomer, found the comet on 30 August 2019 from his MARGO observatory at Nauchnij in Crimea, with a 0.65 m $f/1.5$ astrograph and a CCD. It was about magnitude 17.8 in $R$, with a condensed coma. The discovery circular credits independent early hyperbolic orbits to Davide Farnocchia, Bill Gray and David Tholen (MPC 2019). At 04:15 UT on 8 September, Piotr Guzik and Michał Drahus’s group received an automated alert from their “Interstellar Crusher”, a Python program that watched the MPC’s Possible Comet Confirmation Page and ran Gray’s Find_Orb on every new object (Guzik et al. 2019). In their analysis, 447 positions over 21.1 days were available, and 362 survived outlier rejection. A parabolic orbit left systematic residuals of about 20 arcseconds. An unrestricted fit gave $e=3.38$, $q=2.0119\pm0.0044$ au and $v_\infty\approx32$ km/s. Forcing a parabola with outgassing instead required implausible accelerations. Because Borisov was an active comet, it was found at a larger distance and before perihelion, and it was studied for months. Quanzhi Ye and colleagues then searched the ZTF archive iteratively and traced the comet back to 13 December 2018, at 7.8 au from the Sun, mostly in images that had to be stacked along the predicted path (Ye et al. 2019).

3I/ATLAS (2025)

ATLAS’s Chilean telescope found candidate A11pl3Z in four 30 s survey exposures on 1 July 2025. Quanzhi Ye and Sam Deen supplied immediate follow-up and precoveries back to 14 June (MPC 2025). The object was moving only about 0.49°/day at magnitude 17.7-17.8, unremarkable for a moving object. What hid it was where it lay: in the Galactic plane, a crowded region that some deeper surveys avoid. The initial fit of 132 observations gave $e\approx6.20$, $q\approx1.366$ au, inclination 175.1° and incoming $v_\infty=58\pm1$ km/s, and CFHT images on 2 July showed faint activity (Seligman et al. 2025). Rubin Observatory commissioning images had caught it on 21 June, ten days before discovery, at 4.5 au from the Sun (Chandler et al. 2025). TESS had imaged it from 7 May to 2 June. Single 200 s TESS frames were too shallow, but stacked photometry recovered it, brightening from $T=20.9$ to 19.6 (Martinez-Palomera et al. 2025). The discovery paper’s radius of about 10 km assumed all the light came from a bare nucleus. The coma invalidates that assumption, and later Hubble limits were much smaller (NASA).

What makes an orbit interstellar

An osculating heliocentric eccentricity above one is not proof. Planetary perturbations and bad astrometry can both produce it. The diagnostic is the incoming barycentric orbital energy, computed before the object entered the planetary region, with credible non-gravitational forces allowed for. In the two-body approximation,

The last relation checks the three discoveries against each other. With $GM_\odot=1.327\times10^{20}$ m³ s⁻² and 1 au $=1.496\times10^{11}$ m:

Gravitational focusing makes the Sun a larger target than its geometric cross-section. The cross-section for passing within perihelion $q$ is

so for $q=1$ au and $v_\infty=26$ km/s the bracket is about 3.6. Expected detections are an integral of the number density per unit $H$, the velocity distribution, $v_\infty\Sigma$ and the survey’s selection function. Dorsey et al. show how to compute this efficiently. Instead of sampling a huge volume and discarding almost every orbit, they draw orbits directly, weighted so that every sample enters its magnitude-dependent observable sphere during the survey (Dorsey et al. 2025). The gain comes from importance sampling again, not from faster integration.

How many to expect

The first two rows cannot be averaged, because their populations and discovery definitions differ. Dorsey et al. find that fewer than 40% of ISOs observed at least once by the simulated survey become discoveries under its cadence, and fewer than 10% for $H_r\ge22$, even assuming linking always succeeds. Machine-learning ISO classifiers trained on simulated Rubin tracklets look strong on balanced tests but falter on real objects: a random forest identified 103 of 712 Borisov examples, while a different model did best on ‘Oumuamua (Cloete et al. 2024). There is also a structural trap. Meerkat’s planetary-defence posterior excludes fitted heliocentric orbits with $e\ge1$. An ISO search must keep unbound solutions alive from the first stage, or no later classifier can recover them.

Landmark results

What forecasts say about the next decade

The Rubin Observatory will be deeper than any current NEO survey, but its cadence was designed for many sciences at once. Three 2026 studies simulate its yield of imminent impactors from different inputs. Their headlines differ for reasons that matter.

Cheng et al. tabulate discovery fraction and the median lead time among discovered objects by diameter: 10.5% of 10-20 m impactors are found, with a median lead of 12.4 days; 26.8% of 20-50 m, 21.5 days; 50.3% of 50-140 m, 106 days; and 79.7% of 140 m to 2.2 km, 1,218 days. These are conditional results from an unweighted synthetic sample, not a collision-rate forecast. The authors did not weight by collision probability, and some percentage columns in their second table do not reproduce the counts in the first. The single-night rules in the first two studies are modelled possibilities. Neither paper shows them deployed with their assumed false-positive control. The broader Rubin pipeline is the subject of Chapter 15, and the simulators behind these numbers are the subject of Chapter 16.

Limitations and open problems

Geometry and photons. An object near the Sun, below the horizon, behind cloud or on a masked pixel is not made detectable by a faster linker. ‘Oumuamua was invisible at perihelion. The Chelyabinsk impactor came from the solar direction. Ground-based optical completeness is strongly anisotropic, and only a change of vantage point, for example an infrared telescope in space, changes it (Chapter 23).

Fast motion and curvature. A point-source cut loses flux spread along a trail. A constant-velocity gate rejects curving close approaches. A maximum-speed cut excludes the nearest objects outright. PS1’s deliberate gap between 0.7 and 1.2°/day and WMOPS’s 5°/day ceiling are concrete examples of engineering boundaries drawn through the physically observable population. Raising the speed limit without changing the association logic just adds false hypotheses.

Slow motion. The opposite failure is quieter. A candidate rejected as stationary never reaches digest2, so no improvement to the score can recover 2019 OK.

Artefacts and domain shift. Galactic-plane residuals, bright-star halos, cosmic rays, satellites and detector edges dominate the expensive tail of the candidate stream. Classifier test sets drawn from the same nights as their training sets are optimistic. DeepStreaks itself found a gap between test-set performance and operation on millions of raw candidates.

Stale priors and astrometric weights. digest2’s population model ages as discoveries change the undiscovered population, and a model built on shallower surveys need not stay calibrated for Rubin. Underestimated astrometric errors create spurious curvature and overconfident impact predictions. Overestimated ones throw away information. YR4 showed that weighting choices change risk estimates materially even when the orbit itself hardly moves.

Follow-up capacity. A candidate can fade before confirmation, or its uncertainty can outgrow a follow-up telescope’s field. Discoveries are becoming fainter than most follow-up instruments can reach. YR4’s final answer needed JWST.

Selected samples. Telescopic impactors are selected by the surveys. Fireball-derived test populations are selected by sensor sensitivity and the availability of velocity vectors. Neither is a complete census of warning times.

Missing end-to-end accounting. The literature reports source-detector metrics, linker metrics and orbit outcomes on different samples. What is almost entirely missing is a record of the fate of every candidate, including why it was not followed up. With such a record, schedules could be replayed and one could tell whether the next improvement belongs in the pixels, the associations, the classifier, the orbits or the telescope allocation.

Where the room is

The NEO network is a good place to test the book’s central question because its costs are documented stage by stage. That documentation points away from the most obvious target.

Recover the trailing loss that is algorithmic. The figure of trailing penalties separates two curves. The lower one is physical: once photons from a moving source have mixed with sky along a trail, no software un-mixes them. The gap above it, about 0.7 mag for a trail six seeing-widths long, is lost only because point-source detectors are applied to trails. Finite-trail matched filters on calibrated difference images, with PSF, mask and variance maps, recover it, and the fast Radon transform of Chapter 39 makes the line sums cheap: $O(n^2\log n)$ instead of $O(n^3)$ for an $n\times n$ image (Nir et al. 2018). The right test injects trails over the full range of flux, length, angle, PSF, curvature and crowding, and compares recovery at a fixed nightly candidate burden. The transition from nearly point-like to short trails, where either branch of a split pipeline can reject a real object, deserves special attention.

Use trails to shrink linking. A trail constrains where the next detection can be: its displacement, orientation and speed, with a direction ambiguity. A pair of trails therefore defines a narrow tube of hypotheses instead of a broad gate. Chow et al.’s simulated one-night discoveries, eight of fourteen, are the strongest argument for building this. A vectorised or GPU join of trails over uncertainty tubes, followed by physical ranging, is a well-posed project. Its success metric should be time to a credible, followable candidate.

Do not accelerate what is already idle. ATLAS’s 2018 image path cost ten times its linker. ZTF hit database and file-system limits with CPU to spare. Meerkat answers in a minute and waits 20 hours a day. In each case a heroic kernel at the wrong stage would change nothing. Profile the deployed path first. An order-of-magnitude speed-up of one image kernel is plausible engineering. An order-of-magnitude gain in confirmed NEOs per unit total cost at equal sensitivity is a far stronger claim, and it requires measuring acquisition, transfer, processing, linking, vetting and confirmation together.

Share trajectory sums and move fewer bytes. For synthetic tracking, the 2024 V100 benchmark implies, at face value, $61\times10^{6}\times100\times10^{4}=6.1\times10^{13}$ pixel samples per search. At four bytes each that is about 244 TB of nominal traffic in 440 s, or 0.55 TB/s, before cache reuse. The workload is a bandwidth-bound gather. Tiling neighbouring velocities and image patches so that each frame region is loaded once, fusing interpolation, accumulation and peak finding, and sharing partial sums across velocities hierarchically as in Chapter 21 are the obvious moves. A factor of ten is a reasonable research target, measured against a tuned baseline on the same hardware with the same injected trajectories. A new GPU beating an old K20c is not evidence of an algorithmic gain (Chapter 40).

Keep low-significance evidence and query it along tracks. MOPS noted that dropping the threshold from five sigma to three increased detections about a thousandfold. Lowering every threshold is hopeless. Keeping low-threshold evidence in spatially indexed tiles, or as compact likelihood maps, and querying it only along tracks seeded by stronger detections, is not. Hierarchical searches need calibrated early thresholds, though. A faint body significant only in the full integration can fall below every partial threshold. Early cuts should come from the joint distribution of partial and full statistics (Chapter 38).

Batch the ranging grid, and keep Sentry-II as the baseline. Systematic ranging is many small fits sharing one set of observations and observer ephemerides, which suits GPU batching if unfinished fits are compacted and only posterior-relevant cells are refined. Ensemble orbit propagation is harder: close encounters force adaptive steps, and a common fixed step can miss the encounter geometry. Sentry-II already beat brute force by a factor of 500 through sampling. Any accelerated method must be compared with it.

Schedule for information. Follow-up is a scheduling problem coupled to all of the above. A useful objective ranks a candidate observation $a$ by

where “useful” must be defined by policy: confirming before loss, killing an impact solution, or localising an imminent impact. It should account for the chance that another survey recovers the object anyway, as Wagg et al.’s self-recovery predictor does. Optimising pure posterior entropy can spend telescope time separating harmless orbit modes while a decisive impact branch remains open. YR4 showed the extreme case, in which one well-placed observation eight months later was worth more than many precise ones near discovery. The experiment that would settle these questions is a replay of real nights, with the real candidate stream, weather and telescopes, scored by confirmed objects and the distribution of warning times. The physical limits here are photons, sky access and parallax baselines. Nearly everything else is engineering, and Chapter 42 collects the cases across the book where that distinction is sharpest.

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