Planet X and Pluto: blink comparators, Schmidt plates and the first CCDs

On the afternoon of 18 February 1930, Clyde Tombaugh was about a quarter of the way through a pair of photographic plates of the region around Delta Geminorum, taken on 23 and 29 January. He had been at Lowell Observatory just over a year. The plates went into a blink comparator, an instrument that shows the observer first one plate and then the other through the same eyepiece, switching back and forth so that anything that changed between the two exposures appears to jump. In that instrument he had so far examined about two million star images. Now a faint point jumped back and forth by about the amount expected of a body far beyond Neptune. “The experience was an intense thrill,” he wrote, “because the nature of the object was apparent at first sight” (Tombaugh 1946).

The object was Pluto, and its discovery is usually told as the fulfilment of Percival Lowell’s prediction of a ninth planet. That account is mostly wrong. Lowell’s mathematics did not weigh Pluto, and the residuals he fitted turned out, decades later, not to require any planet at all. What Lowell’s hypothesis did was fund a search. The search found Pluto because it was well designed: a wide-field camera built for the purpose, plates matched with great care, a rule about where in the sky to photograph, and a third plate to kill false alarms. Those are detection methods, and they are the subject of this chapter.

The chapter covers the period from Lowell’s first searches in 1906 to Spacewatch’s automated CCD searches in 1990. In those 85 years, finding a faint Solar System body became a repeatable information-processing task: cover the sky, repeat the observation, suppress what does not move, recognise consistent motion, measure positions, determine an orbit, recover the object. Photography separated observation from recognition. The blink comparator sped up recognition. Schmidt telescopes recorded far more sky deeply. Measuring machines and computers sped up astrometry and orbits. CCDs finally allowed detection while the observations were still coming in.

Lowell’s Planet X

Percival Lowell began a photographic search at Flagstaff in 1906. Tombaugh’s first-person account, written in 1946, gives the details. E. C. Slipher took about 200 plates and K. P. Williams about 50 with a five-inch camera, in three-hour exposures centred on the invariable plane of the Solar System at every five degrees of longitude. Lowell compared plates by laying one on top of another and looking with a hand magnifier. As is now known, Pluto’s inclined orbit put its images just off the southern edges of those plates (Tombaugh 1946).

A series with the Lowell 42-inch reflector followed. Its field was too small for searching, although a Zeiss blink comparator made comparison much easier. In 1914 the Sproul Observatory lent a nine-inch telescope, and from 1914 to 1916 many plates were taken and examined by Lowell and C. O. Lampland. Nothing was found. Tombaugh notes that Pluto was then on a more distant part of its orbit and about half a magnitude fainter than at its discovery.

In 1915 Lowell published his Memoir on a Trans-Neptunian Planet. As Tombaugh summarises it, the solution gave Planet X a mass of 1/50,000 of the Sun, about seven Earth masses, and a mean distance of 43 au. Lowell assumed the planet had low density and high albedo like the giant planets, which gave a disk of about one arcsecond and a magnitude between 12 and 13 (Tombaugh 1946). The brightness prediction came from that assumption about the planet’s nature, not from the perturbations. (These values are taken from Tombaugh’s account. Lowell’s memoir itself was not opened for this chapter.) Lowell died on 16 November 1916, and the search stopped for 13 years.

In 1919 William H. Pickering, using discrepancies in Neptune’s motion, predicted a planet in the same region, of the fifteenth magnitude. Four plates were taken with a 10-inch telescope on Mount Wilson in December 1919. Portions were examined carefully and nothing was found. Pluto’s images were outside the area that was closely examined, and some were nearly obliterated by accidental defects in the emulsion (Tombaugh 1946). These are failures of footprint, inspection and plate quality. The photons were recorded twice, in 1919 and, almost, in 1906–1916. What failed was coverage and recognition, exactly the links in the chain that Chapter 3 found broken at Cambridge in 1846.

An instrument built for searching

In 1925 Lowell Observatory obtained glass for a 13-inch photographic telescope with a wide field. Lowell’s brother, A. Lawrence Lowell, paid to complete it, and the optician C. A. R. Lundin made the objective. In January 1929 the director, V. M. Slipher, invited Clyde Tombaugh to join the staff (Tombaugh 1946).

The 13-inch Lawrence Lowell telescope had a focal length of 66 inches and a plate scale of 30 millimetres per degree. Its plates measured 14 by 17 inches and covered nearly 12 by 14 degrees of sky. To keep the images sharp across so large a plate, special holders bent each plate into a slightly concave shape matched to the focal surface, and every plate was tested to a standard curvature. The faintest star images were consistently smaller than 1/30 of a millimetre, which at this scale is about four arcseconds. The standard exposure was one hour, recording stars to about photographic magnitude 17 except at the extreme ends and corners. A 7-inch refractor served as the guide telescope, and a 5-inch camera on the same mount took simultaneous plates for checking bright suspects (Tombaugh 1946).

The romantic image of the blink search is of a patient observer staring at stars. The reality was a calibration programme. Tombaugh matched each pair of plates in age and sensitivity of the emulsion, exposure time, sky transparency and sky brightness, guide star, steadiness of seeing, hour angle and guiding, avoided moonlight, and developed the plates uniformly. Every one of those choices reduces a nuisance difference between epochs. In modern terms, he was making the two images as close as possible to identical apart from the moving object, so that the difference image, which is what the blink comparator presents to the eye, contains only the signal. Chapter 10 describes how difference imaging does the same thing in software, by fitting a convolution kernel that matches one image’s blur to the other’s.

Physics: why Tombaugh photographed at opposition

Tombaugh started in earnest at the end of March 1929, beginning with Gemini, which was sinking into the evening twilight, and working east along the ecliptic. Two improvements in technique soon followed. The first concerned where and when to photograph.

At opposition, the point in the sky opposite the Sun, an outer body appears to move backwards (westward) against the stars, because Earth is overtaking it on the inside track. For a body on a circular orbit in the ecliptic, the rate is easy to derive. Let distances be in astronomical units and let $n_\oplus$ be Earth’s mean motion. Earth’s orbital speed is $n_\oplus$ au per unit time. A body at heliocentric distance $r$ on a circular orbit moves at $n_\oplus r^{-1/2}$ (from Kepler’s third law). At opposition the two velocities are parallel, so the relative transverse speed is $n_\oplus(1 - r^{-1/2})$, and the body is $r - 1$ au from Earth. The apparent angular rate is

Earth moves 360 degrees in 365.25 days, so $n_\oplus \approx 0.986$ degrees per day, or about 148 arcseconds per hour. At large $r$ the body’s own motion is negligible and $\mu \approx n_\oplus/r$: the apparent motion is a reflection of Earth’s orbit, scaled by the inverse distance. This is the relation that Jewitt and Luu, and every Kuiper-belt survey since, used to turn a rate into a distance (Trujillo et al. 2001).

A worked example connects it to Tombaugh’s plates. For a main-belt asteroid at $r = 2.5$ au, $\mu = 148 \times (1 - 0.632)/1.5 \approx 36$ arcseconds per hour, or about 14.5 arcminutes per day. On a plate at 30 mm per degree that is about 7.3 mm per day. For a body at 40 au, $\mu \approx 3.2$ arcseconds per hour, or about 0.64 mm per day. Tombaugh reported that at opposition the asteroids “moved about 7 millimeters per day on the plates, and exhibited short trails during the hour’s time of exposure, whereas Pluto moved only ½ millimeter per day” (Tombaugh 1946). The simple formula reproduces both numbers well. (Pluto was not exactly at opposition, and its orbit is eccentric and inclined.)

Away from opposition the picture changes. The apparent motion of any outer body slows, stops at a stationary point, and reverses, as the direction of Earth’s velocity swings relative to the line of sight. Near its stationary point an ordinary asteroid moves as slowly as a distant planet. Tombaugh found that he lost “much time, effort and expense” running down suspects that turned out to be asteroids near their stationary points. He gave the angular distances of the stationary points from opposition for bodies at the distances of Mars and Jupiter as 36 and 64 degrees, and he “scrupulously avoided” the sky between those limits. From September 1929 he photographed every region at its opposition point, which moves east through the zodiac at 30 degrees per month (Tombaugh 1946).

Opposition had other advantages. The field was on the meridian at midnight, giving the most observing hours at good altitude, and the target was closest to Earth. For a body as distant as Pluto, Tombaugh noted, the brightness gain at opposition over conjunction is only 0.1 magnitude. The real reason was kinematic. At opposition, rate is close to a monotonic function of distance, so speed alone separates the asteroids from anything distant. A slow rate elsewhere in the sky proves nothing.

The blink comparator and the third plate

The second improvement concerned false alarms. Almost every pair of plates contained a few faint “planet suspects” that were only plate defects, and some pairs had more than a hundred. Most were too faint to check on the 5-inch camera plates. Tombaugh’s solution was to take three plates of each region within one week. He marked suspects while blinking, and at the end of each panel removed the unmarked plate and put the third plate in its place. “Only a few out of several thousand suspects survived the crucial test of the third plate” (Tombaugh 1946). The extra plate increased the photographic work by 50 percent, and it also let him choose the best-matched two of three plates for blinking.

The value of the third epoch is easy to state. Two positions always define a straight line, so a pair of detections, one per plate, can always be read as a mover. A third epoch makes a prediction. If unrelated false detections (defects, noise peaks) have surface density $\rho$ on the plate, and the third-epoch prediction defines a search gate of area $A_g$, the expected number of chance confirmations is about

The gate must allow for measurement error and for uncertainty in the motion. For a slow mover over a week, $A_g$ is a tiny fraction of the plate, so a few thousand pair suspects become a handful of triples. This reconstruction assumes contaminants are independent and roughly uniform. Repeated scratches, diffraction spikes and blends violate that, and Tombaugh’s “several thousand” is a workload observation, not a calibrated false-alarm rate. The same three-epoch logic, with an index in place of a human eye, is the basis of tracklet linking in Chapter 12.

The cost of the method was set by the stars. Plates in Aquarius, Pisces and Aries had about 50,000 star images each, and a pair took about three days to examine thoroughly. Towards the Milky Way in Taurus the work grew. Plates in western Gemini held more than 300,000 star images each. “Since the time spent in the blink examination of plates is proportional to the number of star images,” Tombaugh wrote, “this work fell behind that of taking the plates.” Comparison, not acquisition, was the bottleneck. With $N_f$ fields and $N_*$ star images per field, the human workload scaled as $N_f N_*$, plus the cost of following up survivors. A defect that survived the pair test could cost a night of telescope time, so reducing false suspects improved the whole search, not just the blinking.

18 February 1930

Three plates of the Delta Geminorum field were taken on 21, 23 and 29 January 1930. Having finished the easternmost pair in Taurus, Tombaugh decided to postpone the two very rich Gemini regions and started on the Delta Geminorum pair. On 18 February, a quarter of the way through, he found the images. The shift between 23 and 29 January was about right for a body a billion miles beyond Neptune. Because the plates were taken at opposition he was confident it was not an asteroid. The images were sharp, not diffuse, so it was not a comet. It was about two magnitudes brighter than the faintest stars on the plates. He checked the 5-inch camera plates exposed at the same times, and the object was there in the same positions. He then found it on the 21 January plate, where its position agreed with the motion (Tombaugh 1946).

Tombaugh noted that Pluto was found within six degrees of Lowell’s predicted place. He also noted a selection effect. Pluto was crossing the ecliptic. Had it been far from its node, it would have been outside the first photographic belt and might not have been found until 1932, when two more belts on either side were complete (Tombaugh 1946). Being near a predicted direction does not show that the body found has the predicted mass. A visual magnitude of 15, against Lowell’s 12–13, already said that it was either much smaller or much darker than his giant planet. The question of its mass had to wait for a moon.

After Pluto: what a negative search means

Tombaugh was urged to continue, and he did. By his 1946 account the search went on “until three-fourths of the entire heavens had been explored, and 90 million star images had passed in review in the eyepiece of the blink comparator” (Tombaugh 1946). Robert Harrington’s 1988 summary describes Tombaugh continuing for another 13 years after the discovery, covering much of the northern sky to about magnitude 16 (Harrington 1988).

A rough check shows the scale of the work. At 50,000 stars per pair in about three days, Tombaugh’s sparse-field rate was roughly 17,000 star images per day of blinking (a derived estimate). Ninety million images at that rate is about 5,400 days, more than the calendar days in 13 years, even before crowded fields slowed the work. The totals should therefore be treated as approximate, but the order of magnitude of the human cost is clear.

The depth numbers need care. Magnitude 17 is the nominal reach of a standard plate away from its edges. Magnitude 16 is Harrington’s conservative description of the survey. Ninety million is total visual work. None of these is a uniform completeness curve, and several often-repeated secondary totals for numbers of plates, exact areas or deeper limits are not adopted here, because the original ledgers were not checked. There is also independent evidence that the search was not complete: the Chiron discovery paper notes that the Lowell survey was not deep enough at Chiron’s position in the 1930s and did not cover that region in the 1940s (Kowal et al. 1979).

“No further planet found” therefore means no qualifying detection under the actual brightness limit, footprint, motion, crowding and follow-up. It is not an all-sky exclusion. Turning a null search into a limit on a population requires a recovery model over sky position, magnitude, rate and date, the subject of Chapter 16. Tombaugh’s search predates that kind of accounting.

Palomar–Leiden: a survey becomes statistics

Tombaugh searched broadly for one exceptional slow mover. The Palomar–Leiden Survey, three decades later, set out to obtain a dense, statistically useful sample of faint asteroids with usable orbits. It was initiated by Gerard Kuiper. The work divided across three continents: Tom Gehrels took the plates at Palomar, Cornelis Johannes van Houten and Ingrid van Houten-Groeneveld searched and measured them in Leiden, and Paul Herget computed reductions and orbits in Cincinnati (van Houten et al. 1970).

Gehrels took 130 plates in 1960 with the Palomar 48-inch Schmidt telescope, a wide-field design whose corrector plate gives sharp images over several degrees. The plates were 35.6 cm square and reached about magnitude 20.5, three and a half magnitudes deeper than Tombaugh’s standard plates. The survey covered roughly 18 by 12 degrees near the vernal equinox, chosen to reduce the number of background stars. The original plan was twice as wide in longitude, but telescope time forced a cut. Plates were taken on 23–28 September and on 16, 21 and 23–25 October. Blue-sensitive exposures were generally 10 minutes in September and 12 in October, taken in pairs about 30 minutes apart. The telescope tracked at the mean asteroid motion rather than at the sidereal rate, so asteroids stayed nearly point-like and stars trailed slightly.

The van Houtens blinked the plates with a Zeiss comparator borrowed from Heidelberg and adapted to cover 97% of the plate. Each plate showed 200–400 asteroids. They estimated each one’s brightness and displacement vector, linked observations within a month, and tried to join September and October arcs. Short first-month arcs made some extrapolations unreliable. Herget’s orbit solutions and search ephemerides caught mistaken associations, and re-examination of seven plate pairs found 62 more images (van Houten et al. 1970).

The measuring and computing were industrial. About 14,000 asteroid positions and 7,500 reference-star positions were measured, read in units of 0.01 mm, and sent to Cincinnati on punched cards. Plate reductions ran on an IBM 1620. Orbits were computed on the Naval Ordnance Research Calculator (NORC), averaging about 900 orbits per hour including residuals, or about four seconds per orbit (derived). The final statistical sample contained 1,800 orbits. The paper’s abstract reports more than 2,000 asteroid discoveries. These two counts measure different things, and neither should be confused with later numbered-object credit totals.

Measuring completeness from the data

The survey’s most important innovation was to estimate its own completeness from the repeat observations. Suppose each asteroid has probability $k$ of being found in any one plate pair, independently, and there were three comparable pairs. Of $N$ asteroids, the expected numbers found in all three, exactly two, exactly one and none of the pairs are

The ratios $N_2/N_3 = 3(1-k)/k$ and $N_1/N_2 = (1-k)/k$ give $k$ from observed quantities alone. For example, the first gives $k = 3N_3/(N_2 + 3N_3)$. With $k$ in hand, $N_0$, the number never seen, follows. In the faintest adopted interval, magnitude 19.5–20.0, the average was $k = 0.70$, after excluding one field searched inefficiently. Under the model, the chance of missing an asteroid in all three pairs is $0.30^3 \approx 0.027$ (derived). Missing 30% in one pair does not mean missing 30% in the survey (van Houten et al. 1970).

The model assumes independent, equal chances in each pair. A crowded field, a persistent defect or an intrinsically hard-to-see object correlates the misses, and an object found again with the help of a predicted orbit is not an independent blind detection. The authors were careful about the second point. The method is the ancestor of the injection-recovery and capture–recapture estimates of modern surveys.

The corrected counts rise steeply toward faint magnitudes, roughly a factor of ten every two magnitudes. That steepness is why depth paid off so handsomely, and it is a direct measurement of the asteroid size distribution once the brightness model is applied. For an unresolved body seen in reflected light,

where $H$ is the absolute magnitude (a proxy for size times albedo), $r$ and $\Delta$ are the distances from the Sun and Earth in au, and $\Phi$ is a phase correction. The paper derives absolute magnitudes with this structure (van Houten et al. 1970). Near opposition for a distant body $\Delta \approx r$, so reflected flux falls as $r^{-4}$ (Chapter 2). A non-detection therefore limits a combination of size, albedo, distance and phase, never mass directly.

The orbit quality distribution is unusually informative: 981 first-class, 141 second-class, 144 third-class and 534 fourth-class orbits. The first two classes include observations from both months. The lower classes rest on shorter arcs. A discovery count without that distinction overstates how much secure population information exists.

Chiron: a slow mover and the archive

On 1 November 1977 Charles Kowal at Palomar recognised what he called “Slow-moving Object Kowal” on plates exposed with the 122-cm (48-inch) Schmidt on 18 and 19 October. The discovery report by Kowal, William Liller and Brian Marsden describes asteroid-like images of about magnitude 18 in 75-minute exposures. The object moved less than three arcminutes between the plates, although it was only eight degrees from opposition, where ordinary minor planets typically moved eight to fifteen arcminutes per day. The trails on the two plates matched in length to about six percent, which argued against an unusual nearby trajectory. Gehrels then found the object on an 11 October exposure near the extrapolated position (Kowal et al. 1979).

On the circular opposition formula above, a body moving less than three arcminutes per day lies beyond about 16 au (a derived estimate that ignores the real orbit’s eccentricity and the eight-degree offset from opposition). Early follow-up gave a geocentric distance of 14 to 17 au, but the orbit was poorly constrained. Fifteen observations gave an eccentricity of about 0.35 and a perihelion of about 9.9 au, both uncertain. This is the general rule for distant short arcs: they constrain position and angular velocity well, and distance and radial velocity poorly.

Then the archive took over. A precovery on a 1969 plate changed the leverage dramatically. The orbit became $a = 13.7$ au, $e = 0.38$, perihelion $q = 8.5$ au and period 50.7 years. The 1969 image was not exactly at the first prediction: it lay about 55 arcminutes east and 41 arcminutes north. The report documents further recoveries on 1952 Palomar Sky Survey photographs, on Boyden plates from the 1940s and, finally, on an 1895 exposure with the Bruce astrograph. A trail on a 1941 plate had actually been marked during a 1951 search for galaxies, and never followed up (Kowal et al. 1979).

The procedure was iterative: fit a family of orbits, propagate it to an archival epoch, find plates whose footprints overlap the uncertainty region, search them, add any credible detection, refit, and use the longer arc to shrink the next search. The 55-arcminute offset of the 1969 image shows why a modern precovery search should propagate a whole posterior or admissible family of orbits, not a single nominal position. A precovery is credible when it improves a single coherent orbit and is supported by the image, not merely because a faint feature lies somewhere in a large predicted region. Chapter 13 describes the modern machinery.

Chiron became the prototype of the Centaurs, bodies on unstable orbits among the giant planets. Its discoverers debated whether it was cometary and proposed reserving Centaur names for similar objects. Their suggested resonances and ancient close encounters should be read as contemporary interpretations. The durable result is methodological: an apparently near-circular short arc became a well-constrained eccentric orbit through archival attribution.

Charon: a bump on a planet

On 22 June 1978, James Christy of the US Naval Observatory was measuring plates of Pluto on the STARSCAN automatic plate-measuring machine. The plates had been taken in April and May with the Flagstaff 1.55-m astrometric reflector, three exposures per plate. Pluto’s image was elongated: to the south on 13 and 20 April, to the north on 12 May. The other stars on the plates were round, which excluded a guiding error, and Palomar Sky Survey prints helped exclude a background star (Christy & Harrington 1978).

Christy and Robert Harrington looked at older plates and found supporting elongations from 1965 and 1970. A particularly useful exposure on 2 July and a 6 July observation by J. A. Graham with the Cerro Tololo 4-m followed, and the announcement came on 6 July. The detection here was not motion. It was a change in image shape whose orientation rotated with time.

A partially blended pair has image $I = F_1P(\mathbf x - \mathbf x_1) + F_2P(\mathbf x - \mathbf x_2) + B$, with $P$ the point-spread function and $B$ the background. Its centroid follows the flux-weighted position, and its elongation follows the projected separation. The modern test fits a local PSF from the neighbouring stars and compares single- and double-source models at Pluto’s position, epoch by epoch. Christy’s comparison with the round stars on the same plate was the historical counterpart of that local control.

The mass came from fitting repeated orbital geometry, not from a single night on which Pluto looked lumpy. These were preliminary values that depended on early geometry. But they settled the Planet X question in one direction. If there was a perturbing planet in the Uranus residuals, Pluto was not it.

IRAS: unidentified is not planetary

The Infrared Astronomical Satellite (IRAS) operated from January to November 1983 and surveyed more than 96% of the sky in bands centred at 12, 25, 60 and 100 micrometres. Away from confused regions its point-source catalogue reached about 0.5 jansky in the first three bands and 1.5 Jy at 100 micrometres. The explanatory supplement warned that “infrared cirrus,” wispy interstellar dust emission, could produce well-confirmed apparent point sources that were pieces of much larger structures (IRAS Explanatory Supplement 1988).

A cold planet would emit most of its energy in the far infrared, so IRAS could in principle find what optical surveys missed. The paper behind the famous 1983 “mystery source” stories was James Houck and colleagues’ Unidentified Point Sources in the IRAS Minisurvey. From 8,709 well-confirmed minisurvey sources they selected 133 bright, cool candidates, then removed those with catalogued counterparts, confused emission, and a group associated with a cloud. Nine remained. The paper considered galaxies, Galactic objects and a nearby cold body. Its illustrative thermal calculation was that a 40 K body the diameter of Jupiter would produce about 1 Jy at 60 micrometres at roughly 570 au (Houck et al. 1984).

That was a degeneracy, not a distance. For a body of radius $R_p$ at temperature $T$ and distance $\Delta$, the thermal flux is approximately

where $B_\nu$ is the Planck function and $\epsilon_\nu$ the emissivity. A single flux at a single wavelength fixes only the combination of temperature and $R_p/\Delta$. A small, close, cold body and a large, distant, cold body give the same number. A distant galaxy with a cold dust spectrum can also imitate it. The source catalogue’s reliability requirement, detection in at least two independent scan pairs, gave better than 99.8% confidence that a source was real. It said nothing about whether the source was a planet.

A real distant-mover search in survey data must keep scan times, detector response and observer position. A catalogue built by requiring sources to be stationary over hours to months can suppress exactly the signal sought. The thermal search for planets is the subject of Chapter 24.

Harrington’s search and Standish’s verdict

By the 1980s Planet X had become the hypothesis of a planet whose pull would explain the residual misfits of Uranus and Neptune. Robert Harrington’s 1988 paper The Location of Planet X used Uranus and Neptune observations through 1982, referred to the JPL ephemeris DE200. He averaged the residuals into seasonal normal points and compared them with the perturbations produced by trial planets (Harrington 1988).

The search grid had 172,368 trial cases for each observed planet. Masses ran from three to five Earth masses in unit steps, distances from 30 to 80 au in 10-au steps, longitudes in one-hour steps, latitudes in 15-degree steps, and velocities around the circular value in four energy steps of 10% of the circular energy. For each trial he integrated the perturbation equations (rather than the whole planetary system), projected the perturbations into angles, removed constant and secular terms, and compared the RMS residual. A trial was retained if it improved the RMS by at least 10%. No trial met that criterion for post-discovery Neptune observations. Uranus gave two broad regions of sky. A representative southern solution had $a = 101.2$ au, $e = 0.411$, inclination $32.4^\circ$, period 1,019 years and four Earth masses. Harrington preferred the southern region partly because Tombaugh’s northern search should have found a planet in the north. The often-quoted odds, 153 southern against 30 northern retained trials, are grid counts, not a calibrated probability (Harrington 1988).

The physics of what such a search can detect is the tidal degeneracy already met in Chapter 3. For a perturber of mass $M_X$ at heliocentric position $\mathbf R_X$, the extra heliocentric acceleration at position $\mathbf r$ is

and for $R_X \gg r$ the leading term is

A distant planet appears through the combination $M_X/R_X^3$ and a direction. A short stretch of residuals cannot separately identify mass and orbit.

E. Myles Standish’s 1993 analysis removed the signal. He refitted Uranus’s orbit and substituted the planetary masses measured by the Voyager flybys. The old adopted reciprocal mass of Neptune (solar mass divided by Neptune’s mass) was 19,314. Voyager 2 measured 19,412.240 ± 0.057, so Neptune was about half a percent less massive than had been assumed. Updating the masses and refitting largely removed the supposed signature, and the RMS of the opposition normal points fell by nearly 20% without any Planet X. Standish verified the adjusted solution by integrating a self-consistent experimental ephemeris, DE298 (Standish 1993).

What was left could be traced to the observations. One revealing interval was 1895–1905. The mean right-ascension residuals of three instruments disagreed with each other far beyond their errors.

The USNO nine-inch transit circle gave $+0.90 \pm 0.08$ arcseconds over 165 observations, Besançon gave $-0.39 \pm 0.19$ over 15, and the USNO six-inch transit circle gave $-0.04 \pm 0.10$ over 44 (Standish 1993). A planet does not choose which telescope’s catalogue to perturb.

The general lesson can be written in the same form as the Neptune analysis in Chapter 3. In a linearised weighted fit with weight matrix $W$, let the columns of $A$ be the derivatives of the predictions with respect to every nuisance parameter: the known planets’ states and masses, catalogue corrections, instrument offsets. A candidate perturbation signature $s$ is only evidence for a new planet in the part orthogonal to that subspace:

A residual that can be absorbed by correcting Neptune’s mass or Uranus’s state, or by an offset for one instrument, is not unique evidence for another planet. Harrington’s grid compared trial perturbers against residuals from a fixed reference ephemeris. Standish refitted the reference. More trials, run faster, would not have fixed the problem. The null model was wrong. Standish’s conclusion removed the historical residual argument for Planet X. It did not show that no distant planet exists, a question that Chapter 8 takes up on quite different evidence.

Spacewatch: the detector goes electronic

While Harrington fitted residuals, the detection hardware was changing underneath the field. Tom Gehrels and Robert McMillan founded Spacewatch at the University of Arizona in 1980. Its history distinguishes several milestones: an RCA CCD of 320 by 512 pixels operating in 1983, production drift scanning in 1984, a first version of automatic asteroid-detection software in 1985, and a 2,048 by 2,048 CCD in 1989. It dates the first detection of an asteroid’s motion with a CCD, by image subtraction, to the observation of the known asteroid (110) Lydia on 6 May 1983 (Spacewatch history).

Drift scanning, also called time-delay integration, leaves the telescope fixed and lets the sky drift across the CCD while the charge is clocked along the columns at the same rate. Each star is integrated as it crosses the chip, and the output is a continuous strip of sky read out line by line. There is no readout dead time between exposures, and the data arrive as a stream.

David Rabinowitz’s methods paper, published in 1991 and describing trials in 1990, makes the transition quantitative (Rabinowitz 1991). The Moving Object Detection Program (MODP) searched data from the 0.91-m Spacewatch telescope’s Tektronix TK2048 CCD while it was being acquired. A microcomputer with an Intel 80386 controlled the readout. A Solbourne 5/600 workstation with three SPARC processors and 32 MB of RAM did the analysis and display. In 19 nights in May and June 1990 the trials covered 150 square degrees and detected 304 asteroids, reaching about $V = 20.5$ for untrailed objects.

MODP had two branches. For fast objects, which trail during a scan, a streak classifier used image size, aspect ratio, uniformity along the trail, asymmetry and goodness of fit to a trail template. A streak had to have an aspect ratio greater than two and a minor axis comparable to a faint star. The thresholds were tuned on recorded scans and artificial trails, and candidates were shown to the observer (Chapter 11 develops streak detection).

For slower objects, three scans of the same strip gave a constant-angular-velocity test, the electronic version of Tombaugh’s three plates:

while receiving CCD rows:
    estimate local background and noise
    find sources; append to this scan's source list
    classify elongated sources; display streak candidates
register scan lists using stationary-source cross-correlation
once three scans of a strip exist:
    remove sources that match in position (stationary)
    form physically allowed pairs
    predict the third-scan position
    require a linear track to about 1 pixel and brightness within 50%
    show candidate cutouts to the observer

Stationary objects were removed by matching positions. Binary occupancy images were cross-correlated to find the offset between scans. Surviving detections were joined if they lay on a straight line to about one pixel and changed brightness by no more than 50%. Local maxima only one pixel wide were rejected. More elaborate classification was deliberately avoided, because it could reject real sources and consumed too much computing (Rabinowitz 1991).

Rabinowitz gave an explicit noise model. For a source measured against an equal-length comparison exposure, neglecting dark current and flat-field error,

with $R_*$ the source count rate, $R_s$ the sky rate per pixel, $p$ the number of pixels summed, $t$ the exposure time and $N_r$ the read noise. The factor of two comes from the comparison image, whose noise adds to the science image’s. His calibration used $t = 165$ s (the time a star takes to drift across the chip), $N_r = 15$ electrons and $p = 9$. With those values the read-noise term alone contributes $2\times9\times15^2 = 4{,}050$ electrons squared of variance, a floor of about 64 electrons. The detection threshold was a peak four times the background noise, which corresponded empirically to about six sigma in integrated intensity for untrailed sources. Those are different definitions, and neither is the pipeline’s false-positive rate, which also depends on blends, artefacts, the streak classifier, matching gates and the human reviewer. The paper notes more false candidates near the Galactic plane and in poor seeing.

The data volumes explain the streaming design. A typical scan lasted 30 minutes and produced about 22,000 CCD lines at zero declination. At 2,048 samples per row and two bytes per sample, one scan is about 90 MB and three scans about 270 MB (estimates from the published geometry). The workstation had 32 MB of memory. It could not hold even one scan, so detection had to happen as the rows arrived (Rabinowitz 1991).

On 27 October 1989 Spacewatch discovered the near-Earth asteroid 1989 UP, its first NEO found with a CCD. The trail was recognised on the live display, reported electronically, and followed up from Australia four hours later. The first NEO found automatically, 1990 SS, came on 5 September 1990 (Spacewatch history). These are separate firsts. The 304 detections of the 1990 trials were mostly main-belt asteroids, and included the known Earth-approachers 1990 HA and 1990 MF. They were not 304 new NEOs. The machine had become a streaming detector, but the observer still rejected candidates and arranged the follow-up that turned an electronic event into an orbit. Chapter 14 continues the NEO story.

Landmarks

What these searches could not tell us

Footprint, depth and effort are not a selection function. A standard limiting magnitude does not encode plate age, weather, off-axis image quality, Galactic latitude, trailing or human attention. Tombaugh’s plate edges were shallower, his crowded fields were examined more slowly, and defects generated suspects. A null result needs a recovery model over position, magnitude, rate and date, which none of these surveys had except, in part, Palomar–Leiden.

Completeness estimates rest on assumptions. Palomar–Leiden’s binomial method assumes comparable, independent chances in each pair. Crowded fields, persistent defects and intrinsically variable objects correlate the misses. Agreement between the two ratio estimators is a useful check, not a proof.

A good orbit is not a good image, and vice versa. A convincing moving dot can have a poorly constrained orbit, and a good-looking numerical orbit can rest on a wrong association. Chiron shows why the two tests must support each other, and how much suggested resonances can change as an arc grows.

Infrared candidates remain degenerate. The 2025 IRAS and AKARI papers explicitly need further observations to establish planetary orbits for their candidates. Their fluxes alone leave size, temperature and distance degenerate, and their catalogue cuts differ.

Systematics set the limit for perturbation searches. Standish’s example is not simply that one mass was wrong. The candidate signal lived in the same directions of model space as known-planet masses, orbital states, catalogue corrections and instrument offsets. More trials made the ambiguity look more convincing, not less. The same lesson appears again in radial-velocity activity (Chapter 29) and in astrometric calibration.

Historical completeness can be recovered only in part. Re-scanning the plates could measure today’s detection efficiency on the digitised material. It cannot recover what a particular observer would have noticed in a particular comparator on a particular afternoon.

Where the room is

The historical order-of-magnitude gain was removing serial human work. Tombaugh’s comparison time scaled with the number of star images, and fell behind acquisition. Spacewatch searched while the data arrived. That changed throughput, latency and the chance of successful follow-up. It was not a uniform gain in limiting magnitude due to faster arithmetic: detector efficiency, field size, exposure strategy and the motion limits changed at the same time. Any modern claim of a large speedup should be just as explicit about what else changed.

Plate archives are a data set waiting for a pipeline. The best opportunity in historical material is a digitised-plate pipeline with calibrated geometric and photometric response, local PSF models and joint motion tests. Background estimation, resampling, filtering and likelihood evaluation tile naturally on a GPU (Chapter 40). The expensive searches should run only on plate regions crossed by admissible trajectories, and orbit-assisted precovery should come before blind enumeration when an orbit exists. A credible tenfold efficiency target (an assessment, not a measured result) would compare against a defined baseline on the same plates, injected sources, rate coverage, masks and false-positive rate, and would count total runtime including scan ingestion, calibration, candidate generation, orbit fitting and human review. A faster kernel that produces many more candidates can increase the total work.

Cheap rejection first, exact fitting last. Tombaugh ordered his tests by cost: opposition scheduling to remove asteroids by speed, the pair comparison, the third plate, then telescope follow-up. Modern hierarchical searches use the same ordering: reject stationary and obviously fast sources cheaply, apply a permissive multi-epoch consistency check, then fit pixels and orbits exactly for survivors. For sources too faint to detect in one image, the decision must be deferred until exposures are combined along trial motions (Chapter 17, Chapter 38).

For perturbation searches, the gain is in the null model. Harrington’s trials are trivially parallel, and many nearby trajectories could share ephemeris evaluations or linearised response bases. At his trial-bank size, though, the decisive improvement was covariance-aware joint fitting of the known system and the calibration of the null, not throughput. The ratio of retained trials between two sky regions also depends on how the grid samples parameter space, and should not be advertised as a posterior probability.

Keep the time domain in infrared catalogues. IRAS shows a smaller opportunity: evaluate complete trajectory models on scan-level measurements instead of relying on catalogues that require stationarity, and fit galaxies, cirrus, detector response and a moving source jointly. The gain must be measured with injected moving thermal sources passed through every rejection stage.

The hard limits. Missing photons, finite resolution, unrecorded wavelengths, sky never covered and baselines too short to constrain distance are physical. No GPU recovers a plate that was never exposed or information that saturation destroyed. Grain, blending and cirrus impose effective information ceilings. Slow scanning, repeated data movement, poorly indexed footprints, redundant orbit propagation and serial candidate review are engineering limits, and those are the ones open to new methods. Chapter 42 collects them.

References

1. Chen, A. Y.-A. et al. (2025). A Far-Infrared Search for Planet Nine Using AKARI All-Sky Survey. Publications of the Astronomical Society of Australia. arXiv:2506.12854
2. Christy, J. W., Harrington, R. S. (1978). The Satellite of Pluto. Astronomical Journal 83, 1005–1008. ADS scan
3. Harrington, R. S. (1988). The Location of Planet X. Astronomical Journal 96, 1476–1478. ADS scan
4. Houck, J. R. et al. (1984). Unidentified Point Sources in the IRAS Minisurvey. Astrophysical Journal Letters 278, L63–L66. ADS scan
5. Houck, J. R., Schneider, D. P., Danielson, G. E. et al. (1985). Unidentified IRAS Sources: Ultrahigh-Luminosity Galaxies. Astrophysical Journal Letters 290, L5–L8. ADS scan
6. IRAS team; Beichman, C. A., Neugebauer, G., Habing, H. J. et al., eds. (1988). IRAS Catalogs and Atlases: Explanatory Supplement, §I.A. NASA RP-1190. irsa.ipac.caltech.edu
7. Kowal, C. T., Liller, W., Marsden, B. G. (1979). The Discovery and Orbit of (2060) Chiron. IAU Symposium 81, 245–250. ADS scan
8. Phan, T. L. et al. (2025). A Search for Planet Nine with IRAS and AKARI Data. Publications of the Astronomical Society of Australia 42, e064. arXiv:2504.17288
9. Rabinowitz, D. L. (1991). Detection of Earth-Approaching Asteroids in Near Real Time. Astronomical Journal 101, 1518–1529. ADS scan
10. Rowan-Robinson, M. (2021). A Search for Planet 9 in the IRAS Data. Monthly Notices of the Royal Astronomical Society 510, 3716–3726. arXiv:2111.03831
11. Spacewatch project (accessed 2026). News and History. University of Arizona. spacewatch.lpl.arizona.edu
12. Standish, E. M., Jr. (1993). Planet X: No Dynamical Evidence in the Optical Observations. Astronomical Journal 105, 2000–2006. ADS scan
13. Tombaugh, C. W. (1946). The Search for the Ninth Planet, Pluto. Astronomical Society of the Pacific Leaflets 5, 73–80. ADS scan
14. Trujillo, C. A., Jewitt, D. C., Luu, J. X. (2001). Properties of the Trans-Neptunian Belt: Statistics from the CFHT Survey. Astronomical Journal 122, 457–473. arXiv:astro-ph/0104104
15. van Houten, C. J., van Houten-Groeneveld, I., Herget, P., Gehrels, T. (1970). The Palomar-Leiden Survey of Faint Minor Planets. Astronomy & Astrophysics Supplement 2, 339–448. ADS scan