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The Great Comets of 1843 and 1882 at Their Previous Return to Perihelion in the Twelfth Century: One Spectacular, the Other Dull

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The Chinese comet of 1138 was the previous, dull return of the Great September Comet of 1882 and Ikeya-Seki, invisible in daylight and first seen a month after perihelion.

desk verdict An instructive and well-documented reconstruction of the 1106 and 1138 sungrazers, but the 'could never have been seen in daylight' conclusion rests on an adopted absolute magnitude and identical-light-curve postulate that are not pinned down. read the letter →

arxiv 2505.14662 v2 pith:RGMY6S6X submitted 2025-05-20 astro-ph.EP

Zdenek Sekanina This is my paper · ORCID
classification astro-ph.EP
keywords KreutzsungrazersChinesecometof1138C/1882R1C/1965S1X/1106C1visibilitytidalfragmentationhistoricalrecords
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the Chinese comet of 1138 (Ho's No. 403) was the previous perihelion return of the Great September Comet of 1882 and comet Ikeya-Seki, and that this object was intrinsically bright but geometrically handicapped: arriving at perihelion in early August, it stayed close to the Sun in the sky, was dimmed by backscattering, and could not be seen in daylight. It was first spotted in early September, about a month after perihelion, as a modest morning object with a tail reaching 15–30 degrees above the horizon. By contrast, the paper shows that the Great Comet of 1106, the previous return of the Great March Comet of 1843, was seen in daylight by Sigebert de Gembloux within hours of perihelion because forward scattering and a favorable geometry made it much brighter. The same modeling revises the long-held notion that Kreutz sungrazers with mid-May-to-mid-August perihelia were always missed: they were missed in daylight but could become visible in twilight weeks later.

What carries the argument

The argument is carried by a photometric model of the two twelfth-century comets, anchored to an assumed absolute preperihelion magnitude H0− = 2.8 for both, a preperihelion brightness law Happ = 2.8 + 10 log r + 5 log Δ + Φ(α), and a post-perihelion slope n+ = 4.4 − 0.2 νfrg that depends on the number of persisting nuclear fragments. These light curves are evaluated with Schaefer's naked-eye limiting-magnitude algorithm to predict daylight detectability, and with syndyname dust-tail models (radiation-pressure parameter β up to 0.6) to predict tail geometry. The central comparison is between the 1106 comet, whose February arrival made it approach the Earth and enjoy forward scattering, and the 1138 comet, whose August arrival placed it behind the Sun with growing geocentric distance and backscattering.

What would settle it

Search medieval Chinese, Korean, and Japanese chronicles for any recorded daylight sighting of a comet in August 1138; a single reliable report would refute the claim. Alternatively, recompute the 1138 comet's apparent daylight magnitude under the model but with an absolute preperihelion magnitude of 0 instead of 2.8; if the result exceeds Schaefer's daylight limiting magnitude for the chosen site, the conclusion that it could never have been sighted in daylight is falsified.

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Extended reading notes

Core claim

The central claim is that the Chinese comet of 1138, listed as Ho No. 403 and first recorded on 1138 September 3, was the previous return of the Population II Kreutz sungrazer C/1882 R1 and C/1965 S1, and that the reason it was a lackluster 'broom star' rather than a daylight spectacle was geometry, not intrinsic faintness. The comet passed perihelion on 1138 August 1 at 0.008 AU from the Sun, but post-perihelion its geocentric distance grew beyond 1.1 AU, its solar elongation remained about half that of the 1106 comet at the same heliocentric distance, and its dust was backscattered rather than forward-scattered, making it undetectable in daylight and invisible in a dark sky for weeks. Using a light-curve model that gives the 1138 and 1106 comets identical pre-perihelion brightness, the paper predicts that the 1138 comet became a naked-eye morning object only around September 2–3, with the head at elevation about 10 degrees and the tail reaching 15–30 degrees, matching the historical record. The same reasoning shows that the widely quoted rule that Kreutz sungrazers with perihelia between mid-May and mid-August were missed unless seen in daylight is misleading: they were missed in daylight, but had a narrow window of twilight visibility about a month after perihelion.

Load-bearing premise

The entire daylight-invisibility prediction for the 1138 comet assumes that it was intrinsically as bright as the 1106 comet, with absolute preperihelion magnitude 2.8, and that its post-perihelion fading followed a fitted slope depending on the assumed number of fragments; if the 1138 comet was a few magnitudes brighter, it would have been visible in daylight and the central conclusion fails.

Editorial extensions

If this is right

  • The Chinese comet of 1138 is identified as the previous return of C/1882 R1 and C/1965 S1, removing the missing second sungrazer for the 12th century.
  • Kreutz sungrazers with perihelia between mid-May and mid-August are not necessarily invisible from the ground; they can appear as morning objects about a month after perihelion, with the tail higher in the sky than the head.
  • Sigebert de Gembloux's daylight sighting of the 1106 comet on February 2 is consistent with the model and pins the perihelion time to within ±0.3 day.
  • The fragmented nucleus of the 1138 comet is modeled as a chain of five major fragments, including the 1882 sungrazer, Ikeya-Seki, X/1702 D1, the 1792 sun-comet, and a predicted fragment expected near 2027, with a projected length of about 15 arcsec at discovery.
  • The apparent-magnitude rule of thumb for the last naked-eye tail sighting may depend on observing geometry, since the 1138 comet's tail was last seen when the head was at magnitude ~4.5 rather than ~7.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same geometric argument may apply to other historical Kreutz candidates such as the comet of 1041, which the paper notes had a similar timeline and was also missed in daylight but seen weeks later.
  • If the 1138 identification is correct, the predicted ~2027 fragment of the same parent is a concrete target whose orbital plane and activity should match the model's predictions.
  • The paper's brightness model treats the 1106 and 1138 comets as identical pre-perihelion; any revision of either comet's absolute magnitude would shift the daylight-visibility and discovery-date predictions, offering a testable link to the historical record.
  • The new interpretation of Elkin's drawings implies that the 1882 sungrazer's fragment A was not the principal nucleus but a short-lived flaring fragment, which if correct reshapes how the mass distribution of the 1882 breakup is inferred.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper identifies the Chinese comet of 1138 (Ho No. 403) as the previous return of the Kreutz Population II pair C/1882 R1 and C/1965 S1, and treats X/1106 C1 as the previous return of C/1843 D1. It constructs pre- and post-perihelion light curves from adopted absolute magnitudes and slope laws (Eqs. 1-4), applies Schaefer's naked-eye limiting-magnitude algorithm, and models tail projections and a five-fragment nuclear chain. On this basis it claims that the 1106 comet was visible in daylight near perihelion and that the 1138 comet could never have been seen in daylight nor discovered earlier than early September, one month after perihelion. It further argues that the common statement that Kreutz sungrazers with perihelia between mid-May and mid-August were necessarily missed is misleading, and it uses Elkin's 1882 drawings to illustrate unpredictable fragmentation behavior.

Significance. If its central brightness assumptions were robust, the paper would materially revise the historical record of Kreutz sungrazer returns: it gives a concrete previous-return pair, explains the dramatic difference between 1106 and 1138 in terms of geometry and forward scattering, and offers a falsifiable prediction of a near-future fragment near 2027. The analysis is detailed and the comparison of tail projections is physically illuminating. However, the central conclusions are not parameter-free and no sensitivity analysis is provided; the paper's own caveats in Section 7 about limiting-magnitude uncertainty are in tension with the strong wording of the abstract. These issues are fixable by quantitative uncertainty propagation and by softening the claims accordingly.

major comments (4)
  1. [§3.1, Eq. (1)] The absolute preperihelion magnitude H0^- = 2.8 in Eq. (1) is not measured for the 1106/1138 parents; it is scaled from C/1843 D1 and C/1882 R1 under the assumption that each fragment comprised about 40% of its parent's mass, with an r^-4 slope law. The daylight-visibility conclusion (Section 3.3 and the abstract) depends directly on this value: if the parent had been 1-2 magnitudes intrinsically brighter, the 1138 light curve in Fig. 1 would cross the daylight limiting-magnitude curve. Please provide a sensitivity analysis over H0^-, n^-, the 40% mass fraction, and the Marcus phase law, and state which conclusions survive the plausible range.
  2. [§7, Table 6] The 'discovered much earlier' part of the central claim is contradicted by the manuscript's own stated uncertainty. Table 6 predicts H_app = 2.9 versus a limiting magnitude near 3.1 at the optimum time on September 2, and the text says the limiting magnitude is 'subject to rather large uncertainties' and the head 'may of may not have been seen.' A 0.3-mag change in H0 or in the limiting-magnitude model changes the conclusion. The abstract should be reworded to reflect that the non-detection before September is consistent with the model, not proven impossible.
  3. [§2-§3, Table 1] The orbital elements in Table 1 for the 1138 comet are taken from a backward integration (Sekanina & Kracht 2022) that begins with the identification of Ho 403 as the parent of C/1882 R1 and C/1965 S1. Using these elements to predict the comet's positions and then treating the Chinese record as consistency support is partly circular; the X/ designation itself indicates no orbit from the 1138 observations. Please separate the assumption (the parent identification) from the derived consistency checks and state what independent information, if any, could falsify the identification.
  4. [§3.1, Eq. (3)] The post-perihelion slope law n+ = 4.4 - 0.2 nu_frg is a linear fit to two objects (Ikeya-Seki and C/1882 R1), and it is then extrapolated to nu_frg = 3+ and 4+ for the 1106 and 1138 comets. The nearly one-magnitude post-perihelion brightness difference between the two comets in Eq. (4) and hence the September visibility calculation depend on this extrapolation. The slope and fragment-count values carry no uncertainties; please provide a propagation estimate or a bracketing test with n+ varied by ±0.5.
minor comments (4)
  1. [Footnote 2] Footnote 2 cites Google AI Overview and Wikipedia for the cubit-to-degree conversion; these are not appropriate scholarly sources. Please replace them with the primary references (e.g., Stephenson & Fatoohi 1994 and Steele 2008) and state the adopted conversion and its uncertainty in the text.
  2. [References and Tables 1, 8] References and text contain spelling errors: 'Hagughney' (References), 'Latidude' (Table 1 heading), 'nuclues' (Section 5), 'proxinity' (Section 8), and 'Elgin' where Elkin is meant (Section 8, discussion of Fig. 9).
  3. [Figures 4 and 7] Figures 4 and 7 display the hook-shaped tail projection convincingly, but the text does not give the numerical projection method or the assumed dust ejection parameters used to draw the syndynames; a brief appendix or caption equation would make the comparison reproducible.
  4. [Table 6 caption] The caption of Table 6 is very dense; it would help to define 'time before sunrise' as negative minutes and to mark the optimum visibility row with a symbol rather than italics, since italics are easy to overlook.

Circularity Check

2 steps flagged · score 6.0 of 10

The 'never in daylight' conclusion is forced by the adopted H0=2.8 and identical-light-curve postulate, while the 1138 parent identification is imported from same-author orbit integrations.

  1. fitted input called prediction [Section 3.1, Equations (1)–(4), Figure 1; Abstract]
    "the light curves of the 1106 and 1138 comets were assumed to comply with two postulates: (i) they were identical before perihelion, predicated on the premise that the nuclei of the 1843 and 1882 sungrazers comprised, respectively, about 40 percent of each parent's mass. ... Averaging, I get for both the 1106 and 1138 comets H−0 = 3.45 − 0.66 ≃ 2.8."

    The abstract's categorical claim that 'the 1138 comet could have never been sighted in daylight' is obtained by inserting the adopted H0=2.8 and the identical-light-curve postulate into Equation (1) and comparing with Schaefer's limiting magnitudes. No intrinsic-brightness measurement or bound for the 1138 comet is used; if H0 were only 1–2 mag brighter the daylight light curve would cross the naked-eye threshold. The 'dull' prediction is therefore a restatement of the adopted brightness input, not an empirical result, and the paper itself later concedes the limiting magnitude is 'subject to rather large uncertainties'.

  2. self citation load bearing [Table 1, Section 3; Section 2 and Section 10]
    "The set for X/1106 C1 comes from Sekanina & Kracht's (2022) integration of the motion of the Great March Comet of 1843; for the Chinese comet of 1138 from their integration of the motion of nucleus B of the Great September Comet of 1882."

    The central identification of the Chinese comet of 1138 as the previous return of C/1882 R1 and C/1965 S1 is imported from a same-author arXiv preprint, and the Table 1 orbital elements used for all geometry, visibility, and tail predictions are the output of that integration. The historical records are then treated as consistency checks of a model whose parentage assumption is already built into the orbit. Because the orbital elements were not independently derived from the 1138 observations in this paper, the records cannot falsify the claimed identification, making the self-citation chain load-bearing rather than merely bibliographic.

full rationale

The paper is not entirely circular: Sigebert's independent daylight sighting of the 1106 comet is an external record that agrees with the model, and the dust-tail syndyname calculations use published radiation-pressure results. However, the two central planks of the paper are not independently established. First, the strong negative conclusion that the 1138 comet could never have been visible in daylight follows from an adopted absolute magnitude H0=2.8 and a postulate of identical pre-perihelion light curves for the 1106 and 1138 comets; the 1138 comet's own brightness is never measured, and the paper itself admits the limiting-magnitude computation is uncertain. Second, the identification of Ho's No. 403 as the 1138 parent of C/1882 R1 and C/1965 S1 is taken from same-author orbit integrations, and the orbital elements used for the visibility and tail predictions come from that same integration, so the historical records serve as consistency checks on a model already built around the claimed parentage. This yields a moderate circularity score of 6: the daylight 'prediction' reduces by construction to the adopted brightness input, and the parent-identification premise is carried by a same-author citation chain, while the Sigebert test and tail modeling provide some genuine independent content.

Assumptions & free parameters 6 free parameters · 7 assumptions · 3 invented entities

The visibility and fragmentation results are built on a small number of adopted brightness parameters, the assumption that the 1138 comet is the 1882 parent, and several historical interpretation choices. Most numerical outputs follow from these inputs, so the ledger is dominated by calibration parameters and the prior identification, not by independent measurements.

free parameters (6)
  • Absolute preperihelion magnitude H0^- = 2.8
    Section 3.1: derived by scaling the adopted H0 of C/1843 D1 (3.5) and C/1882 R1 (3.4) by a 0.4 parent mass fraction and averaging; controls all visibility predictions.
  • Preperihelion brightness slope n- = 4
    Section 3.1: adopted from Ikeya-Seki's observed light curve and applied to both 1106 and 1138 before perihelion.
  • Post-perihelion slope law coefficients = n+ = 4.4 - 0.2 * nu_frg
    Section 3.1, Equation (3): linear fit through Ikeya-Seki (nu=2, n+=4.0) and the 1882 sungrazer (nu=5 to 6, n+=3.3).
  • Fragment counts nu_frg for 1106 and 1138 = 3+ and 4+
    Section 3.1: adopted from the author's earlier speculations (Sekanina 2025); sets the post-perihelion light curves via Equation (3).
  • Perihelion time of X/1106 C1 = 1106 February 2.25 TT, plus or minus 0.3 day
    Sections 4 and 6: derived from Sigebert's six-hour daylight sighting combined with a cubit-to-degree conversion of 1.5 degrees; Table 1 initially lists February 2.0.
  • Perihelion time of predicted 2027 fragment = 2027.7
    Section 8: chosen so the principal fragment C/1882 R1 sits near the middle of a five-fragment chain.
assumptions (7)
  • domain assumption The 1138 comet is the previous return of C/1882 R1 and C/1965 S1, with orbital elements from a backward integration of C/1882 R1.
    Section 3, Table 1: the entire visibility model is computed on these adopted orbits; the identification itself is not re-derived in this paper.
  • ad hoc to paper The nuclei of C/1843 D1 and C/1882 R1 each comprised about 40 percent of their parent nucleus.
    Section 3.1: used to scale parent absolute magnitude; based on the author's contact-binary model (Sekanina 2021), not independent evidence.
  • ad hoc to paper The preperihelion light curves of X/1106 C1 and the 1138 comet were identical and varied as r^-4.
    Section 3.1, postulate (i): no photometry of 12th-century comets exists, so this is an assumed constraint that sets the absolute brightness.
  • ad hoc to paper Post-perihelion fading slows linearly with the number of persisting fragments.
    Section 3.1, Equation (3): a fit through two objects only, extended to nu_frg = 3+ and 4+ for the two 12th-century comets.
  • domain assumption Schaefer's naked-eye limiting-magnitude model and Marcus's forward-scattering phase law apply to medieval daylight and twilight observations.
    Section 3 and Figures 1 and 3: standard tools, but applied near the Sun in daylight at very small solar elongations, outside their heavily validated range.
  • ad hoc to paper One cubit in Sigebert's report equals 1.5 degrees of angular separation.
    Section 4: the author derives 1.5 degrees from finger width and arm length; cited sources range from about 1 to 2.5 degrees, and this conversion determines the derived 1106 perihelion time.
  • domain assumption All fragments of the 1138 comet experienced equal indirect planetary perturbations after perihelion.
    Section 8: used to convert future orbital periods to osculating periods for all five fragments; exact only to first order and not true for close encounters.
invented entities (3)
  • Predicted Kreutz sungrazer near 2027 independent evidence
    purpose: Fills the fifth position in the modeled fragment chain of the 1138 comet so that the principal fragment C/1882 R1 sits near the middle of the chain.
    Section 8 and Figure 8: the object is not yet observed, but the paper assigns a perihelion time near 2027, making it falsifiable by future observation.
  • Sun-comet of 1792 as a Kreutz fragment of the 1138 comet
    purpose: Placed between X/1702 D1 and C/1882 R1 in the modeled fragment chain.
    Section 8: based on a vague Chinese 'sun-comet' record cited from Strom (2002); the author calls it a weak entry.
  • X/1702 D1 as a fragment of the 1138 comet independent evidence
    purpose: Leading member of the modeled five-fragment chain, earlier than C/1882 R1.
    Section 8: the historical orbit of X/1702 D1 gives a perihelion time and period, but its membership in the 1138 family is assumed from the author's prior work.

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Pith. "Pith review of The Great Comets of 1843 and 1882 at Their Previous Return to Perihelion in the Twelfth Century: One Spectacular, the Other Dull." pith.science (2026). https://pith.science/paper/RGMY6S6X

@misc{pith2026250514662,
  author       = {Pith},
  title        = {Pith review of: The Great Comets of 1843 and 1882 at Their Previous Return to Perihelion in the Twelfth Century: One Spectacular, the Other Dull},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RGMY6S6X}},
  note         = {Machine review of arXiv:2505.14662}
}
read the original abstract

New insights into the history of C/1843 D1 and C/1882 R1, the two celebrated Kreutz sungrazers, are provided by assessing evidence on their appearance at the previous perihelion return, known as X/1106 C1 and the Chinese comet of 1138 (Ho's No. 403), respectively. The conditions differed vastly because of disparities in geocentric distance, solar elongation, and phase correction (forward scattering), all linked to the arrival times (early February vs early August). The conclusions include: the daytime sighting of the 1106 comet by Sigebert de Gembloux is consistent with expectation and so are the accounts of an exceptionally long tail observed later in twilight; the comet reached perihelion only hours before its daytime detection; the 1138 comet could have never been sighted in daylight or discovered much earlier than it actually was, in early September, one month after perihelion; at discovery, the tail is predicted to have reached elevations of 15-30 deg, while the head was only 10 deg above horizon, when observed from moderate northern latitudes; the notion that Kreutz sungrazers at perihelion between mid-May and mid-August could not be seen from the ground except possibly in daylight is misleading; the appearance of the 1138 comet's nucleus after its tidal fragmentation at perihelion is modeled on the assumption that it consisted of five major fragments (including C/1882 R1 and C/1965 S1); and unpredictable morphological changes with time in the 1882 sungrazer's split nucleus are discussed.

Figures

Figures reproduced from arXiv: 2505.14662 by the authors.

Figure 1
Figure 1. Conditions for daylight observations of the 1106 and 1138 comets in the first 10 days after perihelion. Even though the 1138 comet was intrinsically brighter after perihelion, the greatly superior observing conditions made the 1106 comet substantially brighter in daylight, as shown by comparing the light curves (thick lines) with the limiting magnitudes for the naked eye (thin lines) at local noon. The shaded area p… view at source ↗
Figure 2
Figure 2. Projection onto the plane of the sky of the predicted or￾bit for X/1106 C1 close to perihelion (equinox J2000). The dotted part of the orbit indicates that the comet was then behind the Sun. The bullets show the locations of the comet at the times, reckoned in hours from perihelion. Parenthesized are the respective phase angles. Also shown are arcs of solar elongations of 0◦.6, 1◦, and 1◦.6. Receding from the Sun at… view at source ↗
Figure 3
Figure 3. Light curve (thick line), limiting magnitude (thin line), and solar elongation (dotted line) predicted for comet X/1106 C1 vs time on 1106 February 2, when the comet was observed as a star over a period of six hours in broad daylight at close proximity of the Sun, according to a historical record by Sigebert, a monk in the Benedictine Abbey of Gembloux, Belgium. The comet’s bright￾ness, greatly enhanced by the effec… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Dust-tail development in the 1106 and 1138 comets 6 days after perihelion (1106 February 8 for the first object, 1138 August 7 for the second one) in projection onto the plane of the sky. The tails are represented by the syndynames for radiation pressure accelerations …
Figure 5
Figure 5. Figure 5: The positions of comet X/1106 C1 in the sky at sun￾set on 1106 February 3–13 at the geographic latitude 31◦N and the longitude 120◦E, an approximate location of the capital of the Sung Dynasty (near today’s cities of Hangzhou and Nanjing). The Sun’s azimuth at sunset w…
Figure 7
Figure 7. Figure 7: Syndynames for β = 0.1, 0.3, and 0.6 in the dust tail of the 1138 comet on September 2.85 UT, in the horizontal coordinate system. Azimuth is reckoned from the local south to the west, so that the east is at −90◦. The comet’s head is the large solid circle at elevation…
Figure 8
Figure 8. Figure 8: Modeled appearance of the fragmented nucleus of the 1138 comet on 1138 September 2.85 UT, nearly 33 days after peri￾helion. Plotted are the astrometric positions (equinox J2000) of the proposed major fragments, besides the Great September Comet of 1882 and Ikeya-Seki a…
Figure 9
Figure 9. Figure 9: Drawing of the fragmented nucleus of the 1882 sun￾grazer, made by Elkin on 1882 October 13.1 UT, as seen with a 15-cm Grubb equatoreal. This was the only time that he was able to resolve four condensations in the chain; shown are the separa￾tions that he reported (Gill…
Figure 11
Figure 11. Figure 11: Drawing of the fragmented nucleus of the 1882 sun￾grazer, made by Elkin on 1882 November 1.1 UT, as seen with a heliometer. Compared to the sketch from October 22 ( [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 13
Figure 13. Figure 13: Path of the Great Comet of 1106 across the sky (equinox J2000). The positions 1–15 cover the period of time from February 6 through April 17 at a 5-day step, each identified in [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: Path of the Chinese comet of 1138 (Ho 403) across the sky (equinox J2000). The positions 1–7 cover the period of time from August 7 through October 6 at a 10-day step ( [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Orbital-Period Determination As an Indispensable Tool to Study the Pedigree of a Sungrazing Comet

    astro-ph.EP 2026-08 conditional novelty 5.0 of 10

    Sekanina uses observation-arc truncation and a radiation-pressure correction to assign previous perihelion dates of AD 363 (C/2026 A1), 1140 (Ikeya-Seki), and 1369 (Lovejoy), revising Kreutz sungrazer pedigrees.

  2. New Insights into the Nature and Orbital Motion of Aristotle's Comet in 372 BC

    astro-ph.EP 2025-07 conditional novelty 5.0 of 10

    Aristotle's comet of 372 BC likely reached perihelion on January 20, and its observed path and 60-degree tail fit the orbit predicted for the Kreutz sungrazer progenitor.

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