The corpus, every claim citable.

Āryabhaṭīya, Gītikā 1 (499 CE) fixes the Earth's eastward rotations per yuga at 1,582,237,500 against 4,320,000 solar revolutions — implying 1,577,917,500 civil days per yuga and a sidereal day of 86,164.10 seconds (23h 56m 4.10s). The modern value is 86,164.09 seconds: agreement to about 0.01 s. The verse also encodes the rotating-Earth doctrine numerically ("of the Earth eastward") — the parameter later tradition recast as revolutions of the stars.

The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930

Aryabhatiya Golapada IV.37 (499 CE) gives the correct geometric mechanism of both eclipses: the Sun is obscured when the Moon comes between Earth and Sun; the Moon is obscured when it passes into the Earth's shadow. Brahmagupta directly attacked this in Brahmasphuta- siddhanta XI.9 (628 CE), calling Aryabhata's eclipse account "false" and re-affirming the demon Rahu. The geometric reading did not become Indian astronomical mainstream until the Kerala school ~1500 CE.

The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930

Aryabhatiya I.3 gives the cosmic-cycle structure: 14 Manus × 72 yugas × 4,320,000 years = 4,354,560,000 years per kalpa (~4.35 billion). Modern radiometric Earth age (Patterson 1956): 4.54 billion. ~5% match between a 6th-century Sanskrit recurrence period and 20th-century radioactive-decay measurement. Almost certainly coincidence — Aryabhata was computing planetary cycles, not Earth's age — but striking.

The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930

Aryabhatiya Golapada IV.9 uses the boat analogy to argue that the apparent westward motion of stars is an illusion caused by Earth's eastward axial rotation. Aryabhatiya I.1 quantifies it: 1,582,237,500 rotations per yuga ≈ 366.26 sidereal rotations per year, accurate to ~4 parts per million against modern measurement. Predates Copernicus by 1,044 years; contested within Indian astronomy itself (Brahmagupta rejected it in 628 CE).

The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930

Pañcasiddhāntikā III.21 (505 CE) states that the summer solstice once turned from the middle of Āśleṣā — "then the ayana was right" — but at present begins from Punarvasu: a shift of about 23°, roughly 1,700 years of equinoctial precession separating the old record from current observation. Hipparchus discovered precession c. 130 BCE; this verse documents the Indian tradition registering the same drift by checking its inherited solstice positions against the sky.

The Panchasiddhantika: The Astronomical Work of Varaha Mihira · tr. G. Thibaut & Sudhakara Dvivedi, 1889

Varāhamihira's Pañcasiddhāntikā (505 CE) summarizes and ranks five astronomical schools; the Romaka ("Roman") Siddhānta places in the top three. Its luni-solar yuga of 2,850 years with 1,050 intercalary months is exactly 150 Metonic cycles (19 years, 7 intercalations each), and its epoch is reckoned from sunset at Yavanapura — Alexandria. Greco-Roman astronomy circulated inside the Indian canon, openly named and rated.

The Panchasiddhantika: The Astronomical Work of Varaha Mihira · tr. G. Thibaut & Sudhakara Dvivedi, 1889

Sūrya-Siddhānta i.30 fixes the Moon's sidereal revolutions per Age at 57,753,336; i.37 fixes the Age's civil days at 1,577,917,828. The implied sidereal month, 27.321674 days, differs from the modern 27.321662 by about 1.1 seconds — roughly 0.5 parts per million. Babylonian-Greek lunar theory reached comparable precision by other routes; the Siddhānta's whole-number encoding is the Indian tradition's own and stayed in computational use for over a millennium.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Sūrya-Siddhānta XII.53 (c. 400–500 CE core text, Burgess 1860 translation) states that the Earth is a globe in space with no absolute up or down: every observer takes their own place to be uppermost. Verses 51–52 apply it concretely — dwellers at opposite points of the globe each suppose the other underneath. Greek astronomy established terrestrial sphericity earlier (Aristotle, c. 350 BCE); the Siddhānta's plain statement of the relativity of "up" is among the clearest in any ancient text.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Āryabhaṭīya IV (Gola) 5, 499 CE: half of the Earth, the planets, and the asterisms is dark — shadowed by the body itself — and the half turned toward the Sun is light. Applied to the Moon, this is the reflected-sunlight account of moonlight and of lunar phases. The insight has earlier independent precedents (Anaxagoras, c. 450 BCE, in Greece); Aryabhata's formulation embeds it in a quantitative astronomy curriculum used continuously in India for over a millennium.

The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930

Surya-Siddhanta III.9 (~5th c. CE) gives 600 equinoctial revolutions per mahayuga (4,320,000 years) — ≈50 arcseconds per year, close to the modern 50.3″/yr. Whether the motion is monotonic (progressive precession) or oscillatory (libration/trepidation between ±27°) is ambiguous: III.11-12 suggest libration, III.9 alone reads as progression. Burgess 1860 reads libration; modern scholarship leans toward original progression later edited for libration.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Surya-Siddhanta I.30 (~5th c. CE) gives Mars's revolutions per mahayuga (4,320,000 years) as 2,296,832. Period = 4,320,000 / 2,296,832 = 1.8809 sidereal years = 687.05 mean solar days. Modern Mars sidereal period (NASA): 686.971 days. Off by 0.08 days = ~2 hours over a 23-month orbit. ~120 parts per million accuracy, pre-telescopic. The same I.29-34 verse block gives every planet to this kind of precision.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Aryabhatiya I.6 (Dasagitika, 499 CE) gives Earth's axial tilt (the obliquity of the ecliptic) as 24°. Modern measurement is 23.44°. The 0.56° discrepancy isn't a measurement error: Earth's obliquity oscillates between ~22.1° and ~24.5° on a 41,000-year cycle (Milankovitch orbital forcing), and was ~24° several thousand years before Aryabhata wrote — consistent with his value reflecting inherited observational tradition from earlier Indian astronomy.

The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930

Aryabhatiya I.5 (Dasagitika, 499 CE) gives Earth's diameter as 1,050 yojanas. The yojana is an Indian unit of distance whose conversion to modern units is disputed in Sanskrit-scholarship (estimates 5-8 miles, depending on text and period). With the most-cited mid-period value of ~7.5 miles per yojana, 1,050 yojanas = 7,875 miles — within 0.5% of the modern measurement of 7,917 miles. The Sun, Moon, and planet diameters in the same verse (in ratios to Earth's) are similarly close.

The Aryabhatiya of Aryabhata · tr. W. E. Clark, 1930

Surya-Siddhanta I.29-34 (~5th c. CE) gives the revolutions of each celestial body in one mahayuga (4,320,000 years). The sidereal year derives by arithmetic: (asterism revolutions − sun revolutions) / sun revolutions = (1,582,237,828 − 4,320,000) / 4,320,000 ≈ 365.2587 civil days per year. Modern sidereal year: 365.25636 days. The text is 3.5 minutes / ~7 parts per million long, pre-telescopic. Ptolemy's Almagest (~150 CE) gives 365.2467 — off by ~14 minutes.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Surya-Siddhanta I.32 (Burgess 1860 trans) gives Saturn's revolutions in one mahayuga (4,320,000 years) as 146,568. Dividing yields a sidereal period of 10,765.5 days. NASA's modern measurement: 10,759.22 days. The match is 0.063% — extraordinary for a pre- telescopic observational tradition. The accuracy reflects ~1000 years of accumulated Indian observational records aggregated into the mahayuga period parameters.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Sūrya-Siddhānta iii builds working astronomy from a gnomon: on a leveled surface, a drawn circle and a twelve-digit vertical stick yield the cardinal directions (from the shadow-tip's morning and evening crossings), the observer's latitude (equinoctial noon shadow, iii.17), and time-of-day quantities. Burgess's commentary works the rules for Washington, D.C. and gets its latitude right. The gnomon procedures are the observational ground floor of the siddhānta's parameter system.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Sūrya-Siddhānta xiii (the "astronomical upaniṣad" chapter) directs the teacher to build an armillary sphere — an earth-globe ringed by the circles of the asterisms and ecliptic — explicitly "in order to the instruction of the pupil," then covers other instruments, especially for timekeeping (xiii.17–25). Burgess notes Indian practice paired a meridian circle with the clepsydra, closely analogous to later Western method: the hardware behind the siddhānta's precision parameters.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860

Pañcasiddhāntikā XII (505 CE) preserves the Paitāmaha Siddhānta: a five-year luni-solar calendar of 1,830 civil days, intercalating every 30 months, with its epoch at the asterism Dhaniṣṭhā — the winter-solstice marker of the Vedāṅga Jyotiṣa tradition, datable by precession to c. 1400–1200 BCE. Varāhamihira transmits the system faithfully while ranking it "far from the truth" — the Indian canon documenting and superseding its own oldest astronomy.

The Panchasiddhantika: The Astronomical Work of Varaha Mihira · tr. G. Thibaut & Sudhakara Dvivedi, 1889

Pañcasiddhāntikā XIV (505 CE) teaches graphical methods: construct a degree-marked circle of 180 aṅgulis with auxiliary declination circles and strings, from which the ascensional difference for any latitude — and related rising-time quantities — are read directly off the figure. Thibaut's commentary describes the procedure as finding the result "without calculation, by the mere inspection of a kind of diagram": a worked analog-computing device inside a 6th-century astronomy curriculum.

The Panchasiddhantika: The Astronomical Work of Varaha Mihira · tr. G. Thibaut & Sudhakara Dvivedi, 1889

Sūrya-Siddhānta iv.1 gives the Moon's diameter as 480 yojanas; with the Earth's diameter fixed at 1,600 yojanas (i.59), the implied Moon-to-Earth size ratio is 0.30, against a true value of 0.27 — accurate to about ten percent. The same verse's solar diameter (6,500 yojanas ≈ 4 Earth-diameters) is too small by a factor of ~27: lunar parallax was within naked-eye reach and solar parallax was not. The accuracy tracks the observable.

Translation of the Surya-Siddhanta · tr. Ebenezer Burgess, 1860