Two of the nine Navagraha temples don't fit neatly into the east or west cluster, and each needs its own dedicated leg of travel. One of them, despite being geographically the most awkward to reach, is also the single most important temple in the entire circuit.
Alangudi sits in Pudukottai district, roughly 32-35 km south of Kumbakonam — close enough to add as a detour, but far enough that it needs deliberate planning rather than a casual stop on the way to somewhere else. Shiva is worshipped here as Apatsahayeswarar, "one who rescues devotees from danger," fitting Guru's traditional role as the gods' own counselor and protector. Thursday and Guru Peyarchi (Jupiter's roughly 12-13 month transit) are the busiest times; most other days are calm.
Thirunallar is about 60 km east of Kumbakonam, in Karaikal district — technically part of Puducherry, not Tamil Nadu, and administered separately from the other eight HR&CE-run temples in the circuit. Despite the distance, this is the most-visited Navagraha temple by a wide margin, and arguably the most mythologically significant: it's where Shani is said to have yielded to Shiva and earned the rare title "Eshwaran," and where the legendary King Nala was freed from Shani's curse after twelve years of misfortune. For the full story, see the dedicated Thirunallar guide.
Most pilgrims fold Alangudi into an extended western-cluster day, since it's the closer of the two outliers to Kumbakonam. Thirunallar, given both its distance and its crowds, is usually treated as its own dedicated day — ideally starting before 6 AM if visiting on a Saturday, when waits after 8 AM can run several hours.
Saturdays at Thirunallar and Tuesdays at Vaitheeswaran Koil are the two days to actively avoid across the whole Navagraha circuit unless you're arriving before 7 AM — both draw exceptional crowds on their respective graha's day.
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