Arcot

City · c. 1713 CE · in South Asia

Capital of Carnatic Sultanate (1713–1768).

Karlsruhe (1715 CE): Capital of Electorate of Baden (1803–1805), Grand Duchy of Baden (1806–1870).
Hanover (c. 1709 CE): Capital of Electorate of Hanover (1709–1802), Kingdom of Hanover (1814–1865).
Kandahar (c. 1709 CE): Capital of Hotaki Dynasty (1709–1737), Durrani Empire (1748–1776).
Qoqon (c. 1709 CE): Capital of Khanate of Kokand (1709–1876).
Nuuk (1721 CE): Capital of Greenland (1734–1940).
Kingstown (1722 CE): Capital of Saint Vincent (1979–today).
Saint Petersburg (1703 CE): Peter the Great founded Saint Petersburg on the Neva delta in 1703 as a 'window to Europe'. It was Russia's capital from 1712 to 1918.
Montevideo (1723 CE): Capital of Federal League (1815–1819), Oriental Republic of Uruguay (1828–today).
Dushanbe (1700 CE): Capital of Republic of Tajikistan (1992–today).
Tashkent (c. 1729 CE): Capital of Kazakh Khanate (1729–1781), Republic of Uzbekistan (1992–today).

Around the same time and place

Aurangzeb (1618 CE – 1707 CE): Sixth Mughal emperor under whom the empire reached its greatest extent; his long Deccan wars strained its resources.
Shivaji (1630 CE – 1680 CE): Founder of the Maratha state who fought the Bijapur Sultanate and the Mughals and was crowned Chhatrapati at Raigad in 1674.
Maratha Empire (1674–1818 CE): Maratha state founded by Shivaji's coronation in 1674, which became the dominant power in India in the 18th century before defeat by the British.
Pondicherry (c. 1673 CE): Capital of French India (1673–1847).
Calcutta (Kolkata) (1690 CE): English East India Company trading post established in 1690 that became the capital of British India until 1911.
Tipu Sultan (1751 CE – 1799 CE): Ruler of Mysore who fought the East India Company in several wars and pioneered the military use of iron-cased rockets.
Raigad Fort (c. 1677 CE): Capital of Maratha Empire (1677–1818).
Vallabhi (c. 476–1948 CE): Capital of Maitraka Dynasty (476–731).