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The accurate calculation of the distance between the Sun and Earth's nearest point in orbit, known as the perihelion, was a gradual process that involved centuries of scientific observations and advancements. The determination of this distance is based on the study of planetary motion and celestial mechanics.

One crucial step in accurately calculating Earth's perihelion distance occurred in the late 17th century with the development of Kepler's laws of planetary motion by the German astronomer Johannes Kepler. Kepler's laws provided a mathematical description of the motion of planets around the Sun, including the shape of their orbits.

However, it wasn't until the late 18th and early 19th centuries that more precise measurements were made, refining our understanding of Earth's orbit and its closest point to the Sun. During this time, advances in observational techniques, such as improved telescopes and instruments, allowed for more accurate measurements of celestial objects and their movements.

One significant contribution was made by the French mathematician and astronomer Urbain Le Verrier. In the mid-19th century, Le Verrier conducted detailed calculations and observations, including the study of the motion of the planet Mercury, which led to the discovery of small discrepancies in its orbit. To explain these discrepancies, Le Verrier hypothesized the existence of an additional planet closer to the Sun, which was later confirmed as the planet Vulcan.

Although the hypothetical planet Vulcan turned out to be non-existent, Le Verrier's meticulous calculations and observations helped refine our understanding of Earth's orbit and its perihelion distance. This contributed to a more accurate determination of the distance between the Sun and Earth's nearest point in orbit.

Therefore, while there isn't a specific year to pinpoint when the distance was first accurately calculated, it was a gradual process of refinement over several centuries, with significant contributions made by various scientists and astronomers along the way.

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