What equation do astronomers use to calculate the sun-earth distance?

The first step in measuring the distance between the Earth and the Sun is to find the relative distances between Earth and other planets. The first known person to use geometry to estimate the Earth-Sun distance was Aristarchus (c. 310-230 BC), in Ancient Greece. He measured the angular separation of the Sun and the Moon when the Moon was half-illuminated to derive the distance between Earth and Sun in terms of the distance between the Earth and the Moon. ancient Greek astronomer, Eratosthenes (276-194 BC), estimated the distance between Earth and Sun to be either 4,080,000 stadia or 804,000,000 stadia.

Earth-Sun distance, a = roughly 150 million km, defined as one Astronomical Unit (Au)

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