We can write an equation that gives this value to within a few cm using the golden ratio and a new cosmological parameter, but is there an equation for the value 149,597,870,700 m?
The value of 149,597,870,700 meters for the astronomical unit (AU) is a defined constant, not derived from a fundamental physical equation. It was fixed by the International Astronomical Union (IAU) in 2012 to provide consistency in celestial mechanics and astronomical calculations. While it is based on highly accurate measurements (such as radar ranging to planets), it is not the result of a deeper theoretical expression involving constants like the golden ratio or cosmological parameters. Any numerical approximation using such values is coincidental unless supported by a verified physical framework.