Summer Solstice Mathematics

The summer solstice occurs when Earth's axial tilt of 23.5° points maximally toward the sun. The length of the longest day depends on latitude — calculable via spherical trigonometry: cos(H₀) = −tan(φ)tan(δ), where H₀ is the hour angle at sunset, φ is latitude, and δ is the sun's declination. At the Arctic Circle (66.5°N), the sun never sets. Ancient megalithic monuments like Stonehenge were precisely aligned to the solstice sunrise — the first astronomical instruments, built before any written mathematics, embodying geometric reasoning in stone.