In an alternate reality, God made a sign error early on in his working. He then inadvertently corrected it with a slapdash differentiation of the cosine function, before forgetting a constant of integration. Consequently, the equation for Earth’s motion was not as it should have been.
The planet we know as Earth thus came to be called Zygos. Her tendrilous residents constructed a mighty capital on the equator called Zygocity, which served as a popular tourist trap for cosmonauts from light-years around.
Zygos has precisely the same mass and radius as Earth, but rotates at such a rate that those in Zygocity experience apparent weightlessness.
Question: How many days are there in the Zygosian year?