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I am creating an Earthlike planet with a year length of 515 Earth days and 9 Earth hours. I am aware that Kepler's third law of planetary motion states that warmer stars are needed for longer orbital periods with an Earthlike climate.

However, my planet differs from Earth because its climate resembles Earth during the last glacial maximum, and its seasons are caused by fluctuations in the distance between the planet and the star rather than axial tilt (it has a near-zero axial tilt of only 0.2 degrees). How far would the planet have to orbit from the star on average? My planet has a mass of 1.18 times Earth's mass, if that affects anything.

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There are way too many variables for a single answer.

Orbit wise, here is a calculator https://www.omnicalculator.com/physics/orbital-velocity

For 515 days, star mass equal to Sun, satellite mass 1.18 of Earth one possible solution is semi-major axis 1.257 AU, semi-minor 0.9 AU.

What climate your planet end up having depends on star temperature, atmosphere composition, water coverage and probably few more hundred parameters. If you claim that climate resembles Earth during the last glacial maximum no one will be able to argue. Climate is just too complex. Well, there would be differences - your polar areas would be extremely cold due to lack of axial tilt. Just don't go there.

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