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Are the Sun’s and the Earth’s Polar Axes Aligned When the Earth is on the Sun’s Equator?

Question:
Hi, I’m a 72 year-old retired chemist in search . . .
If the earth is on the sun’s equator, then is Polaris the sun’s north pole also?
In 12,000 years when our north pole is Vega, where will the sun’s north pole be?
If also Vega, is there a casual relationship?
Thanks,
Steve
Answer:
Since the Earth’s axis is tilted by about 23.5 degrees relative to its orbital plane, Polaris would be tilted by about that amount when the Earth is on the Sun’s equator. So, in fact, the position of the Sun’s and the Earth’s north pole do not align. After 12000 years of precession only the position of Earth’s north pole will change, not that of the Sun’s north pole.