Imagine yourself positioned at the exact location of the sun. Try to ignore the heat. You’re rotating in such a way that the Earth is always directly in front of you. To make it easier, pretend none of the other planets exist. How would you describe the apparent motion of the Earth? I can think of three motions the earth would appear to undergo. Did I miss any?

The sphere would be spinning around its axis once every 24 hours. Nothing spectacular here; it’s the same as we experience in our reference frame - day and night.

The sphere would oscillate about about some mean distance from you. This is due to the non-spherical orbit of the Earth around the sun, or its eccentricity.

And the sphere would “bobble”. The north pole would point a little toward the sun and slowly it would point away from the sun until the south pole would point toward the sun. The cool thing is that the oscillation above and this bobble would be in phase. When the north pole would be facing the sun, the oscillation would be in a state where the earth would be further from the sun. And when the south pole faced the sun, it would be closer to the sun.

If you were in such a reference frame and didn’t know it was non-inertial, there’d be some funky things going on with the physics to explain the oscillation and bobble.

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