Earth is in a stable orbit sure, and I don’t think the aphelion and perihelion are changing but the orbit is slowly rotating around the Sun ultimately drawing a kind of flower-like shape. Why? Why does that not end up changing our aphelion and perihelion?
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The Earth’s orbit around the sun is roughly ellipsoid; there’s no flower shape in the orbit. Are you sure you’re not looking at the moon’s orbit? Since the moon is orbiting the Earth, which is then orbiting the Sun, the moon’s “orbit” around the sun is not regular; at times, it may seem to stop in space, or even travel backwards.
Can you give a visual of what you’re talking about? Because as far as I’m aware, Mercury is the only planet with significant precession of it’s perihelion.
Aphelion and perihelion do change a little bit each orbit. It’s precession. It’s caused by the earth accelerating as it gets closer to the sun and from the effect of gravity from everything else in the solar system. Stable does not fixed and constant.
The earth and moon orbit each other. The earth is not fixed as the moon revolves around it. They are a pair and rotate around a point between the earth and moon. So the earth’s orbit around the sun would look like a flower.
You’re talking about [apsidal precession](https://en.wikipedia.org/wiki/Apsidal_precession). It happens for a few reasons, but the dominant one is the effect of the gravity of the other planets. (Relativity also plays a role, because gravity is not quite the 1/r^(2) force it would be in Newtonian gravity; there’s an extra 1/r^(3) force unique to relativity that is very small but nonzero. But the relativistic effect, while historically important, is small relative to the effects of the other planets.)
Note that the effect on Earth is *very* small; it takes many millennia for the Earth’s orbit to precess around the Sun one time.
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