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It is true. Earth moving around the Sun, WITHOUT any other objects in the Universe, and WITHOUT considering General Relativity, would be an unchanging ellipse. However:* As a result of the warping of space-time (General Relativity), the periapsis will change over time. That is, the ellipse, while maintaining its shape, will change its position in space.

* Other objects, mainly in the Solar System, pull on the Sun and on the Earth. This will actually change the shape of the orbit over time.

The effect, in both cases, is very small, at least in the short term.

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