If gravity is transmitted by a four-dimensional fabric of spacetime and the Sun creates a bend in it ,which causes planets to orbit it , shouldn't the planets move in a circular orbit around the Sun rather than the elliptical orbit which they follow now ?
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For the same reason as in Newtonian gravity, which after all is an emergent framework from General Relativity: the equations have to be solved. In Newtonian gravity the orbits are solutions of conic sections, circles , elipses, parabolas and hyperbolas.
In general relativity, the apsides of any orbit (the point of the orbiting body's closest approach to the system's center of mass) will precess—the orbit is not an ellipse, but akin to an ellipse that rotates on its focus, resulting in a rose curve-like shape (see image). Einstein first derived this result by using an approximate metric representing the Newtonian limit and treating the orbiting body as a test particle
Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star
For him, the fact that his theory gave a straightforward explanation of the anomalous perihelion shift of the planet Mercury, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations
