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I understand that Gravity will effect on space-time and create a curvature, which tells the mass how to move, therefore, the SUN can rotate smaller objects because it has stronger gravitational pull. I also understand that the sideways velocity keeps the Earth in its rotation circularly.

What I can't understand is: How curvature of Space-time moves the Object? How for example Curvature of space-time for Sun and Earth Looks like?

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  • $\begingroup$ Space-time curvature is given by the Riemann tensor, which is a field of four-tensors, this is hard to show. Moreover, you ask for a 3D model, but space-time is in 4 dimensions. However, you can just take the square root of the Kretschmann scalar which, for the Schwarzschild solution is $\propto 1/r^6$ (so the square root is $\propto 1/r^3$). It gives you the modulus of the Riemann tensor at any point of space-time. If you want to know how is the Earth attracted by the sun, you should solve the geodesics equations: wikiwand.com/en/Schwarzschild_geodesics. $\endgroup$ – Jeanbaptiste Roux Aug 25 '20 at 15:46
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I found two 3D models: https://www.youtube.com/watch?v=im9PuBdIjMY

Ref: https://www.youtube.com/watch?v=im9PuBdIjMY

enter image description here

Ref: https://www.youtube.com/watch?v=a7uTKwbsFtg

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