When we study general relativity and the effect of a mass on the structure of space, we often use a visual description such as this one : https://i.ytimg.com/vi/GJ20reLYfvQ/maxresdefault.jpg where a massive sphere creates a hollow portion of a 2D space in which smaller spheres are trapped and revolve around the massive sphere.
But this description is not correct as the sphere is a 3D object and thus is not inside the 2D space. If we consider this 2D space, the sphere would become a disc and would bear the deformation as well, as would also the smaller discs revolving around it. Supposing all the discs are homogeneous, the center of the bigger disc would be the center of the deformation and (discarding the effects of the smaller disc) the big disc would be radially deformed. But the small disc would be deformed inhomogeneously, the part nearing the big disc would be more distorted than the rest.
If we come back to our 3D space, the big disc being the sun and the small disc a planet, then the sun would bear an radial deformation which we cannot see. But a small planet near the sun, such as Mercury, would be deformed and we should be able to detect this deformation from here on Earth. Is this correct, and has anybody seen or detected this deformation?
The Sun produces a tide on Earth just like the Moon. When they combine you get a "spring" tide, when they are out of phase a "neap" tide:
https://oceanservice.noaa.gov/facts/springtide.html
Both bodies also raise tides in solid ground but of much lower amplitude because the material cannot flow.
Bad luck ! The tidal forces only come from the gravity by a very small minority. The inertia plays the big role. 60 times more in the case of the Moon, several thousands more in the case of the solar tide.
Isaac Newton had the excuse that in the 17th century, the mathematics of the inertia was not yet done. One had to wait Elie Poinsot and Gaspard de Coriolis. In the 21st century, we have not more any excuse.
I'm aware there has been much discussion of that aspect, perhaps this will clear it up:
https://arxiv.org/ftp/arxiv/papers/1506/1506.04085.pdf
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