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In the Framework of Newton's laws of motion gravity is a force. Therefore when a small body falls or is deflected towards a large mass like the Earth due to the force of gravity, it is said that the Earth also feels this force by Newton's 3rd Law.

In general relativity, the gravitational field of the Earth distorts spacetime, which deflects the path of the small body. In a strict sense, if we neglect the gravity of the small body, does the Earth feel any force or deflection, or respond at all?
How does this relate to the idea that in curved spacetime, momentum is not strictly conserved? Finally, if the Earth does not feel any reaction force, it seems that the Newtonian view that the Earth feels a reaction force but with negligible acceleration because of its overwhelming mass, is simply a fiction, falsifiable by hypothetical measurements of the required precision?

Qmechanic
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RC_23
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In terms of their reduced mass $\mu$ and orbital angular momentum $\vec{L}$, the distance between two masses evolves like a Cartesian coordinate in $1$-dimensional space seeing effective potential $-\frac{Gm_1m_2}{r}+\frac{L^2}{2\mu r^2}-\frac{G(m_1+m_2)L^2}{c^2\mu r^3}$, with only the last term exclusive to general relativity. This is symmetric in the masses. Of course, if one mass is much larger than the other, it's not accelerated as much. But the fact we can then try a test-mass approximation doesn't mean the underlying theory predicts an asymmetry, in either a Newtonian force or Einsteinian spacetime interaction.

J.G.
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