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The force on parts of an extended body in a non-uniform gravitational field, due to residual gravitational attraction between the overall effect on the body and the expected effect on the point in question. Tidal forces are most notably in large moons orbiting near their primaries.

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Is the distance between the Sun and the Earth increasing?

I think your reasoning is correct, but the values involved are very small. In one year r will increase by 1mm, so in 1 billion years it will have increased by 1000 km or by about0.01%
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