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This tag is for questions regarding the Newtonian model of gravity in which the force between two objects is given by $~GMm/r^2~.$ It is a natural phenomenon by which all things with mass or energy – including planets, stars, galaxies, and even light – attract one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides.

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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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