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Is the Earth losing or gaining distance from the sun overall? Could asteroids over time add weight to the Earth and push it farther from the sun more than having a degrading orbit around the sun? Does asteroids and space dust increase the mass the the outer planets over sustaining or pulling the Earth from the Sun?

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What determines the Earth's orbital separation from the Sun is the total mass of the Sun and Earth, as described by Kepler's third law.

The orbital radius of the Earth is increasing because the Sun is gradually losing mass both by emitting radiation and through the solar wind at a rate of around 5 million tonnes per second (e.g. Noerdlinger 2008).

Any gain of mass through the accretion of dust or asteroids (by the Earth or Sun) is negligible by comparison.

This mass loss rate is only sufficient to widen the Earth's orbit by about 1.5 cm per year.

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