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Calculate change in Earth's orbit due to mass loss in the Sun.
Each second, the Sun loses about 4 million tonnes of its mass, by its conversion to energy. More exact figures: "The Sun loses mass 4.289x10^12 g every second to energy. Or, in other units, the Sun loses mass 1.353x10^20 g every year to energy". (http://solar-center.stanford.edu/FAQ/Qshrink.html). Because the Sun's mass is diminishing, it will exert less gravitational attraction on the Earth. A calculation is wanted on how much the Earth's orbit changes (and its direction) over 1 million years, and over 1 billion years, because of this. Other influences on the orbit, and changes in the Sun's output, may be ignored. (ZBL#161).
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Darin Ragozzine's response in the attached Vault file shows that the effect of the loss of mass in the Sun by conversion to energy has only a tiny effect on the Earth's orbital distance, and is negligible compared to other factors affecting this distance.
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