The Impact of Solar Mass Loss on Earth's Orbit

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Ian
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If the sun is converting matter to energy it must be losing mass at roughly one Earth mass per 43 million years (calculated from the solar constant).

How would the loss of solar mass affect the Earth's orbit?
 
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The sun also loses mass via the solar wind. This is presently about about 30% of mass loss due to radiation, but was significantly greater in the young sun. The combined effect is currently about 9e-14 solar masses per year. The orbital radius increases in proportion to the solar mass loss; the period increases at twice this rate.