We know that the sun loses an amount of it's mass equivalent to the amount of energy it produces, according to the $E=mc^2$ equation. so the sun is losing mass every second. Does this affect the space-time curvature it creates. Or does this affect the distance between the Sun and the Earth. Does losing mass affects the gravity of Sun or other planets?
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3$\begingroup$ If you are only looking at the effect of the sun loosing mass, then the earth should get farther away over time, not closer. $\endgroup$– Olin LathropMay 28, 2014 at 14:18
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1$\begingroup$ Possible duplicates: physics.stackexchange.com/q/208/2451 , physics.stackexchange.com/q/71652/2451 and links therein. $\endgroup$– Qmechanic ♦May 28, 2014 at 14:26
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$\begingroup$ There are at least three effects to consider: solar mass loss by radiation, solor mass loss by out gassing and tidal angular momentum transfer. And I suppose viscus friction between the Earth and the out-gassed material. $\endgroup$– dmckee --- ex-moderator kittenMay 29, 2014 at 14:56
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The answer is here
There exists the effect of the loss of mass and therefore gravitational attraction between the earth and the sun but it is small:
If we assume that the Sun's rate of nuclear fusion today is the same as the average rate over those 10 billion years (a bold assumption, but it should give us a rough idea of the answer), then we're moving away from the Sun at the rate of ~1.5 cm (less than an inch) a year. I probably don't even need to mention that this is so small that we don't have to worry about freezing.
There is also the even smaller effect of the tides induced on the sun by the earth:
It turns out that the yearly increase in the distance between the Earth and the Sun from this effect is only about one micrometer (a millionth of a meter, or a ten thousandth of a centimeter). So this is a very tiny effect.
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1$\begingroup$ You might want to read arxiv.org/pdf/0801.4031v1.pdf. This suggests that, in 7.6 Gy, the radius of the earth will have increased 40 to 60%. The mass loss due to energy loss is dwarfed by loss due to solar wind. $\endgroup$ Jun 19, 2015 at 11:10
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$\begingroup$ What about the effect of friction with the cosmic medium (dust, gas)? $\endgroup$– AnixxJul 8, 2018 at 21:40
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$\begingroup$ @Anixx It must be negligible , the range of density I remember is from 1 molecule per cm^3 to 1 per m^3. Solar wind as in the link in the comment is a different story, that predicts engulfment as per comment above, but it is another story $\endgroup$– anna vJul 9, 2018 at 4:22