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?
Answer
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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