# Does the Sun's Gravity Decrease as it Loses Mass?

*Most recent answer: 12/20/2016*

- Jay (age 37)

USA

Yes, but not very much. Inside the Sun, nuclear fusion is converting hydrogen to helium at a rate of about 700 million tons per second, and about 5 million tons of that hydrogen mass is converted into other forms of energy (light, heat, neutrinos, etc). In kilograms, and using slightly more accurate numbers, that works out to about 1.35×10^{17} kg per year lost to other types of energy.

That certainly seems like a lot, and it is compared to the largest fusion energy release on Earth—the most powerful US nuclear weapons test only converted about 0.7 kg of mass to energy. But the mass of the Sun is about 2×10^{30} kg, so a loss of 1.35×10^{17} kg per year is only about 0.00000000000007% (7×10^{-14}) of the Sun's total mass. The force of gravity is directly proportional to the mass of the Sun, so it decreases by the same miniscule amount.

The radius of the Earth's orbit around the Sun is inversely proportional to the force of gravity between them.* If we assume the Earth's orbital speed and mass stay constant, the mass lost to energy in the Sun causes the radius of the Earth's orbit to increase by about (7×10^{-14})(1 AU) = 1 cm per year (which is actually more than I expected when I started the calculation!)

Rebecca H.

ps. I got the same surprising result. LeeH

*This assumes that the angular momentum is held constant. That's the right assumption here because the radiation carrying energy away from the Sun leaves in a symmetrical way, not changing the angular momentum of the system./Mike W

*(published on 12/20/2016)*