If Earth mass is doubled, what is the change of earth's orbit

I built a magic system that rationalized the creation of energy, so the energy source of magic is not a problem. (How this system works is not the main point of this question.)

When people keep using magic, the amount of energy on the earth increases.

Energy can also generates gravity. $$E=mc^2$$

If the amount of energy on the earth increases, the mass of the earth also increase. Will the change of mass affects earth's orbit? If yes, how would the orbit change? Assume $5.3748 \times 10^{41} J$ is generated by magic, that means the earth mass is doubled. (I need answers involve mathematics, thanks!)

What is the safe level of yearly generation of energy? Is it safe if the energy generation per year is below $8.694 \times 10^{24} J$ ? (equal to the mass loss per year) https://en.wikipedia.org/wiki/Earth_mass#Net_losses

Atmospheric escape of gases. About 3 kg/s of hydrogen or 95,000 tons per year[15] and 1,600 tons of helium per year[16] are lost through atmospheric escape.

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The mass created have the same velocity as the earth.

I need the math involved in accounting for the rest of the solar system and the eccentricity of the Earth's orbit,

@AlexandervonWernherr I designed the method to remove the same mass from the earth. (related to the rationalization of the creation of energy, it is pseudo science so I am not trying to mention it in a hard science post). I only put the problems of mass increase in an extreme way to see if there is problem.

posted about 7 years ago

fairytale‭

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