The loss of mass is a tiny fraction of the total. As its fuel is used, its temperature rises so it also expands. The orbital radius of the Earth is measured from the centre so is not affected by either of those. Gravitational interactions between Earth and the other planets will have a larger effect but don't follow a simple trend.

@George, does that means that the mass is not reducing?

Or the reduction in mass is inrevelant

Yes, that is exactly what is happening. Less mass of the Sun means, that the orbital radius - given there is no loss of kinetic energy - will increase. Associated with Earth's orbital speed (on average about 29 km/s) is a centrifugal force, which is Earth's mass times v2 / r, with r as the orbital distance. The orbital distance is fitting the centrifugal force opposing the gravitational acceleration, they are in balance. If the gravitational acceleration is reduced, due to the Sun's mass loss, this directly results in an increase in orbital distance to a point where the centrifugal force and gravitational acceleration balance each other out again.

The mass loss is 4*106 tonnes per second but the total mass is 2*1027 tonnes so the loss is a very small fraction, roughly one part in 1015 per year, or 1 part per million in a billion years. The Earth's orbit is 149.6 million km so that would be 150km over a billion years. The pull of Jupiter on the Earth causes a much larger variation.

I agree George, I just wanted to point out where this is coming from. Given the fact that the solar system is a multi-body system, the effect is drowned in noise of course.

Sorry Volker, I should have made it clear that I was replying to Emmanuel's question:

EOE: George, does that means that the mass is not reducing? Or the reduction in mass is inrevelant

I'm sure your additional description will be useful for Emmanuel too.

@George and Volker, thank you, I now understand better.

@Emmanuel You are welcome. :)