expansion of solar system

[Copernicus]

The earth orbit is expanding. Is the expansion of the earths orbit accelerating? What causes this expansion and what would cause the expansion rate to increase, stay the same or decrease?

[Van Rijn]

The earth orbit is expanding.

Do you have a reference for that?

Is the expansion of the earths orbit accelerating? What causes this expansion and what would cause the expansion rate to increase, stay the same or decrease?

I've seen calculations based on the sun's mass loss, as hydrogen is fused to helium, along with some lost from solar wind (though my recollection is that fusion is the currently dominant cause of mass loss). The rate of mass loss will increase somewhat as the sun's luminosity increases, but still on the main sequence. The calculations I've seen talk about an increase of the radius of the Earth's orbit by a few hundred thousand kilometers over ten billion years. I'm not aware of confirmation by observation, which I'd expect would be hard over human lifetimes.

After the sun goes off the main sequence, it will shed significant mass, and the Earth's orbit is expected to increase substantially (along with the other planets). On the other hand, there would be tidal effects that would counteract some of that. Ultimately, it's thought to be unlikely that the Earth would survive the sun's red giant phase.

[ExplorerAtHeart]

Mass loss in the sun is the main factor.

[chornedsnorkack]

What is the effect of perturbations by other major planets, like Venus or Jupiter, on the semimajor axis and orbital period of Earth? Which planets are currently losing energy and migrating inwards, which are gaining energy and migrating outwards?

[Hornblower]

What is the effect of perturbations by other major planets, like Venus or Jupiter, on the semimajor axis and orbital period of Earth? Which planets are currently losing energy and migrating inwards, which are gaining energy and migrating outwards?

The major axis precesses slowly as a result of the perturbations, with a period of over 100,000 years if I am not mistaken. The amount of eccentricity varies over a very long period from almost none to about 0.05, as compared to the present day value of about 0.017. My educated guess is that the orbital period may fluctuate slightly. For comparison, the Moon's period varies by some 1% in a cycle lasting several months as a result of severe perturbations by the Sun. The perturbations on Earth by the other planets are much milder.

If I am not mistaken, the planets are no longer migrating with respect to one another. That ended when the formerly massive swarm of planetesimals in which the were immersed was finally ejected from the solar system by gravitational perturbations imposed on it by the planets.