Is the orbit of Earth currently decaying?

Question

As we know, interplanetary space is not completely empty. This would cause a drag to Earth, spiralling it towards the sun in a long enough timescale, which appears to be what has happened for many exoplanets. Also, gravitational radiation emitted by Earth is another contribution to decaying orbit.

On the other hand, there are several mechanisms which would counteract this. Mass of the Sun is decreasing due to nuclear fusion, and the photons which hit Earth concentrate a resultant force of $10^8$ Newtons, away from the Sun.

Taking all into account, what is the rate of orbital decay of Earth? It sounds like an incredible coincidence to me, if all these effects would completely cancel each other out.

Answer 1

You're mixing up some effects, and you're vastly overestimating the influence of pretty much all of them. Let's take them in turn:

• interplanetary space is not completely empty [which] would cause a drag to Earth, spiralling it towards the sun

  This is correct in that the effect is nonzero, but it is entirely negligible as far as planet-scale effects are concerned. This paper puts the density of interplanetary dust at $\rho_0 = 9.6\times 10^{-20}\:\mathrm{kg/m^3}$; it's a nice exercise to show that the effect of this drag over one year reduces the Earth's velocity by about two parts in $10^{18}$ at best; play that out over a billion years and you still have nothing bigger than a rounding error.

• which appears to be what has happened for many exoplanets.

  This is incorrect. Current models do indicate that many exoplanets show large migrations from their formation radii to their current position, but they also indicate that those migrations are due to gravitational interactions with other planets. That would be my gut-feeling guess for the long-term determinants of the evolution of the Earth's orbit, but given that we don't know for sure that the solar system is stable, those kinds of long-term calculation are at present impossible to perform.

• Also, gravitational radiation emitted by Earth is another contribution to decaying orbit.

  This is also nonzero and it is also entirely negligible.

• Mass of the Sun is decreasing due to nuclear fusion

  Again nonzero, and again negligible. As shown in this question, this would increase the radius proportionally to $1/M_\odot$. Given a fusion rate of $6.2\times 10^{11} \:\mathrm{kg/s}$ and a total mass of $2\times 10^{30}\:\mathrm{kg}$, that gives a fractional decrease of about $10^{-12}$ per year. Much the same goes for solar wind.

• the photons which hit Earth concentrate a resultant force of $10^8$ newtons, away from the Sun

  Again nonzero, again negligible, given the Earth's mass.

It appears that measurements of the change of the size of the Earth's orbit report an uncertainty bigger than the effect size. Given that we don't know which way it is changing, I would be reluctant to even put forward a guess as to which mechanism dominates.