Correction – 07/07/2019: I’ve been informed that the journal title is actually Scientific Reports, not Nature Scientific Reports. I’ve edited the text, but not the title.

Michael Brown made me aware of a new paper in Scientific Reports by Valentina Zharkova called Oscillations of the baseline of solar magnetic field and solar irradiance on a millennial timescale. Michael has, in the past, been critical of Scientific Reports because of the dodgy science it seems willing to publish. This new paper seems, unfortunately, to be another such piece of science.

What this paper focusses on is the motion of the Sun around the barycentre of the Solar System, commonly referred to as the Solar Inertial Motion (SIM). This motion is a consequence of the gravitational influence of the Solar System planets, primarily Jupiter. What surprised me about the paper was a claim that

[t]he solar inertial motion means for the Earth that the distance between the Sun and the Earth has to significantly change (up to 0.02 of a.u) at the extreme positions of SIM, and so does the average solar irradiance, which is inversely proportional to the squared distance between the Sun and Earth.

This seems to be suggesting that the typical, or average, distance of the Earth from the Sun can change quite substantially due to the motion of the Sun around the barycentre of the Solar System. Although influences from the other planets in the Solar System can perturb the orbit of the Earth, the semimajor axis (or, average distance) is expected to remain constant. Suggesting that it can vary by up to 0.02 a.u. would seem to be at odds with our understanding of orbital dynamics.

However, since I’m easily confused, I thought I would actually look into this. I use a package called MERCURY6, which can integrate the orbits of planetary systems. You can download a version here. The default setup is to simply integrate the orbits of the Solar System bodies. So, I integrated the Solar System back in time for 800000 years, and then forward in time for 800000 years. I then plotted (below) the eccentricity of the Earth’s orbit.



The above variations are known as Milankovitch cycles. If you compare the above figure with the eccentricity plot here , you should see that it is essentially the same.

I then considered the motion of the Sun around the barycentre of the Solar System, for the period 1945 to 1996. This is the Solar Inertial Motion (SIM) that Zharkova’s paper is suggesting plays a key role in climate change through changing the distance from the Sun to the Earth. It’s shown in the figure on the right. If you compare it with this figure, it’s pretty much as expected. So, the code (as expected) seems to be working fine.

The claim in Zharkova’s paper appears to be that this motion of the Sun around the barycentre will substantially influence the distance from the Earth to the Sun. So, I then plotted this for the next 80 years (which was mainly so you can see the variations due to the small eccentricity of the Earth’s orbit). As you can see, the distance does change, but this is simply because the orbit is slightly eccentric ( ). The dashed lines show the expected perihelion (closest) and aphelion (furthest) distances.

So, even though the Sun is moving around the barycentre, the orbit of the Earth around the Sun is entirely consistent with an orbit of fixed semimajor axis and eccentricity (technically, the eccentricity does change, but not very much over a period of 80 years). We can even plot the semimajor axis of the Earth’s orbit, which is shown on the right. Here I’ve plotted it for a time of 1000 years and, as you can see, it is constant (as expected).

So, Scientific Reports appears to have published a paper that makes a claim about the Earth’s orbit around the Sun that violates some pretty basic orbital dynamics and that then uses this to suggest that most of our warming is natural. Firstly, you would hope that a Nature journal would at least pay particular attention to papers that make strong claims about important topics. Secondly, you would also hope that they would check that this isn’t based on some pretty basic error about an extremely well-understood topic. When it comes to Scientific Reports, such hopes would appear to be in vain.