## The planets could be modulating solar activity

Carsten A. Arnholm, April 2008

# Update April 2009

The spin-orbit coupling hypothesis has been falsified.

As the original title indicates, this page was created as part of an investigation to try to determine what causes solar activity, and in particular if there is any way we can predict grand minima like the Maunder or Dalton. Charvátová and others have promoted the idea that angular momentum is conserved in the solar system through an exchange between orbital angular momentum of the sun+planets and the Sun's own spin, the latter presumably causing solar activity via inertial effects [as per Charvátová below]. This hypothesis is referred to as the spin-orbit coupling hypothesis.

One of the first steps in my investigation of this hypothesis was trying to verify whether the solar motion diagrams presented by Charvátová represented reality. The simulator software I wrote, and which is presented here, shows that indeed the diagrams are generally correct, the Sun does move as shown, if rather slowly. This gave some incentive to investigate further.

As the spin-orbit coupling hypothesis rests 100% on conservation of angular momentum, it does not really prove or displove anything to show interesting correlations of movements. So I had to test the hypothesis in a better way. To do that I developed the The Solar system 3d Gravitator which uses only Newton's law of universal gravitation to compute the movements of the Sun and the planets. Angular momentum has 2 main components for objects in the solar system: Orbital Angular Momentum coming from the orbital movements around the Sun, and Spin Angular Momentum coming from the spin around a planets own polar rotation axis.

Once the positions and movements are known, we can easily compute orbital angular momentum for the Sun and the planets. According to the laws of physics, angular momentum for an isolated system such as the solar system, must be conserved. So if we add together all the components, the result should be the same constant for any time. We might express it like this:

```K = SSAM + SOAM + POAM + PSOAM

where,
SSAM 	= Solar Spin Angular Momentum
SOAM 	= Solar Orbital Angular Momentum
POAM 	= Planetary Orbital Angular Momentum
PSOAM 	= Planetary Spin Angular Momentum
K 	= constant (ref. law of conservation of angular momentum)
```
As the planets have rather constant spin, and if we combine solar and planetary angular momentum (OAM = SOAM + POAM), we can write a simpler formula:
```K' = SSAM + OAM
```

In order for SSAM to be varying over time, OAM must be varying too (compensating to keep K' constant according to the conservation law). So what I had to do was to compute OAM for many different points in time and see if it showed any variation. Using 3d vector formulation for angular momentum, the result showed that OAM stays constant over time.

See the results in AM_1940_1992_20090327_r1.pdf, in the form of angular momentum graphs for all the major solar system bodies. Observe especially the last few pages where the Sun's orbital angular momentum is shown to be exactly balanced by the orbital angular momentum of the other plamets, meaning that OAM stays constant over time. Since K' must be constant, it means SSAM must be constant too: it does not vary over time. There is no missing angular momentum to drive any spin-orbit coupling.

### Conclusion: Spin-orbit coupling is not possible.

Below follows the original text:

### Ordered (left) and disordered (right) solar orbits

The orbit of the Sun around the centre of mass of the solar system is shown for different time periods from 1192 to 2134, using a heliocentric coordinate system. The ecliptic plane is in the plane of the screen. The green curves represent the orbit of the solar system centre of mass relative to the centre of the Sun. The position of the solar system centre of mass is computed from the actual masses and positions of the Sun and the planets. The yellow filled circle is the solar disk, the outer red circle is 2 solar radii from the centre of the Sun. The solar system centre of mass can wander up to ~2.2 solar radii away from the centre of the Sun.

The left column shows 50 year segments of the orbit at approximately 178 year intervals. There is a clear cyclic pattern, the orbit almost repeats itself when an overall rotation is taken into account. The orbit shows a rather ordered trefoil-like pattern. The ordered nature of the left column orbits is further illustrated in a GIF animation of trefoil pattern rotation.

The right column show varying length segments of the orbit at 150-200 year intervals. These orbits are intermediate disordered states between the ordered states shown in column 1. The 4 first disordered states coincide in time with historic solar minima.

• Wolf minimum (1280 to 1340)
• Spörer minimum (1420 to 1570)
• Maunder minimum 1645 to 1715)
• Dalton minimum (1790 to 1820)
• The current period (1985 to 2040) appears to be another disoredered state, looking a bit like the Dalton minimum.

Could it be that solar activity is driven by these mechanisms? If so, then we might expect the coming solar cycles 24 and 25 to be similar to the Dalton minimum (1790 to 1820), with very low activity.

### Acknowledgements

The images shown here were generated from my "Solar Orbit Simulator" program. The program calculates solar system orbits based on the theory presented in Astronomical Algorithms by Jean Meeus. The planetary position algorithms in the book are implemented in the AA+ library by P.J. Naughter. Based on the planetary position data as well as solar and planetary masses, the solar system centre of mass is computed. Inspiration for this work was found in Can origin of the 2400-year cycle of solar activity be caused by solar inertial motion? by I. Charvátová.