Website Paper Published.

After much encouragement from Nicola Scafetta and others I have finally produced a document that summarizes the articles on this site in a scientific format. The document is 15 pages in PDF format and hopefully will enable easier understanding of the entire theory presented on this site.

The paper was published May 31 2010 in Physics/Geophysics, Cornell University Library.

Thanks to G. E. Pease for providing peer review and content.

Also many thanks to Nicola Scafetta for providing advice and initial peer review.

Download PDF file (2.4mb)

Spin Orbit Coupling – The Missing Angular Momentum Found?

Spin Orbit coupling is the transfer of orbital angular momentum to spin momentum between orbiting bodies. Total angular momentum (AM) is made up of orbital & spin momentum and both must balance. If there is an imbalance between solar AM and Planet AM we might have the missing AM to fuel a rotation change at the Sun. In a recent paper by Ian Wilson et al  “Does Spin Orbit Coupling Between the Sun and Jovian Planets Govern the Solar Cycle?” Ian discusses a viable theory of spin orbit coupling but also states there is no mechanical link. Perhaps now there is a new line of inquiry that may provide this mechanical link.

AM must always be conserved and this basic principle of the universe is seen all around us, one example is the Earth/Moon system where the reducing rotation speed of the Earth caused by tidal friction sees a conservation where the Earth/Moon distance increases by about 5cm a year.

Spin orbit coupling could be one area that may provide a link between the Planetary motions and a changing rotation speed of the Sun, basically if there is a mismatch in orbital AM it can be transferred to spin momentum (rotation speed). The Sun has it own angular momentum as it orbits around the centre of the solar system. 99% of this comes from the gravitational affects from the combined positions of the Jovian planets, this is clearly seen in Carl’s famous graph. Each planet also has its own AM which is  mass x distance x velocity, and as I have shown previously AM can be calculated using the SSB (solar system barycenter) or the Sun as the orbit axis point. If we measure the planet AM it can be compared against the solar AM and if done correctly any variation or missing AM can be determined. In the past this has been done by wiggle matching which is comparing 2 graphs, rescaling one to fit the other and comparing. This method does not provide mathematical results and the detail can be hidden in the scale of the graph.

I have always wanted to do my own comparison and in particular use the Sun as the orbit axis point when calculating planet AM. Gerry and I have collaborated on this project and combined our skill sets to produce an outcome.

To compare planet AM with Solar AM the inertial frame should be the same. The planet inertial frame calculated from JPL was another surprising result which looks to suggest it is in the barycentric frame rather that heliocentric. For our project we needed to make allowances. The project calculates planet AM using the Sun as the orbit axis point and the solar AM is calculated using the SSB as the axis point, then the solar AM is subtracted from the planet AM and the results recorded, Gerry explains ” By subtracting the solar orbital AM, we are making a simple Galilean transformation from the barycentric inertial frame for the freefall motion of the Sun about the solar system barycenter to the inertial frame of the Sun itself.  The reason we have to do this is that your planet position and velocity vectors are heliocentric.  Coordinates, and properties like AM derived from them, have to be in the same inertial frame as the inertial body (or alternatively a barycenter) to which they are referred.  That’s why I was surprised to see that the heliocentric Horizons data was referred to the barycentric frame used by the JPL DE ephemerides.”

The planet AM values were carefully calculated specifying the planet barycenter coordinates where applicable, and using planet mass measurements (13 decimal places) and velocity/distance coordinates xzy from the JPL Horizons database. The asteroids Ceres, Juno, Vesta and Pallas have been included. The initial planet AM values when summed showed a moving variation (not a constant as some have suggested) of each daily measure and when wiggle matched, lined up precisely with the solar AM curve, BUT there is detail missing that must be uncovered.

The next step was to subtract the solar AM from the planet AM to achieve the same inertial frame. The finished data showed a remarkable result that is still a work in progress value but at this stage looks promising. We have calculated an underlying fluctuating AM value that nearly follows the same curve as previously calculated by Carl. It makes up roughly .0000035% of Jupiter’s AM and could represent .2% of the average solar AM. These calculations are still in progress.



Here we have a comparison of Solar AM and the Planet AM variance…there is no way we can wiggle match these two data sets, the divergence points are of particular interest. The spreadsheet will be available in full detail shortly.

UPDATE: Some food for thought, below is the solar AM vs solar velocity graph (another wiggle match attempt). I have mentioned before that the two curves go out of sync which is strange for 2 data sets that are reliant on one another. It may be just a result of the mix between distance and velocity. The bigger variances look to line up with the bigger variances on the Sun vs missing AM graph.

If there proves to be an imbalance between solar and planet AM it could be traded off in velocity or spin or distance. Distance is unlikely and as seen the velocity does not follow a consistent pattern (although it is still a pattern). The first disturbance of the set (green arrows) sees a decrease in velocity, the second disturbance shows an increase…its not uniform. The blue dots also showing a divergence in the same places as the previous graph.










Sunspot Cycle Phasing with Conjunctions of Jupiter and Inner Planets.


A presentation by G.E.Pease

The Sunspot cycle which averages 11 years is still a mystery, with no real conclusive science that has been put forward with any certainty on what controls the varying length of the Sunspot cycle.

Previously in my Neptune/Uranus article we discussed the work of Desmoulins who has graphed the “most aligned days” of Jupiter, Earth and Venus which shows a good correlation with the sunspot record. The two sets of data can drift away slightly but have always kept in sync in the last 400 years. Currently The most aligned days is lagging behind the  Sunspot record slightly and going by past occurrences should catch up during SC24 max. Hung as also done some similar research showing the same result as well as Ulric Lyons who presented his case on this blog last year.

Now we have another study by G.E.Pease which backs up this previous work and provides many diagrams and tables to support the Planet Tidal Theory. The presentation is in powerpoint format and can be downloaded HERE

Desmoulins graph

Desmoulins graph: green peaks =JEV most aligned days

Jovian Angular Momentum Graphs.


Several months ago I attempted to find some sort of data or graph on the angular momentum (AM) of the Jovian planets. After an exhaustive search it seemed as though nothing would be forthcoming. While there have been attempts to graph the Jovians using the solar system barycenter (SSB) as the orbit axis point, my research has suggested all the solar system planets orbit the Sun. Using the SSB as an axis point might be useful for some analysis, but it still remains an inaccurate method of calculating a planets AM if the orbit axis point is the Sun. The orbit axis point of the Jovians is still a contentious issue, but I believe the results of this project will add further evidence that indeed the Sun is king.

Using JPL Horizons I can retrieve the necessary XYZ coordinates and velocities and plug them into Gerry’s angular momentum formula. Many thanks go to Gerry, this project would not have been possible without him.

It must be noted that the JPL data for each planet uses the Sun centre for calculating distance. Technically this is still not correct and the Sun/Planet barycenter would be more accurate but at this stage I am not aware of this data being in existence.

Jupiter Angular Momentum Graph.

jupiter angular momentum graph

Very evident is the influence of Saturn along with the timing of the Jupiter perihelion (closest orbit point) and aphelion (furthest). The blue line is a moving average with the background grey areas being the actual data taken every 5 days. Because the centre of Sun was used as the axis point the actual data is a little choppy (theory). Although the modulation of the planet AM is obvious, very little of this change would be felt at the Sun. For further data on the Jupiter axis point and orbit perturbations see my previous article here:


Although over a shorter period the Planet AM graphs using the SSB as axis point showing a clear difference…

Neptune Angular Momentum Graph.

neptune angular momentum graph

The Neptune angular momentum graph is quite different, being on the outskirts of the solar system the data is less choppy and the clear influence of Jupiter every 13 years approx is quite staggering. The majority of Neptune’s orbit perturbations are in line with Jupiter, only the modulation of the peaks and troughs is influenced by the remaining Jovians.

Notice the very clear difference between the 2 axis points. Source

The SSB derived Neptune graph is clearly a product of the sun moving away from the SSB and dragging Neptune with it, this gives a false reading in the Neptune distance measurement which can also be seen on the Jupiter SSB graph at 1970. I believe the latest Jovian AM graphs prove the existence of the Jovian orbit axis point and also show the correct planet AM data (as near as possible to date). Another outcome of this research will be to nail down exactly what proportion each planet contributes to the overall AM at the Sun. The project is still incomplete but the Jupiter proportion looks to be about 60%. Saturn and Uranus graphs to follow.

UPDATE: P.A.Semi has a paper at

where he produces graphs of all planets calculating planet AM using both axis points. His data is in complete agreement with mine (using Gerry’s formula) and he also shows long term views of the SSB axis graphs.


This long term view of Neptune is particularly interesting, its shows the 172 year down spike each time Uranus is in conjunction, which moves Neptune closest to the SSB and also shows a background trend. The elephant in the room though is that all SSB graphs show a modulation of planet/SSB distance, where as the Sun centered graphs show the planetary perturbations. The failure of the SSB centered graphs to show the all important planetary perturbations suggests to me that all our solar system planets have the Sun as their axis point.

Gerry and I are currently working on a project looking for the missing AM that could finally give a solid link to the Spin-Orbit Coupling debate. Our initial results are very encouraging but we need to double check the data…stay tuned.

Earth's Future Climate.

Click on pic for larger view

Reader Ron De Haan suggested a graph showing future Angular Momentum Disturbance Strength might be of interest. We only have JPL data out to 3000AD so this is the current limit, but the outcome is indeed very interesting. If the Solar activity follows the Angular Momentum trend we are headed for another Medieval Warming Period type era on even a grander scale.

After the Landscheidt Minimum which will be short and sweet, there looks to be another Dalton type event which is not considered all that strong. After that the planet will stay on a warm plateau for hundreds of years, lets hope we have learned by then that the warming we will enjoy is a natural state. The graph shows us how unusual the preceding strong Grand Minima are in our history, which was ruled by strong Type “A” disturbances or as Gerry calls them “Retrograde Bumps”. From here on the AM strength is moving to weak and gradually the disturbances are moving back to Type “B” which are known for periods of reasonable solar stability. So there is no need for pessimism, our children will have it good.

The JPL data used to create the AM graphs as per Carl’s Graph has a range from -3000 to 3000, but I am working on another quantifying method using purely the Jovian planet angles which should allow us to check against the complete Holocene record as well as looking out as far as necessary. Thanks to Tayla Sharp for helping with the graph.



Angular Momentum Disturbance Strength.

This is the first time Angular Momentum Disturbance Strength has been quantified and is depicted by the purple line in the above graph. This purple line shows how Angular Momentum Disturbance Strength is the driver of solar downturns, it is the background curve of the proxy records. The method used is a preliminary method using visual observation of each disturbance of the graph period. With the discovery of Carl’s graph we are now able to easily see the different types of disturbance that comes in groups every 172 years average.

These disturbances always line up with periods of solar downturn. The Solanki/Steinhilber data shows regular solar downturns that vary in intensity, by observing the shapes of the disturbances that align with these downturns we are able to see a pattern that is repeatable. An example of this is the regular appearance of strong Type “A” disturbance occurring at times of severe grand minima. Weak Type “B” disturbance always is associated with very minor grand minima. There is no indication of this pattern not following suit except in the rare occasion of strong Type “A” disturbance not fully firing when not meeting the “Wilson’s Law” test. This test states that for a disturbance to fire the Jupiter/Saturn opposition or conjunction must happen before cycle max. This has been tested over the Sunspot numbers but is not available for accurate testing beyond that as the cycle max is not known. 1830 and -530 are examples of this phenomena.

Described in previous articles Type “A” is nearly always stronger than Type “B” disturbances. Type “A” affecting the inner loop of the Sun’s path around the SSB and Type “B” affecting the outer loop. The Sun’s velocity is 100% higher when traveling the outer loop.

By matching the disturbance patterns with solar downturn strength I gave each disturbance a score. Disturbance’s that align with deep grand minima (on a constant basis throughout history) get the highest score and so on.

On the solar proxy graph at the top of this article I have recorded the strength of each disturbance group that comes along every 172 years average. This was achieved by scoring each individual disturbance and summing. The individual disturbances can be viewed at and


This table is a result of that process. The “Count” column being the sum of the individual disturbances for each 172 year centre. To plot this trend on the Solanki data it needs to be scaled and inverted. For the scale I tried to approximate the Solanki derived sunspot number and use a conversion process to do this within a set scale. For every increment of the “Count” I have associated it with 4 Solanki sunspots as seen on his graph. This gives a reliable method and displays the trend accurately. Once the conversion was done the data was entered into the Solanki spreadsheet.

Although the counting process is subject to the eye of the observer resulting in perhaps a slightly different Count, the overall trend will still be evident and should not vary greatly from my analysis. Future Counting could be performed more accurately by measuring the precise angles of the Jovians during individual disturbances and rating them according to a set scale. The ideal time to measure the angles is when Jupiter and Saturn are in opposition (measuring Neptune & Uranus angle in respect to Jupiter) for type “A” and when Jupiter and Saturn are at conjunction for type “B” disturbances. The position of the hump at disturbance is a direct result of the timing of Neptune and Uranus in respect to Jupiter.

Below is a table showing the conversion process.


The spreadsheets is available from



New 10Be Study Confirms 14C Record.

The Carbon 14 record (INTCAL98) used as a solar proxy as used by Solanki and Usoskin is sometimes called into doubt. There have been attempts to cross check the results using  beryllium 10 (10Be) comparing running means over different time periods. But now we have a new report that produces 9300 years of 10Be data that can be compared with the 14C record. Initial results show a very promising match up.

The new report which can be found here shows one graph in particular that can be used to cross check the 14C record. Click on graphs for a full size view.

The comparison graph is a first pass and should be extended the full 9300 years and if possible the new data needs to be merged with Solanki’s data in a spreadsheet. My method of comparison as follows: The 14C data is taken directly from the Solanki data and graphed via excel spreadsheet. The Steinhilber graph saved from the original document is traced onto a transparent gif image layer and saved then overlaid onto the original Solanki graph. The Steinhilber overlay is then rescaled for X & Y coordinates to match the original Solanki scale.

There are a few anomalies between the 2 data sets but overall a very good match is found. The 14C record is now confirmed with perhaps some minor anomalies but some confidence is expected. The planetary line ups with their disturbance to Angular Momentum that cause Grand Minima are now validated by another independent source.

Vale Carl Smith.

Wednesday 24th June 2009 at 3:35pm at Gold Coast Hospital (Wed gold coast time) Carl Smith lost his battle with cancer. Its a very sad day for his family, friends, associates and myself. I didnt have a lot to do with Carl and respected his wish of not interrupting the remaining quality time that was left for him.

Carl will be sadly missed and I know a lot of people have spoken highly of him. Carl was the originator of this website and only gave up the day to day running when he learned of his severe illness. He will be remembered for perhaps making the biggest discovery in the Planetary Theory Arena, Jose and Landscheidt were in the ballpark but Carl nailed it with his Angular Momentum graph that today allows us to predict solar activity and Grand Minimum down to the solar cycle.

I will continue to progress Carl’s work , he was a great man.

May I pass on sincere condolences from us all to the Smith Family.

Geoff Sharp.

UPDATE:25 july 2009

Carl’s brother Dave is keen to ensure that Carl’s work wont be wasted. I personally wont let that happen and consider myself with a new life’s work.

Dave has kindly donated a new domain and webspace to further this cause which will be run in conjunction with the original landsheidt auditblogs site.

The new site will be a showcase for Carl’s discovery and the further work I intend to do on the same topic. The site has all the bells and whistles and I encourage all to register.

The new site can be found here:


200 Year Solar Cycle Prediction

Predicting solar cycle modulation using angular momentum is relatively easy, but like any prediction it needs to be tested. Interested parties who rely on solar activity predictions might like to make a copy for future reference and compare with the regular methods of prediction which typically only go out for one cycle, which can hamper long term planning in some industries.

One thing we cannot predict is solar cycle length, so this prediction is more about modulation rather than precise timing of upcoming solar cycles. One other factor in play is whether “Wilson’s Law” will contribute to future grand minima, by 2190 I predict we will know the mechanics of this law. As can be seen here and on the 11000 year 14C graph there are no high solar activity peaks at times of low angular momentum.

There is a possible case for a repeat of the 1870 type reduction in solar activity at 2050, but this time around the disturbance is very weak as the Jupiter/Saturn angles continue to weaken. On most occasions we are presented with 3 disturbances per cycle but in the current cycle we may only get 2, SC28 & SC29 remain the subject of more research.

Below is Carl’s now famous original graph showing angular momentum in a different form. The green arrows showing times of angular momentum disturbance.

New Angular Momentum Graph.

Its been a long time coming, but this graph is an easier way to appreciate the effect the outer planets have on our Sun. This is the same information Carl used in his now famous graph, but instead of a sine wave we have the absolute power shown in a conventional form. Angular momentum can be measured in different ways leading to confusion. Now we have a reliable power guide directed at the Sun from the Jovian planets.

Source: Carl’s JPL data assuming 2E+47 as a zero point and inverting all points below.

This next graph shows the sunspot cycle superimposed on the angular momentum strength…showing strong correlations. Notice how after a sudden slowdown the high angular momentum peaks are not fully utilized.

UPDATE 11/05/09:
The same graph but with the solar orbital velocity as it orbits the SSB overlaid. This shows the connection between Angular Momentum and the fluctuating speed of the Sun as it orbits the solar system barycenter, this orbit path being controlled by the outer planets. Conservation of angular momentum has consequences.

Below: This time I have compared the Sun’s velocity with the typical AM graph as per Carl….the altered velocity obvious at 1650, 1830 and 2010 which also correspond with radical Solar path changes caused by the outer planets. The Sun’s orbit speed is surprisingly slow and goes from around 30 km/h up to around 60 km/h (100% increase) when Angular Momentum is at its highest. This still allows the Sun to move over 1.5 million km from the SSB over 5 years. Note when the two lines diverge there is a corresponding slow down in solar activity.

This graph showing the velocity of the Sun is a product of Angular Momentum (red line = velocity). Interestingly velocity can exceed AM and also not use the full potential of AM. A conservation is required? Is there another force involved that modulates the usage of AM?

Now the question is, are there any other consequences, is the changing velocity also changing the rotation speed of the Sun as well. I have been searching for solar rotation rates but it seems we are unable to record this presently, there are no fixed points on the surface of the Sun which has a highly movable outer layer. The idea of a solar rotation change due to the planets is highly speculative, but until we can get an accurate measurement of solar rotation it cant be ruled out. If we could record the solar rotation accurately this discussion would be over…but we CAN record the rotation rate of Earth, and I postulate on the following with some brain food…… The Earth’s rotation rate is calculated by recording the Length of Day which shows our longest days (slower speed) are always in January. Theories suggest this is because of weather patterns that always occur in January but it also coincides with our planets fastest velocity which shows a very regular pattern each January.

Interesting pattern similar to the Jovian orbits…expecting earths orbit to follow the same trend.

Length of day graph from USNO showing the yearly rotation speed pattern of our planet. The slowest days are in January each year, which coincides with our closest approach to the Sun in our slightly elliptical orbit.

Which Point do the Jovian Planets Orbit?

This is an intriguing question, I have read many different opinions but nothing to clearly substantiate their claims. Others in the Scientific arena when pressed are afraid to give an answer. Checking the JPL data which is an ephemeris produced by the Jet Propulsion Laboratory shows that Jupiter certainly doesn’t orbit around the SSB (although at first because of an error I made, it looked as if it did) and probably orbits around the Jupiter/Sun barycenter. After checking the Jupiter/Sun distances (which I will refer to as the radius vector which is quite different from the semi-major axis) through JPL it became obvious there was a substantial variance each orbit that was measured each time in the same place. Originally I saw this as an opportunity to look for a solid link between Angular Momentum and the Solar modulation re the planets, but soon discovered Jupiter and all the other planets have a modulating Perihelion/Aphelion distance. The quest was on the find out why and involved many weeks searching for any data I could find. Others on this site got involved and I even emailed an Astronomer but to no avail, very sparse detail available. Dr Svalgaard suggested it was a result of planetary perturbations and while correct his understanding was also far from complete. Below is an account of the progress along with what I think is the complete answer to what perturbs Jupiter and how.

My research shows the Jupiter/Sun distance varies on average 300,000 km each orbit of Jupiter. Check graphic above.
The Earth is seen to orbit the Sun directly. If we use NASA’s JPL data it shows the Earth/Sun distance is varying by 0.0001AU per year (approx 15000 km). The AU measure is the average distance between the Sun and Earth. If we measure The Earth to SSB (solar system barycenter) distance it shows a much larger variance.
What I have done is measure the Jupiter/Sun distance at exactly the same point in the elliptical orbit of Jupiter each 4331.572 days, this should isolate any aphelion/perihelion changes. I also measured the Jupiter/SSB distances.

As can be seen in the first graphic there is a large variance each orbit between BOTH measurements (Sun & SSB). This makes it hard to pinpoint any point of orbit, although the variances seem smaller on average with the Jupiter/Sun data. I also compared the Heliocentric longitude (angle away from Sun) and found each Jupiter/Sun reading had an angle of 359 deg, but the solar position at perihelion does return very closely to the same position each orbit.

The above graph was made from reliable data by blogger JimP (thanks for the spreadsheet). Once blown up it shows some remarkable detail. It shows the Perihelion distance (closest point) for each Jupiter orbit over 400 years. There is a definite pattern, what causes this modulation? The movement between the closest and furthest perihelion is 1.2 million km’s , the Sun is capable of moving 1.5 million km’s from the barycenter, Neptune’s radius vector moves by 1.4 million km. Importantly the corresponding movement at the other end (aphelion) is the same value on each orbit but in the opposite direction, if one end shortens the other end lengthens.

Jupiter/Sun distances 1600-2020 with Jup/Sat conjuncture, Jup/Sat opposition and Jup/Sat quadrature (square) positions plotted for every third occurrence. Note the phase change around 1880. If the Variance in distance is caused by angular momentum J/S conjunction & J/S opposition both produce high angular momentum. Regular reader lgl and myself suspect the other Jovians need to come into the equation, but what is needed is a new method of displaying angular momentum other than Carl’s graph. A total strength with both J/S conjuncture and J/S opposition shown as high points instead of a sine wave is required, manipulation of the current JPL data via a spreadsheet can do it. Update: There is a new article covering this.

Saturn/Sun distance showing the same 60 yr pattern as Jupiter. After 1880 they are in unison with Jupiter but not before. There is a reason for these fluctuations but I have not found any literature on this phenomena.

UPDATE 13/05/09:

This diagram has been adapted from “Linkages between solar activity, climate predictability and water resource development” Alexander et al. Bailey has been criticized for claiming the Sun-Earth distance varies by the Sun-SSB distance, although not correct there is a fluctuation caused in the same manner as per Jupiter but to a smaller degree….0.0001 AU.

UPDATE 27/05/09: Here is another suggestion Dr. Svalgaard has provided to explain the modulating Jupiter Perihelion.

“The general principle is that to change the orbit, you have to apply a force along the orbit, so Saturn’s effect is largest when it is ‘to the side’ (approximately quadrature I think the astrological term is), rather than in conjunction. All of this has been understood for 250 years, and there are no other forces involved. Saturn doesn’t ‘push’ (gravity is attractive, not repulsive). And the Sun is not ‘dragging’: the force is always along the line connecting two bodies.
To recapitulate how Kepler’s second law works: To move an orbit out a bit (increase perihelion distance if you are near perihelion), you apply a force along the orbit in the same direction as the movement of the planet, e.g. by Saturn being ahead of Jupiter. That force produces a ‘delta-v’ (google it), which ‘lifts’ the orbit a bit out of the gravitational well, to another (higher) orbit, where it actually moves slower than before. Because of the periodic movements, the lifting is counteracted over time by a similar but oppositely directed movement, so that the semi-axis stays constant. This takes a couple of orbits to accumulate, so you have to consider the integrated effects over many years.”

There is substantial merit in Dr. Svalgaard’s rejigged explanation, but there still remains some pertinent questions. The explanation works well for perturbations occurring in the 1/2 to 3/4 region before Perihelion, but perhaps not so well in others. Dr. Svalgaard explains its a matter of the smaller background oscillations that make it hard to track the source of the perturbation. This is plausible but maybe a little weak and may be the reason it is near impossible to find any reliable data on this topic via the web. In particular I have questions why the “force along the orbit” fails to work when Jupiter approaches Perihelion and actually looks to have an opposite effect. Remember, when Jupiter & Saturn are in conjunction the Perihelion distance is at its shortest, but as you can see in the following diagrams the substantial pull along the orbit fails to elevate Jupiter’s orbit to a higher state.

The red dots signifies Perihelion in this 1762 example:

I wanted to see the perturbation affects plotted with successive orbits to see how the planets contribute to Jupiter’s orbit changes. Although fairly easy when you know a couple of tricks (thanks to Dr. Svalgaard) this task took me many days. I plotted the JPL data into excel and once the orbit was expanded to a size too big to display here it was easy to see each individual orbit. I was lucky with my data selection because it included a very strong perturbation of the 1987 Perihelion. The orbit has Jupiter doing a fly past Saturn, Uranus and Neptune before Perihelion which manages to take it away from its more normal path by 6 million kilometers. Once Jupiter passes all 3 planets its orbit is dramatically “braked” which brings it back into line around Perihelion, but still manages a very long perihelion distance. This is a good example of the perturbation theory in practice.

The corresponding planetary view shows the relative positions of planets which line up with the above average perturbation.

So do we have a situation where the perturbation theory works in some parts of the orbit only? Could other forces be overriding this perturbation? The orbit changing mechanics have been described as speeding up the planets velocity (I have serious reservations that this occurs) which raises it up the gravity well to a higher orbit before settling into a slower overall velocity.
UPDATE:After much research I think I finally have the cause for Jupiter’s Perihelion distance modulation….and it surprising how little is known or published in this area. The above example is not worded very well and leads you to think an acceleration lifts the orbit higher then slows the velocity (that’s at least how I read it), from what I now understand it actually happens in reverse…the acceleration moves the orbit closer (following Kelper’s 2nd Law) but then unlike a rocket using boost, Jupiter is then immediately subjected to deceleration from Saturn’s gravity which slows velocity in turn lengthening the radius vector or raising Jupiter to a higher orbit. As Jupiter moves further away from Saturn the Sun takes over and reins in its sibling and waits for the next perturbation. So now it becomes obvious, and completely explains why a Jupiter/Saturn conjunction causes a short Perihelion, Jupiter is always in acceleration mode during this lineup which causes it to move closer and the plotted orbit agrees. Also of note, Neptune and Uranus also help out and can be strong when together as we see elsewhere on this site.

The orbit spreadsheet is able here:

Latest Solar Differential Rotation Information.

Click on images for a larger view.

Some may be aware I have been trying to track down if we are experiencing any change to the differential rotation rates of the Sun. If angular momentum changes can be tied to solar differential rotation rates, we might have a solid causation. Solar differential rotation can be measured in different ways but basically, different parts of the Sun rotate at different speeds, keeping in mind the Sun is not a solid object. The equator rotation rate is around 27 days, with the poles at around 34 days, as seen from earth. But there is a lot more to consider, if we look at the solar equator there is another speed difference showing the possible rotation speed of the Sun. Recently I heard back from Dr. Rachel Howe from NOAO who specializes in this area, and the results were quite amazing.

Her hot off the press paper here:

The graphic above is a Doppler image from GONG which shows the regular patterns of the changing rotation speed of the Sun with the yellow sections being the fastest. The image is taken at 0.99R which is around 7000Km beneath the top of the Convection zone. It is thought these patterns (darker zones mostly) are generated at the Tachocline (a thin sheer layer between the radiative core and the Convection zone at around 0.71R) and they spiral out to the top of the Convection zone and are subject to spin momentum like a garden sprinkler. As we go deeper, like the graphic below (0.99R to 0.84R) the patterns break up, which is not what I would expect. The overall scale of the pattern seems to remain but loses clarity. Perhaps this is a condition of going deep with Doppler equipment or maybe the frequency is a lot higher as we go down?

Dr. Howe’s paper suggests that the travel time interval from Tachocline to the solar surface is around 2 years and, as we will see, these Doppler patterns align very closely to the sunspot butterfly image when overlayed. If so, then sunspot activity is a historical account of what happened at the Tachocline 2 years ago.

In the next graphic we go back further and it displays an apparant rotation change. During past grand minima, observations suggest a faster rotating Sun, as can be seen at the equator. After 2000 there is a greater acceleration occurring, but we need to keep in mind that the surface is not static. UPDATE May 2015, recent information suggests the opposite, ie the rotation rate has slowed during SC24

Also noted is the much longer length of cycle 23 (96- ?) compared to cycle 22 (86-96). So here we see two direct links to the highly possible effect from Angular Momentum created by the Gas Giants, increased decreased rotation rate and the stretching of the cycle length as the Sun takes its abnormal path every 172 years.

The last time this occurred was in SC4 just before the Dalton Minimum and the retrograde motion we are now part of is very similar to SC4. On average the retrograde orbit (purple) is around 9 years, SC23 & SC4 have orbits of over 11 years.

Below is a graphic I produced by rescaling the SIDC sunspot butterfly plots then overlaying over Dr. Howe’s graphic, as can be seen there is a direct correlation between the two sets of data. It is thought the sunspots are created at the poleward edge of the fast and slow zones (yellow /green), but I am sceptical. The slower zones are what travel all the way to the Tachocline (its like a “brakes on” feedback) and we might have to possibly shift the overlay to the right to allow for angular momentum as the Doppler image is taken from 7000Km below. I have asked Dr. Howe her opinion. UPDATE May 2015: New data suggests that sunspots are created on the yellow flows.

Animation: Dr.Howe’s diagram with the SIDC butterfly sunspot scatter with re scaled X & Y coordinates to match..

You can see in the pattern why early cycle sunspots appear at high latitudes then gravitate to the equator. Looking at butterfly graphs of solar activity, they suggest the majority of sunspots occurring between -40 & +40 latitude, ruling out the dark blue/blacks areas at high latitudes.I speculate they are reserved for Coronial Mass Ejections. The purple arrows show where a “flow” starts.

Some more speculation:  Some suggest the modulation of a sunspot cycle is governed by the strength of the solar poles, which are a late product of the previous cycle (this product can also be severely downgraded as seen in SC19) . Maybe the poles are a player, but not the main influence as the main source of power is coming from the Tachocline. This is where the poles eventually get their flow from. But it may explain why we have a weak cycle after a grand minima cycle, as the following cycle after could have very low pole strength.

Worth saving and blowing up to see the detail.

Angular Momentum could vary the speed of the outer convection layer of the Sun, creating less torsion on the Tachocline sheer layer, resulting in reduced solar activity 2 years later. The Doppler diagrams will reveal some of this as we move forward and I believe these diagrams are an invaluable tool and would greatly appreciate access to this data easily, like the WSO polar strength graph and watch each move through the cycle. I informed Dr. Howe of this, lets hope it gets something going.

Geoff Sharp.

11000 year Solar Record & Angular Momentum.

Click on the graphs for a full sized view and then magnify.

Graph 1. shows how the power of Angular Momentum matches up with the movement in the 11000 year 14C graph. Each high point on the 14C graph lines up with the regular high points on the Angular Momentum charts. Even more importantly, each Grand Minimum also lines up with the Grand minima type disturbances on the Angular Momentum charts. Strong Angular Momentum gives us strong Grand minima and also the high peaks on the 14C graph. Weak Angular Momentum gives us weak results, and lots of shades of gray in between.

Graph 2.This graph shows all the angular momentum disturbances taken straight off the angular momentum charts showing each individual Type “A” & “B” disturbance as well as each non Grand Minima angular momentum high, each green or red square corresponds with grand minima type angular momentum that comes along roughly every 172 years, these disturbances line up with almost all downward trends.. Its a wave of power over the centuries, with very strong correlations on each peak and trough and shows how the changing angles distribute the phases of type “A” & “B” disturbance. Type “B” normally produce weaker Grand Minima, but also spread out the available opportunities (more than 3 red or green squares) each 172 yrs avg. Other observations show during times of weak angles the Sun is able to recover quickly from the slowdown and doesn’t look to remain in Grand Minima mode for several sunspot cycles as we observe recently. Remember as in 1790, Grand Minima can occur on the disturbance or just after. I recommend saving this file and enlarging to see the full detail.

Graph 3. Excel spreadsheet graph using original Solanki data. Outstanding correlation of deep grand minima and high strength Type”A” angular disturbance signified by green arrows. -585 event not complying with “Wilsons Law” on first 2 occasions. (see below) Spreadsheet available at .UPDATE 11/03/09: Dr. Svalgaard could not find fault with the original JPL data (angular momentum) and the Solanki 14C data, along with my placement of that data.

Graph4. Showing each individual angular momentum disturbance (green/red) and how they sculpt the 14C silhouette. Now that I have the actual figures there is some subtle difference from my original graph. A very common occurrence over the centuries is Solar activity peaks happening just after angular momentum peak and DURING a period of angular momentum disturbance just like we had at the start of the Dalton around 1790. It may be a matter of timing, determining whether grand minima starts on the disturbance or the cycle after? Its obvious the Sun is agitated on a regular basis in the past, because the Dalton finished early and we missed grand minimum at SC20, we have experienced a prolonged era of solar activity in recent times.

solanki, sharp AM

Graph5. New compilation of Solar Proxy records showing a very good match between 14C & 10Be. Angular Momentum Disturbance Strength curve in purple showing another very good match. The Holocene Solar activity and Temperature a direct result of Angular Momentum?

Does Angular Momentum drive the 11000 year 14C (carbon 14) graph which is backed up by the 10Be graph (Beryllium-10), my evidence strongly suggests so. If a theory on what controls the output of the Sun doesnt show a very strong correlation with the 11000 year 14C graph it cant be taken seriously, it is the best record of solar activity we have before the 1700’s. I have looked at that 14C curve and wondered whats behind it for months, and now I believe we have the driver. Basically these 2 isotopes are used as proxy records to measure the output of the Sun over 1000’s of years, and before 1700, is the only source of data to record solar activity. 14C & 10Be are laid down in ice core and tree data and both follow the same trend. Usoskin and Solanki et al has provided in a recent paper HERE, a graph that displays past grand minima based on 14C records (kindly alerted to me by Dr. Svalgaard). But I believe Usoskin set the bar way too low, ignoring events such as the Dalton minimum (Usoskin determines grand minima is >15 SSN). Although I don’t agree with Usoskin’s methodology or outcomes, I do thank him and Solanki for providing the graph. Note: If you havent read my basic theory on grand minima here is the link which will put things in perspective.

Continue reading

Spin–Orbit Coupling Between the Sun & Jovian Planets.

This Paper by I. R. G. Wilson, B. D. Carter, and I. A. Waite is now available free onliine.


Abstract:We present evidence to show that changes in the Sun’s equatorial
rotation rate are synchronized with changes in its orbital motion about the
barycentre of the Solar System.We propose that this synchronization is
indicative of a spin–orbit coupling mechanism operating between the
Jovian planets and the Sun. However, we are unable to suggest a plausible
underlying physical cause for the coupling. Some researchers have proposed
that it is the period of the meridional flow in the convective zone of the Sun
that controls both the duration and strength of the Solar cycle.We postulate
that the overall period of the meridional flow is set by the level of disruption
to the flow that is caused by changes in Sun’s equatorial rotation speed.
Based on our claim that changes in the Sun’s equatorial rotation rate
are synchronized with changes in the Sun’s orbital motion about the
barycentre, we propose that the mean period for the Sun’s meridional flow
is set by a Synodic resonance between the flow period (?22.3 yr), the overall
178.7-yr repetition period for the solar orbital motion, and the
19.86-yr synodic period of Jupiter and Saturn.

Some very interesting sections of this paper discuss changes in angular momentum and solar equatorial rotation change. I would like to see more work in this area, as there is scant amount of detail available on my searching. There must be someone working on comparing current solar differential rotation with other periods?

In another section the paper acknowledges the work done by Fairbridge & Shirley 1987 in using all of the Jovian planets to calculate angular momentum but unfortunately dont include Neptune & Uranus any further. I believe Fairbridge & Shirley were SO close in 1987 but failed to see the absolute importance of Neptune & Uranus…they had a graph like Carl’s but didnt cross check it against the planetary line ups. Incredible that they went so far but didnt go the extra step. Its now some 22 years later.

But the most important discovery by Wilson et al in this paper in my view, is their “phase locking” theory. Grand Minima type events (SSN less than 80) have happened in the past when the conjunction of Jupiter & Saturn happens before that cycle’s maximum, implying a mechanism of catch up, keeping the Jupiter/Saturn sysygies in line with solar cycles. I refer to this in other articles as “Wilson’s Law”. If SC24 peaks after March 2011 it will fit that criteria as well as SC25 if it peaks after Nov 2020. This phenomenon has always happened at or just after the “camel hump” disturbance on Carl’s graph, and begs the question: Does this phenomenon happen as a result of the major disturbance to the angular momentum or is that just coincidence? To test this I might plot all the sysygies and cycle max’s on Carl’s Graph.

UPDATE: below is a graph showing J+S sysygies with sunspot peaks, Note: pre 1700 solar cycle maxima is derived geomagnetic aa proxy figures, click on the graph for a larger image.

Ian’s work has answered some of my questions and explains why 1830 didnt invoke further Grand Minimum action, also why 1880 (SC12) was low during higher angular momentum, Its obvious if the aa records are correct that we have a higher frequency of early J+S sysygies with the higher angular momentum caused by N+U.
Black dots are J+S together, Blue dots J+S opposed, and Red dots are solar cycle maxima…..reduced solar activity occurs if we get a black or blue dot in between cycle minimum and before cycle maximum


Ian Wilson's Theory on the Planetary Influence on Grand Minima.

Ian Wilson, highly respected Australian scientist working in the area of planetary influence on solar activity has provided us with his paper outlining his theory on some possible drivers of solar grand minima. This area of science seems to be on the fringe where no matter what funds are available no real knowledge can claim with total confidence how the next cycle will pan out, let alone when the next Maunder type minimum might happen, its an open arena waiting for a credible explanation.
Landscheidt Cycles welcomes Ian’s paper which can be accessed through this link:
Below is a graph from Ian’s paper showing the heliocentric latitude of Venus (solid line) and the mean distance of Jupiter from the Sun in astronomical units (dashed line), we welcome constructive debate.


Neptune & Uranus Control Grand Minima & Solar Modulation?

Thanks to Carl for the kind words and I hope you overcome your challenge. I and many others thank you for setting up this wonderful site and for extracting some extra important data from Dr. Landscheidt’s work.


I am looking forward to contributing to this alternative view on how we interact with the cosmos. I will be reporting on news and scientific papers concerning planetary involvement connected with influencing the Sun and the global climate. Carl’s work has inspired me, and this first article is a work in progress report that was born by his SSB graph which showed to me the importance of Neptune and Uranus. We are living in exciting times and may witness a brand new area of science, especially if we DO experience a Grand Minimum beginning with Solar Cycle 24.


Some time ago while researching some of my interests in areas such as meteorology, the cosmos and perceived man-made global warming I came across this website and in particular a very interesting graph which Carl Smith created showing an extension to Dr. Landscheidt”s work. After studying Carl’s graph it became apparent to me that Neptune & Uranus are responsible for Solar Grand Minima as well as Solar Cycle Modulation.

In this article I will present Solar System Charts and Sunspot charts which correspond with some of the Angular Movements below in Carl’s graph.

The basic theory on how Neptune & Uranus control Solar Grand Minima and Solar Cycle Modulation is as follows: Shown in Carl’s graph below is a wave modulation mainly created by Jupiter & Saturn together (top of wave)and Jupiter & Saturn opposing (bottom of wave) which effectively is the momentum engine of the Sun, the top of the wave is strong, the bottom is weak (weaker means stronger cycle). Every 179 yrs Neptune & Uranus gather behind Jupiter (the largest gravity source besides the Sun) giving it extra momentum force and IF Saturn is on the other side of the Sun, the “down” cycle is shortened and not as weak because of the reduced momentum to Saturn….this coincides every time with less sunspot activity for the last 1000 yrs at least. Just discovered in an extension I recently finished to Carl’s graph back to 900AD is another line up that also causes Grand Minima before the Medieval Warm Period, over time Jupiter and Saturn gather on the other side of Neptune & Uranus causing disturbance at the top of the “wave” and substantially shortening the “up” cycle. Neptune and Uranus are the controllers of the 2 main drivers creating angular momentum, they can add or take away that momentum. The sunspot cycle modulation follows that control or momentum curve as shown in a graph later in the report.

I believe we can now confidently predict Solar Grand Minima and Solar Cycle Modulation strength.
Fig.1 shows the 2 planetary positions that create the majority of angular momentum in our solar system. “A” corresponds with the bottom of the wave in Carl’s graph and “B” with the top of wave. The resonance created from large strength in “B” and near zero strength in “A” as Jupiter & Saturn balance each other out.

Fig.2 shows the 2 planetary positions capable of creating Grand Minima. “A” robbing Saturn at bottom of wave and “B” robbing Jupiter/Saturn at top of wave. Both positions responsible for the recurring “camels humps” in Carl’s graph

Note: Click on the graphs to view a full size image.
Sun - SSB angular momentum 900 to 1640 graph
Sun - SSB angular momentum 1620 to 2180 graph
Carl’s original graph above.


Carl’s graph is a representation of the suns angular momentum as affected by all planets of our solar system. The interesting features in particular is the camel shaped humps (green & red arrows) that occur every time during Grand Minima and more recently (967, 1005, 1290, 1470, 1650, 1790, 1830, 1970 & 2010). Researching the planetary positions I found a recurring pattern, it seems that Neptune and Uranus aligning with Jupiter and Saturn opposing (doesn’t have to be in perfect alignment) creates a disturbance which changes the regular pattern. This disturbance coincides with the Dalton, Maunder, Sporer and Wolf and Oort minimums. In the past we had a build up of solar cycle strength immediately before Grand Minima which is due to the extra momentum in the system from N+U. When we get a Grand Minima event, the next 2 cycles after are always very weak even though Angular Momentum is strong, this phenomena is still a mystery but perhaps it simply takes time to “restart the system”.
There are 3 phases to consider but only if the angles of J+S are favorable as N+U start to come together( and I am just discovering that it doesnt happen often, 1280 to now is truly a golden period), basically we have a strong lead up of solar peaks before grand minima event then if the partial line up (1st phase) is strong enough we have grand minima like we did for the Dalton, Maunder, Sporer and maybe Wolf. Next we have 2 cycles of very reduced activity followed by the optimal lineup of N+U+J with S opposite which starts the cycle again until we get the remaining partial line up and if that is strong enough we get more grand minima action. The Sporer and Maunder experienced all 3 phases but the Dalton only endured the first 2 (the J/S angles are now weakening) and thats why we didnt get a grand minimum in SC20 (first phase, partial lineup).
The Oort minimum steps away from the usual pattern because of the weaker lineup of J+S, but shifts to the alternate line up of N+U & J+S opposing . The Neptune/Uranus factor is a lot weaker around the time of the Medieval Warm Period (Jupiter & Saturn not aligning) with very little disturbance (not unlike the overall weakening trend we are starting to experience now), but still I predict a weak solar grand minimum (see prediction at end of report).

Compare Carl’s Graph to the solar system views below, especially 1651, 1830, 1790 and (2010 near end of report). Note: Solar system views dont take into account the slight elliptical orbits present in the system that do contribute to the overall momentum modulation.



This view above also coincides with my birthday

The chart below shows the partial line ups that can cause a Grand Minima Event and if not a large degree of reduced solar activity.



Here is a graph I made showing sunspot peaks plotted against calculated cycle angular momentum and the obvious correlation. No allowance made for inertia or grand minima effects (history shows the cycles stay low for 2 cycles regardless of momentum after minima event).
This graph answers lots of questions, but also creates some new ones. Why doesnt the Dalton continue in 1830. Did SC11 cause SC12 to be reduced (SSB graph shows disturbance). Some might ask why the angular momentum is so high in 1880 right near the opposition of N+U? Answer: All planets create angular momentum and in 1882 they are nearly all lined up except U. Most notable is that there are no high peaks during times of reduced momentum. UPDATE Ian Wilson’s latest paper now addresses these questions, see link here

The Neptune, Uranus factor could be effecting the Sun is several ways, perhaps causing a slowdown in the rotational difference at the high and low latitudes thereby reducing the input to the solar dynamo. There are several papers that discuss this observed phenomena during past minima and I am currently researching the differential latitude speeds but finding the data hard to come by. Its also been noted the Solar polar magnetic strength is substantially reduced at present which could be as a result of the rotation change if it is occurring. There are at least 2 papers that talk about a “phase catastrophe” during the Maunder and Dalton minima implying either a period when the solar poles are both the same polarity for an extended period or the cycle goes to 22 years instead of 11, I also think its highly possible that both poles could fluctuate between positive and negative through the entire cycle if the new polar inflows are not strong enough to change the polarity. This could also dramatically slow down the
production of sunspots. As can be seen from the graph below with normal fluctuations and a low solar pole strength that would certainly be possible. It would be interesting if possible to see the polar strength of 1790 but it has only been accurately recorded since 1967, but notice the low polar strength pre 1970 in Dr. Svalgaards’ graph of the MWO data.



Other points of interest to the theory is SC4 (1788 peak) that lasted perhaps 16 years and is questioned by I. G. Usoskin, K. Mursula, and G. A. Kovaltsov at as being 2 cycles recorded incorrectly (records before 1850 are considered shaky). The planetary lineup of that period is very similar to today and their revised sunspot group SC4 could mirror SC24.


The chart below kindly supplied by Carl shows angular momentum from 995 – 2895. The green arrow represents the optimal line up of N,U,J with S opposite . The Oort minimium steps out of line as the line up goes out of sync, the planets dont quite come back exactly the same each 179 yrs and it seems from the Wolf until now is a window of line ups that might take 1000’s of years to return, during the medieval warm period J+S were poorly aligned as the phase gradually shifted. The MWP could be stated as a phase transition period, further bolstering the theory.



The C14 chart from Wiki shows via the green & red dots the same position as above as the green & red arrows in the SSB graphs. The green dots are the optimal position of alignment and as can be seen the previous minima (Wolf may be in doubt) began at the partial line up state and except for the Dalton continued thru the optimal alignment and on to the remaining partial line up in the phase before returning to “normal”. 1970 failed to be strong enough to start a Solar Grand Minimum explaining the extra heat in the system, SC21,22 & 23 were let off the hook this time. So the typical pattern as can be seen in Carl’s graph above is partial/optimal/partial, but the ideal time for this being between 1280-1830, before and after this period the Jupiter/Saturn alignments begin to weaken and shift. Grand Minima conditions DO NOT occur every 179 years but only if Jupiter & Saturn are in the right position.

As you can see we are due for a slow down if we follow the same pattern but perhaps not as big a slow down as past minima.

Prediction: Some points to digest, the strength of the Neptune/Uranus influence seems to be waning, in the past 4 grand minima the Sun went into Grand Minima on the partial lineup of Neptune/Uranus as can be seen in the C14 Wiki graph and the green squares (also look at Carl’s 995-2985 graph showing the changing trend). This time around we past that stage (1970) without falling into grand minimum and the Dalton minimum shows a weakening trend coming out of minimum not long after the best lineup of Neptune/Uranus (1830) at the time.

Based on this information I predict a short Grand minimum beginning during Cycle 24 which may possibly look like the end of SC23 or be a very low peak in its own right lucky to rise above 50 SSNmax, followed by another low peak. The SC24 peak is particularly hard to predict, the planetary alignments suggest early 2010 or early 2014 but the sunspot peak (see below in Desmoulins and Hung’s graphs) is currently running ahead of the alignments by at least 3 years (Neptune/Uranus doing their thing). Going on history the SC24 peak may get back into line with Desmoulins plot like it did in 1805, if so Feb 21 2010 is looking like a good date, if not early 2014.
UPDATE… Ian Wilson’s latest paper has raised some doubt in my prediction, he has noticed Grand Minima or low cycles always have the conjunction of Jupiter & Saturn before solar cycle max, SC24 needs to have its peak after 2011 to fall into this category, it will be interesting to watch.

There is still a chance that SC24 could look like the end of SC23 like it may have in SC4…this is new ground and if so that will push out or perhaps add another small cycle. Click on the chart to view an expanded version from 1700AD-2070AD

Note the alignment on Feb 21 2010 (also coincides with my birthday) Both Cycles coming together J+V with E apposing and N+U+J with S opposing. (See the J+E+V cycle below)

The SSB and Solar System data has been cross checked.

The Solar System Viewer can be seen at:

Could Tidal forces control the 11 year sunspot cycle?

Here are 2 pieces of work that look at smaller 11 year cycles (approx) that theorize on Jupiter/Earth/Venus rotations that line up with sunspot cycles.

Here NASA has reported on possible links between sunspot cycles and the planetary movements

EDIT: The NASA paper basically looks at the Heliocentric sysygies of Jupiter, Earth and Venus and how they line up with sunspot peaks. Jean-Pierre Desmoulins has also done some great work on his site where you can view this graph below showing that alignment (green peaks are J+E+V most aligned with the Sun and solar cycle peaks shown in red). Notice how the alignment gets slightly out of sync around 1790 and now, when out of sync we experience much less solar activity…Neptune and Uranus are close together at these times possibly dragging the sync out of line but it should return like it did in 1805. Certainly worth further investigation.


The table is a plot of J+E+V alignments with each date corresponding with the green peaks on Desmoulins graph above. The odd cycle numbers are J+V with E opposing and even is J+E+V aligned. The G/O rule keeping mainly true. These alignments naturally include the Sun.

A Similar graph from the NASA paper below.


The compelling evidence is that both graphs plot 2 cycles that although slightly different in length remain in step with one another.