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A correlation is found between changes in Earth's length of day [LOD] and the spatio–temporal disposition of the planetary masses in the solar system, characterised by the z axis displacement of the centre of mass of the solar system [CMSS] with respect to the solar equatorial plane smoothed over a bi-decadal period. To test whether this apparent relation is coincidental, other planetary axial rotation rates and orbital periods are compared, and spin–orbit relations are found. Earth's axial angular momentum moment of inertia, and internal dynamics are considered in relation to the temporal displacement between the potential stimulus and the terrestrial response. The differential rotation rate of the Sun is considered in relation to the rotational and orbital periods of the Earth–Moon system and Venus and Mercury, and harmonic ratios are found. These suggest a physical coupling between the bodies of an as yet undetermined nature. Additional evidence for a resonant coupling is found in the relation of total solar irradiance (TSI) and galactic cosmic ray (GCR) measurements to the resonant harmonic periods discovered.
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Pattern Recogn. Phys., 1, 199–202, 2013
www.pattern-recogn-phys.net/1/199/2013/
doi:10.5194/prp-1-199-2013
©Author(s) 2013. CC Attribution 3.0 License.
Open Access
Pattern Recognition
in Physics
Apparent relations between planetary spin, orbit,
and solar differential rotation
R. Tattersall
University of Leeds, Leeds, UK
Correspondence to: R. Tattersall (rog@tallbloke.net)
Received: 6 October 2013 – Revised: 26 November 2013 – Accepted: 28 November 2013 – Published: 16 December 2013
Abstract. A correlation is found between changes in Earth’s length of day [LOD] and the spatio–temporal
disposition of the planetary masses in the solar system, characterised by the zaxis displacement of the centre
of mass of the solar system [CMSS] with respect to the solar equatorial plane smoothed over a bi-decadal
period. To test whether this apparent relation is coincidental, other planetary axial rotation rates and orbital
periods are compared, and spin–orbit relations are found. Earth’s axial angular momentum moment of inertia,
and internal dynamics are considered in relation to the temporal displacement between the potential stimulus
and the terrestrial response. The dierential rotation rate of the Sun is considered in relation to the rotational
and orbital periods of the Earth–Moon system and Venus and Mercury, and harmonic ratios are found. These
suggest a physical coupling between the bodies of an as yet undetermined nature. Additional evidence for
a resonant coupling is found in the relation of total solar irradiance (TSI) and galactic cosmic ray (GCR)
measurements to the resonant harmonic periods discovered.
1 Introduction
Earth’s length of day [LOD] varies cyclically at various
timescales. These small variations in the order of a millisec-
ond are believed to be related to exchanges of angular mo-
mentum between the atmosphere and Earth, the displacement
of oceans away from and toward the equator (Axel-Mörner,
2013), and the changing Earth–Moon distance. On longer
timescales, the variation is considerably larger, on the order
of several milliseconds, and these variations take place over
several decades or more. It is thought by Gross (2007) that
the cause of the longer-term variation is due to shifts in the
circulation of convecting molten fluid in Earth’s fluid outer
core. If this is the case, it begs the question: what is the cause
of those shifts?
2 Data and method
LOD Data from (Gross, 2007) is plotted against the zaxis
motion of the centre of mass of the solar system [CMSS] with
respect to the solar equatorial plane using the NASA/JPL
DE14 ephemeris. This curve is smoothed at around the pe-
riod of two Jupiter orbits (24yr) in order to mimic the damp-
ing eect of the changes of motion in a viscous fluid (like
that in Earth’s interior). The curve is shifted temporally to
obtain the best fit to the LOD curve, and the period of the lag
is found to be 30yr (Fig. 1).
3 Result
The result is suggestive of a dynamic coupling between
changes in the disposition of solar system masses, predomi-
nantly the gas giant planets. These planets possess an over-
whelming percentage of the mass in the solar system out-
side the Sun, and also possess a high proportion of the entire
system’s angular momentum. Resonant coupling between
Jupiter–Saturn and the inner planets in the early history of
the solar system had significant impact on the planets’ even-
tual orbits (Agnor and Lin, 2011).
If the planets are able to transfer orbital angular momen-
tum to the axial angular momentum of neighbour planets, we
might expect to see evidence of this in the axial rotation peri-
ods of smaller planets relative to the orbital periods of larger
neighbours. To investigate this possibility, the rotation rates
Published by Copernicus Publications.
200 R. Tattersall: Planetary spin–orbit coupling and solar differential rotation
2
3. Result
Figure 1: z-axis motion of the CMSS relative to the solar equatorial plane plotted against LOD (Gross 2010) 1840-2005
The result is suggestive of a dynamic coupling between changes in the disposition of solar
system masses, predominantly the Gas Giant planets. These planets possess an
overwhelming percentage of the mass in the solar system outside the Sun, and also possess
a high proportion of the entire system’s angular momentum. In the early history of the solar
system, resonant coupling between Jupiter-Saturn and the inner planets had significant
impact on their eventual orbits. (Agnor & Lin 2011)
If the planets are able to transfer orbital angular momentum to the axial angular
momentum of neighbour planets, we might expect to see evidence of this in the axial
rotation periods of smaller planets relative to the orbital periods of larger neighbours. To
investigate this possibility, the rotation rates and orbital periods of several planets are
compared with the rotation rate and orbital period of Jupiter.
4. Inner Planet Synchrony
It is observed that the ratio of Venus and Earth’s rotation rates divided by their orbital
periods is 1.08:0.0027. This is equivalent to the ratio 400:1. During their respective synodic
periods with Jupiter, Venus completes 1.03 rotations and Earth completes 398.88. This is
close to a 400:1 ratio. Looking at the Earth and Mars’ axial rotation and orbital periods we
observe that:
Earth 1/365.256 = 0.0027
Mars 1.0275/686.98= 0.0015 The ratio of these numbers is:
0.0027: 0.0015 = 1:0.546
Earth completes 1.092 orbits between synodic conjunctions with Jupiter, while
Mars completes 1.18844. The ratio of these numbers is:
1.092: 1.18844 = 1: 1.088
The ratio of the ratios is 2:1 (99.6%)
The reason for the 2:1 ratio becomes apparent when we observe that the Mars-Jupiter
synodic conjunction period is in a 2:1 ratio with the Earth-Jupiter synodic period (97.7%)
Figure 1. z-axis motion of the CMSS relative to the solar equatorial
plane plotted against LOD (Gross, 2010) 1840–2005.
and orbital periods of several planets are compared with the
rotation rate and orbital period of Jupiter.
4 Inner planet synchrony
It is observed that the ratio of Venus and Earth’s rotation rates
divided by their orbital periods is 1.08 :0.0027. This is equiv-
alent to the ratio 400 :1. During their respective synodic pe-
riods with Jupiter, Venus completes 1.03 rotations and Earth
completes 398.88. This is close to a 400:1 ratio. Looking
at Earth and Mars’ axial rotation and orbital periods, we ob-
serve that:
Earth 1/365.256 =0.0027.
Mars 1.0275/686.98 =0.0015.
The ratio of these numbers is
0.0027:0.0015 =1 : 0.546.
Earth completes 1.092 orbits between synodic
conjunctions with Jupiter, while
Mars completes 1.18844. The ratio of these numbers is
1.092:1.18844 =1 : 1.088.
The ratio of the ratios is 2 : 1 (99.6%).
The reason for the 2 : 1 ratio becomes apparent when we ob-
serve that the Mars–Jupiter synodic conjunction period is in
a 2 : 1 ratio with the Earth–Jupiter synodic period (97.7%).
Once again there appears to be a quantisation of spin and
orbit into simple ratios involving the largest planet in the sys-
tem, the Sun and the inner planets between them.
As a further test, it is observed that:
The Neptune rotation rate divided by the Uranus rota-
tion rate=1.0701427.
The Jupiter–Uranus synodic period divided by the
Jupiter–Neptune synodic period is 1.0805873.
1.0805873/1.0701427 =1.00976 (99.03%).
These observations strongly suggest that Jupiter aects the
rotation rates and orbital periods of both Earth–Venus and
Earth–Mars. In combination with the other gas giant plan-
ets, the combined eect produces the curve seen in Fig. 1,
notwithstanding the much smaller contributions of the in-
ner planets. Having established that the spin and orbit of the
four inner planets relates to Jupiter’s orbital period, greater
weight can be given to the possibility that Earth’s decadal
LOD anomalies may have a celestial cause in planetary mo-
tion.
4.1 Inertia and fluid damping
Earth’s high axial rotation rate, along with its density, cause
Earth to have a high angular momentum which resists
changes in angular velocity. A theory developed from the
observation of magnetic anomalies on Earth’s surface sug-
gests that columnar vortices surround Earth’s core which pro-
duce flows in the viscous mantle and liquid outer core (Lister,
2008). Modelling such fluid dynamics as these is beyond the
scope of this paper, but the temporal stability of these mag-
netic structures suggests that small, externally applied forces
will take a considerable period of time to produce a terres-
trial response. The eect of these stabilising structures will
produce a terrestrial response which can be characterised as
a fluid-damped oscillation. The signature of Jupiter’s motion
above and below the solar equatorial plane over the course of
its orbital period of around 11.86yr is not seen in LOD data.
If the correlation in Fig. 1 is indicative of a physically cou-
pled relationship, it is then evident that the damping of the
oscillation is sucient to smooth out both the Jupiter orbital
period and the Jupiter–Saturn conjunction period of 19.86yr.
It is found that the best fit of the celestial data to the LOD
variation magnitude is at two Jupiter orbital periods. This
matches well with the temporal lag between the celestial data
and the LOD data of around 30yr. The peak-to-peak oscil-
lation period seen in the celestial data indicates a cycle of
around 180 yr. This period was found by José (1965). The lag
of the terrestrial response appears to be at around 1/6 of this
periodic length. This is around the half period of the major
oceanic oscillations observed on Earth (Axel-Mörner, 2013).
These oceanic oscillations are in phase with the changes in
LOD and the lagged celestial data.
4.2 Differential solar rotation rates relating to planetary
motion
The periods in which the Sun’s visible surface makes one
sidereal rotation vary with latitude. Near the equator the pe-
riod is near 24.47 days. This period is known to vary on a pe-
riod relating to the orbits of Jupiter, Earth and Venus (Wilson
et al., 2008). Near the poles, the period of rotation is around
35 days. These periods relate to variation in total solar irradi-
ance (TSI) (Scafetta and Willson, 2013).
Pattern Recogn. Phys., 1, 199–202, 2013 www.pattern-recogn-phys.net/1/199/2013/
R. Tattersall: Planetary spin–orbit coupling and solar differential rotation 201
Considering the relationships between the spin and orbit
of Mercury (three rotations per two orbits of the Sun) and
Venus (three rotations per two Earth orbits and two rotations
per synodic conjunction with Earth), a test is made to see if
similarly simple harmonic relations exist between these plan-
ets and the Sun’s dierential rates of rotation.
Firstly, it is noted that the lengths of day of Mercury and
Venus form a ratio that is close to 2 : 3 ratio, and that the
equatorial and polar rotation rates of the solar surface also
form a ratio close to 2 : 3.
Mercury makes one sidereal rotation per 2/3 (240 degrees)
of orbit in 58.65days. A point on the Sun rotating at a rate
which brought it directly between Mercury and the solar core
in the same period would have a sidereal period of 35 days
(184 days making one full rotation plus 2/3 of a rotation,
i.e. 240 degrees). Mercury makes two sidereal rotations per
480 degrees (1, 1/3 orbits) in 117.3days. A point on the Sun
rotating at a rate which brought it directly between Mercury
and the solar core in the same period would have a sidereal
period of 27.06 days, making four sidereal rotations plus 1/3
of a rotation (120 degrees). It is noted that this is close to the
Carrington period.
In summary, it can be seen that Mercury has a 3: 2 spin-
orbit ratio which is in 3 :5 spin–spin and 2 : 5 orbit–spin ra-
tios with a solar rotation period of 35.18 days, and is in 6 : 13
spin-spin 4 :13 orbit-spin ratios with a solar rotation period
of 27.06days.
Two Mercury rotations occur in 117.3days. In a similar
period of 116.8days, Venus makes a full rotation with re-
spect to the Sun, while orbiting 180 plus 6.18 degrees (0.52
orbits) and rotating (retrograde) 180 minus 6.18 degrees in
the sidereal frame. A point near the solar equator rotating at
a rate which brought it directly between Venus and the so-
lar core in the same period after 4.52 rotations would have a
sidereal solar rotation period of 25.84days.
Points near the solar poles rotating at a rate which brought
them directly between Venus and the solar core in the same
period after 3.52 rotations would have a sidereal period of
33.2days. It is noted that the average of these two solar ro-
tation periods is 29.51days, which is close to the period of
rotation of the Earth–Moon system with respect to the Sun
(29.53days). A solar rotation period of 29.32days is found
to be in a 1 : 3 ratio with a period of 87.97days; the Mercury
orbital period, and 1 : 4 ratio with a period of 117.3days; the
period of two Mercury rotations and close to one Venusian
day.
The relationship of Venus with the Earth–Moon system is
more clearly seen by considering that the period of a Venus
rotation with respect to the Sun of 116.8days is exactly 1/5
of the Earth–Venus orbital synodic conjunction period of
1.6yr. Five synodic conjunctions occur over a period of 8
Earth years as Venus makes 13 orbits, bringing the two plan-
ets back to within two degrees of their original longitude. At
the end of this period, the various solar periods calculated in
the preceding observations make whole numbers of sidereal
6
Figure 2: Comparison of GCR measurements over Carrington rotations with planetary frequencies
The coincidence of peaks in the GCR curve with multiples of the Carrington rotation period CR
indicates a resonant effect of this frequency (27 days). Similarly, the coincidence of other peaks in
the GCR curve with multiples of the periods at which a point on the solar equator passes between
inner planets and the solar core is indicative of resonant effects. Also shown are Mercury and Venus
orbital and half orbital periods. Venus orbital periods lie close to multiples of the Venus-Solar
rotation periods near the peaks in GCR activity at 4.15 and 8.3 CR. The sharp, high amplitude peak at
4.2 CR lies between the half periods of Venus’ orbit and sidereal rotation, which are four days apart.
7. Conclusion
Harmonic ratios between the planets orbital periods are the principle cause of their
quantised semi-major axes. These ratios also affect the rate at which planets rotate, which
sets their LOD. The discovery of simple ratios of LOD between planets further underlines
the resonant nature of the effect which quantises their relations. These resonances also
affect the Sun, which has developed a differential rotation in response to the resonant
forces to which it is subjected by the planets, whose orbital elements may be modulating
the resonant periods. Cyclic variations induced in the rate of rotation of various latitudinal
plasma belts on the solar surface affect its activity cycles such as the Hale, Schwabe and
Gleissberg cycles which are found to be in synchronisation with planetary alignment cycles.
(Wilson 2013b). Further research is required in modelling the resonant frequencies present
and studying their resultant interactions in order to better understand the magnitudes of
inertia and damping present in the oscillating subsystems which constitute the rotating solar
surface layers.
Figure 2. Comparison of GCR measurements over Carrington ro-
tations with planetary frequencies.
rotations: 113×25.84 days, 108×27.06 days, 88×33.18 days,
and 83×35.18days.
5 Discussion
A physical mechanism linking solar rotation rates with plan-
etary rotation and orbital periods may involve resonance if
the ratios are 1 : 2 or ratios such as 1 : 4, 2 : 3, 2 : 5, 1 : 3,
3 : 5, 5 : 8 etc. (Agnor and Lin, 2011). As a first approximate
observation, the rotation rates of the solar equator and solar
poles are in a 2 : 3 ratio.
The average of the periods relating to Venus, 25.84 and
33.2days, is 29.51days. This is very close to the Earth–
Moon system rotation period relative to the Sun (29.53days).
The ratio of 25.84 to 29.51 is 7 : 8. The ratio of 29.51 to 33.2
is 8 : 9.
The ratio of the periods relating to Mercury, 27.06 and
35.184, is 20 : 26. The average of the periods is 31.12days.
The ratio of 27.06 to 31.12 is 20 : 23. The ratio of 31.12 to
35.184 is 23 :26. There are 12 Mercury orbits in 26 periods
of 27.06days each.
These observations indicate that in addition to resonance
between the orbital and rotation periods between individual
planets and the Sun, we may hypothesise that there is also
resonance between the solar rotation rates at various latitudes
reinforcing the eect. If there is an eect of this resonance on
solar activity levels, we would expect to see evidence of it in
accurate TSI measurement, such as the strong peaks seen at
periods around 25–27 days and 33–35days in spectrographic
analysis of TSI (Scafetta and Willson, 2013).
6 Additional analysis
Further evidence to support the hypothesis may be found in
spectrographic analysis of galactic cosmic ray incidence at
Earth, which is also indicative of solar activity levels, and is
found to be modulated at the Carrington-period length (Gil
and Alania, 2012).
A comparison of periods at which various fractional mul-
tiples of the solar equatorial rotation rate which bring a point
on the solar equator directly between the inner planets and
www.pattern-recogn-phys.net/1/199/2013/ Pattern Recogn. Phys., 1, 199–202, 2013
202 R. Tattersall: Planetary spin–orbit coupling and solar differential rotation
the solar core, and the peaks in the galactic cosmic ray mea-
surements (A27l) is made in Fig. 2.
The coincidence of peaks in the galactic cosmic ray (GCR)
curve with multiples of the Carrington Rotation (CR) pe-
riod indicates a resonant eect of this frequency (27days).
Similarly, the coincidence of other peaks in the GCR curve
with multiples of the periods at which a point on the solar
equator passes between inner planets and the solar core is
indicative of resonant eects. Also shown are Mercury and
Venus orbital and half-orbital periods. Venus orbital periods
lie close to multiples of the Venus–Solar rotation periods near
the peaks in GCR activity at 4.15 and 8.3CRP. The sharp,
high amplitude peak at 4.2CRP lies between the half peri-
ods of Venus’ orbit and sidereal rotation, which are four days
apart.
7 Conclusions
Harmonic ratios between the planets orbital periods are the
principle cause of their quantised semi-major axes. These ra-
tios also aect the rate at which planets rotate, which in turn
sets their LOD. The discovery of simple ratios of LOD be-
tween planets further underlines the resonant nature of the
eect which quantises their relations. These resonances also
aect the Sun, which has developed a dierential rotation in
response to the resonant forces to which it is subjected by the
planets, whose orbital elements may be modulating the reso-
nant periods. Cyclic variations induced in the rate of rotation
of various latitudinal plasma belts on the solar surface aect
the Sun’s activity cycles; these include the Hale, Schwabe
and Gleissberg cycles, which are found to be in synchroni-
sation with planetary alignment cycles (Wilson, 2013). Fur-
ther research is required in modelling the resonant frequen-
cies present and studying their resultant interactions in order
to better understand the magnitudes of inertia and damping
present in the oscillating subsystems which constitute the ro-
tating solar surface layers.
Acknowledgements. The author wishes to thank the following
people for their generous assistance in the production of this
unfunded work: Stuart Graham, Ian Wilson, Roy Martin, Wayne
Jackson, Graham Stevens, Roger Andrews, and many other people
oering insight and comment at “Tallbloke’s Talkshop”.
Edited by: N. A. Mörner
Reviewed by: two anonymous referees
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The idea that planetary effects may modulate, or even control solar variability is old; having been investigated by Rudolf Wolf from 1859 until his death in 1893. Many further efforts to measure and explain the possible mechanisms for planetary solar effects have been made by researchers at frequent intervals through the years. Despite this it has remained a hypothesis, favoured by some, neglected or rebutted by others. Today we are in a stronger position to address the question, with accurate data, computer aided methods and new insights. Therefore, the guest editors and handling editor think the time is right for a broader and more extensive investigation of, “the possible planetary modulation of solar variability”. In this special issue of ‘Pattern Recognition in Physics’, we present a new, multi-component input to the question, with the aim of elevating the hypothesis to the status of a theory. We hope this work will lead to better understanding and prediction of solar and terrestrial variation, strengthening the scientific value and policy relevance of a promising new paradigm.
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A Venus-Earth-Jupiter spin-orbit coupling model is constructed from a combination of the Venus-Earth-Jupiter tidal-torquing model and the gear effect. The new model produces net tangential torques that act upon the outer convective layers of the Sun with periodicities that match many of the long-term cycles that are found in the 10Be and 14C proxy records of solar activity.
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Herein we adopt a multiscale dynamical spectral analysis technique to compare and study the dynamical evolution of the harmonic components of the overlapping ACRIMSAT/ACRIM3 (Active Cavity Radiometer Irradiance Monitor Satellite/Active Cavity Radiometer Irradiance Monitor 3), SOHO/VIRGO (Solar and Heliopheric Observatory/Variability of solar Irradiance and Gravity Oscillations), and SORCE/TIM (Solar Radiation and Climate Experiment/Total Irradiance Monitor) total solar irradiance (TSI) records during 2003.15 to 2013.16 in solar cycles 23 and 24. The three TSI time series present highly correlated patterns. Significant power spectral peaks are common to these records and are observed at the following periods: 0.070 yr, 0.097 yr, 0.20 yr, 0.25 yr, 0.30–0.34 yr, and 0.39 yr. Less certain spectral peaks occur at about 0.55 yr, 0.60–0.65 yr and 0.7–0.9 yr. Four main frequency periods at 24.8 days ( 0.068 yr), 27.3 days ( 0.075 yr), at 34–35 days ( 0.093–0.096 yr), and 36–38 days ( 0.099–0.104 yr) characterize the solar rotation cycle. The amplitude of these oscillations, in particular of those with periods larger than 0.5 yr, appears to be modulated by the 11 yr solar cycle. Similar harmonics have been found in other solar indices. The observed periodicities are found highly coherent with the spring, orbital and synodic periods of Mercury, Venus, Earth and Jupiter. We conclude that solar activity is likely modulated by planetary gravitational and electromagnetic forces acting on the Sun. The strength of the Sun’s response to planetary forcing depends nonlinearly on the state of internal solar dynamics; planetary–Sun coupling effects are enhanced during solar activity maxima and attenuated during minima.
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We study quasi-periodical changes in the amplitudes of the 27-day variation of the galactic cosmic ray (GCR) intensity, and the parameters of solar wind and solar activity. We have recently found quasi-periodicity of three to four Carrington rotation periods (3 – 4 CRP) in the amplitudes of the 27-day variation of the GCR intensity (Gil and Alania in J. Atmos. Solar-Terr. Phys. 73, 294, 2011). A similar recurrence is recognized in parameters of solar activity (sunspot number, solar radio flux) and solar wind (components of the interplanetary magnetic field, solar wind velocity). We believe that the 3 – 4 CRP periodicity, among other periodicities, observed in the amplitudes of the 27-day variation of the GCR intensity is caused by a specific cycling structure of the Sun’s magnetic field, which may originate from the turbulent nature of the solar dynamo.
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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.
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The Earth does not rotate uniformly. Not only does its rate of rotation vary, but it wobbles as it rotates. These variations in the Earth's rotation, which occur on all observable timescales from subdaily to decadal and longer, are caused by a wide variety of processes, from external tidal forces to surficial processes involving the atmosphere, oceans, and hydrosphere to internal processes acting both at the core-mantle boundary as well as within the solid body of the Earth. In this chapter, the equations governing small variations in the Earth's rotation are derived, the techniques used to measure the variations are described, and the processes causing the variations are discussed.
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We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. We identify six secular resonances between the nu_5 apsidal eigenfrequency of Jupiter and Saturn and the four eigenfrequencies of the terrestrial planets (g_{1-4}). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. If Jupiter and Saturn migrated with eccentricities comparable to their present day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration (\tau~5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e.g. \tau<~ 0.5 Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j=2,3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Further, results of orbital integrations show that very short migration timescales (\tau<0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets' eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9+/-0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.
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Earth's rocky mantle and solid inner core are separated by the 2,300-kilometre-deep layer of molten iron that constitutes the outer core. Yet the sluggish pattern of mantle convection creates structure in the inner core.
Solar Wind, Earth's Rotation and Changes in Terrestrial Climate
  • N A Mörner
Mörner, N. A.: Solar Wind, Earth's Rotation and Changes in Terrestrial Climate, Physical Review & Research International, 3, 117-136, 2013.