Mathematics and Astronomy: some ideas and examples

Mathematics and Astronomy: some ideas and examples

Planetary dynamics and solar
activity : truth and / or
consequences ?
João Fernandes
Centro de Geofísica da U. Coimbra
Observatório Geofísico e Astronómico da U. Coimbra
Departamento de Matemática da U. Coimbra
Dep. Física U. Aveiro (23/10/13)
Talk plan
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Solar cycle(s)
The correlations. Yes ! So what ?
Physical models:
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Torque
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Tidal forces
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An extra “idea”
Future implications: Sun, planets and
… exoplanets
Dep. Física U. Aveiro (23/10/13)
O modelo físico (Abreu et al.
2012)
R ~700 000 km
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Well studied subject (~ 3000 journals, since 1900)
Heinrich Schwabe “Solar Observations During 1843”
(Astronomische Nachrichten, vol. 20., no. 495, 1843)
“From my earlier observations, which I have
reported every year in this journal, it
appears that there is a certain periodicity in
the appearance of sunspots and this theory
seems more and more probable from the
results of this year.”
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)


Well studied subjcet (~ 2800 journals, since 1900)
Heinrich Schwabe “Solar Observations During 1843”
(Astronomische Nachrichten, vol. 20., no. 495, 1843)
“From my earlier observations, which I have
reported every year in this journal, it
appears that there is a certain periodicity in
the appearance of sunspots and this theory
seems more and more probable from the
results of this year.”
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)


Well studied subjcet (~ 2800 journals, since 1900)
Heinrich Schwabe “Solar Observations During 1843”
(Astronomische Nachrichten, vol. 20., no. 495, 1843)
“From my earlier observations, which I have
reported every year in this journal, it
appears that there is a certain periodicity in
the appearance of sunspots and this theory
seems more and more probable from the
results of this year.”
Dep. Física U. Aveiro (23/10/13)
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years Solar cycle:
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years sun cycle:
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years Solar cycle: the butterfly diagram
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years Solar cycle: 22 years in fact
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years Solar cycle: other evidences
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years sun cycle: other evidences
Nota:
Gonçalves, Lopes, Dorotovic, Fernandes e Garcia (2013)
9.0 < 10.6 <13.7
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years sun cycle: other evidences
9.0 years < 10.6 years <13.7 yeras
Gonçalves, Lopes, Dorotovic, Fernandes e Garcia (2013)
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years Solar cycle: reasons …
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years Solar cycle: reasons …
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years Solar cycle: reasons …
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years sun cycle: reasons … TACHOCLINE (with a
thickness of 0.04 times the solar radius)
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Eleven years sun cycle: reasons …
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Other cycles
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Other cycles
Charbonneau (2013)
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Other cycles
Production of radio-carbono 14C increase during the minima
(1n + 14N → 14C + 1p). See also10Be
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Other cycles
Dean (2000)
Dep. Física U. Aveiro (23/10/13)
Solar cycle(s)
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Other cycles:
Dean (2000)
Dep. Física U. Aveiro (23/10/13)
The correlations. Yes ! So what ?
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Planets/Solar activity connection idea:
R. Carrington (1863)
Charbonneau (2002)
Dep. Física U. Aveiro (23/10/13)
The correlations. Yes ! So what ?

Planets/Solar activity connection idea:
Sideral period of Jupiter
~ 11.86 years
Charbonneau (2002)
Dep. Física U. Aveiro (23/10/13)
The correlations. Yes ! So what ?
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Planets/Solar activity connection idea:
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Schwentek e Elling (1984): coincidence between solar cycle
solar and the product of the periods of the Jupiter-Saturn
aligment (19.9 anos) by the ratiof their distances to the
Sun (0.55)
Grandpierre (1996): coincidence between planetary
alignments Earth, Venus and Jupiter period (11,395 years)
and the solar cycle
Charvatova (2000): coincidence between the 2400 years
solar cycle and the Sun's motion around the center of mass
of the Solar System
Bumba (private com.): coincidence between the angle of
the directions Jupiter and Venus-Earth pair with the
maximum and minimum of the solar cycle.
Dep. Física U. Aveiro (23/10/13)
The correlations. Yes ! So what ?
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A hipótese planetária:
Dep. Física U. Aveiro (23/10/13)
http://animalspiritspage.blogspot.pt/2010/12/sunspots-and-stock-market-returns.html
The correlations. Yes ! So what ?
Dep. Física U. Aveiro (23/10/13)
The correlations. Yes ! So what ?

Planets/Solar activity connection idea:
Charbonneau (2002)
Dep. Física U. Aveiro (23/10/13)
The correlations. Yes ! So what ?

Astronomy and Astrophysics:
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No evidence for planetary influence on solar activity, Cameron and
Schussler (2013)
Journal of Atmospehric and Solar-Terrestrial Physics:
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Is there a planetary influence on solar activity ?, Abreu et al. (2012)
The influence of planetary attractions on the solar tachocline,
Callebaut et al (2012)
Comment on “The influence of planetary attractions on the solar
tachocline”, Scafetta et al. (2013)
Reply to “Comment on “The influence of planetary attractions on the
solar tachocline””, Callebaut et al (2013)
Nature:
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Solar physics: The planetary hypothesis revived, Charbonneau
(2013)
Dep. Física U. Aveiro (23/10/13)
The correlations. Yes ! So what ?

Solar physics: The planetary hypothesis
revived, Charbonneau (2013)
Dep. Física U. Aveiro (23/10/13)
Physical models: torque
Abreu et al. (2012)
Dep. Física U. Aveiro (23/10/13)
Physical models: torque
Abreu et al. (2012)
Dep. Física U. Aveiro (23/10/13)
Lovis et al. (2011)
Dep. Física U. Aveiro (23/10/13)
Physical models: torque
Hipothesis: a = b = c
1. e = f (Nx = 0) → YZ
2. f = d (Ny = 0) → XZ
3. d = e (Nz = 0) → XY
Abreu et al. (2012)
Dep. Física U. Aveiro (23/10/13)
Physical models: torque
Abreu et al. (2012)
Dep. Física U. Aveiro (23/10/13)
Physical models: torque
Tacocline is
oblated on the
equator ! !
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This is strongly attacked by Cameron & Schussler (2013)
Dep. Física U. Aveiro (23/10/13)
Physical models: tidal forces
In total < 8 ×10-10 m/s2 << 1.2 ×10-6 m/s2
Callebaut et al (2012)
Dep. Física U. Aveiro (23/10/13)
Physical models: an extra “idea”
Seixas, Salgueiro, Fernandes (work in progress)
Dep. Física U. Aveiro (23/10/13)
Future implications: Sun,
planets and … exoplanets
 Sun: indications about the tachocline
geometry ?
 Planets : better celestial mechanics ?
 Exoplanets: host exoplanets activity ?
Dep. Física U. Aveiro (23/10/13)
Future implications: Sun,
planets and … exoplanets
 Sol: indicações sobre a geometria da
tacocline
 Planetas do SS:
 Exo-Sistemas Planetários:
Dep. Física U. Aveiro (23/10/13)
Future implications: Sun,
planets and … exoplanets
Up to seven planets
orbiting HD 10180: a
solar type star (similar
age)
Lovis et al. (2010)
Dep. Física U. Aveiro (23/10/13)