SlideShare a Scribd company logo
ON THE STRUCTURAL LAW OF
EXOPLANETARY SYSTEMS
Patricia Lara, Arcadio Poveda & Christine Allen
Instituto de Astronomía, UNAM
ICNAAM 2012
Kos, Greece
19-25 September 2012
Titius-Bode Relation
n
a 2
3
.
0
4
.
0 


donde n = -∞ (Mercury), 0 (Venus),1 (Earth), 2,…
Titius-Bode relation
Johann DanielTitius
(1729-1796)
Johann Elert Bode
(1747-1826)
On the structural law of exoplanetary systems.pptx
Titius-Bode Relation (TBR)
Original TBR
where n = 0, 3, 6,12 ..
Classic TBR
(modern formulation)
where n = -∞ , 0, 1, 2, …
10
4


n
a n
a 2
3
.
0
4
.
0 


Exponential TBR
where n = 1, 2, 3, …
n
n k
P
P 
 0
Dermott´s law
where n = 0, 1, 2, …
bn
n
n e
a
C
a
a 0
0 


TBR in the Solar System
Sistema Solar
a = 0.1912e0.5594n
R
2
= 0.992
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7 8 9 10
n
a
(AU)
Poveda &Lara, 2008
Solar System
On the structural law of exoplanetary systems.pptx
55 Cancri
Distance
12.34 (± 0.4) pc
Spectral Type
K0IV-V
Mass
0.905 (± 0.015) M
Age
10.2 (± 2.5) Gyr
Radius
0.943 (± 0.01) R
Metallicity [Fe/H]
0.31 (± 0.04)
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
55 Cnc e b c f d
Orbital period (days) 0.7365449
± 5e-06
14.651262
± 0.0008
44.3446
± 0.007
260.7
± 1.1
5218
± 230
Eccentricity 0.057 0.0159 0.053
a (AU) [measured] 0.0156 0.1148 0.2403 0.781 - 5.76 -
a (AU) [predicted] 0.0239 0.074 0.2292 0.7103 2.2011 6.8214 21.14
exoplanet.eu
υ Andromeda
Distance
13.47 (± 0.13) pc
Spectral Type
F8 V
Mass
1.27 (± 0.06) M
Age
3.8 (± 1) Gyr
Radius
1.631 (± 0.014) R
Metallicity [Fe/H]
0.09 (± 0.06)
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6
Ups And b c d e
Orbital period (days) 4.6171
± 4.7e-05
237.7
± 0.2
1302.61 3848.86
± 0.74
Eccentricity 0.013 0.24 0.274 0.00536
a (AU) [measured] 0.059 - 0.861 2.55 5.2456 -
a (AU) [predicted] 0.069 0.218 0.683 2.145 6.732 21.13
μ Ara
Distance
15.3 pc
Spectral Type
G3 IV-V
Mass
1.08 (± 0.05) M
Age
6.41 Gyr
Radius
1.245 (± 0.255) R
Metallicity [Fe/H]
0.28 (± 0.04)
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6
mu Ara c d b e
Orbital period (days)
9.6386
± 0.0015
310.55
± 0.83
643.25
± 0.9
4205.8
± 758.9
Eccentricity 0.172 0.0666 0.128 0.0985
a (AU) [measured] 0.09094 - 0.921 1.5 5.235 -
a (AU) [predicted] 0.098 0.263 0.704 1.885 5.046 13.507
Gliese 876
Distance
4.7 (± 0.01) pc
Spectral Type
M4 V
Mass
0.334 (± 0.03) M
Age
2.5 (+2.5
-2.4) Gyr
Radius
0.36 R
Metallicity [Fe/H]
0.05 (± 0.2)
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
Gliese 876 d c b e
Orbital period (days) 1.93778
± 2.0e-05
30.0881
± 0.0082
61.1166
± 0.0086
124.26
± 0.7
Eccentricity 0.207 0.25591 0.0324 0.055
a (AU) [measured] 0.020807 - - 0.12959 0.208317 0.3343
a (AU) [predicted] 0.022 0.038 0.067 0.117 0.205 0.36 0.63
KOI-730
Apparent Magnitude V
15
Mass
1.07 M
Effective Temperature
5590 K
Radius
1.1 R
n = 1 n = 2 n = 3 n = 4 n = 5
KOI-730 e c b d
Orbital period
(days)
7.3831
± 4.0e-04
9.8499
± 3.0e-04
14.7903
± 0.0002
19.7216
± 0.0004
a (AU) [measured] 0.076 0.092 0.12 0.145 -
a (AU) [predicted] 0.075 0.094 0.117 0.146 0.182
HR 8799
Distance
39.4 (± 0.1) pc
Spectral Type
A5V
Mass
1.56 M
Age
0.06 (+0.1
-0.03) Gyr
Radius
1.5 (± 0.3) R
Metallicity [Fe/H]
-0.47
n = 1 n = 2 n = 3 n = 4 n = 5
HR 8799 e d c b
Orbital period (days) 18000 41 054 82 145 164 250
a (AU) [measured] 14.5 27 42.9 68 -
a (AU) [predicted] 15.214 25.333 42.183 70.239 116.957
Gliese 581
Distance
6.21 (± 0.1) pc
Spectral Type
M2.5 V
Mass
0.31 (± 0.02) M
Age
8 (+3
-1) Gyr
Radius
0.3 (± 0.01) R
Metallicity [Fe/H]
-0.135
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
Gliese 581 e b c d
Orbital period (days)
3.14945
± 1.7e-04
5.36865
± 9e-05
12.9182
± 0.0022
66.64
± 0.14
Eccentricity 0.32 0.031 0.07
a (AU) [measured] 0.028 0.041 0.073 - - 0.22 -
a (AU) [predicted] 0.029 0.043 0.066 0.099 0.15 0.227 0.344
Kepler-20
Distance
290 (± 30) pc
Spectral Type
G8
Mass
0.912 (± 0.035) M
Age
8.8 (+4.7
-2.7) Gyr
Radius
0.944 (+0.06
-0.095)R
Metallicity [Fe/H]
0.02 (± 0.04)
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 n = 8
Kepler-20 b e c f d
Orbital period (days) 3.6961219
6.098493
± 6.5 e-05
10.85092
± 1.3 e-05
19.57706
± 0.00052
77.61185
Eccentricity < 0.32 - < 0.4 0.09 < 0.6
a (AU) [measured] 0.04537 0.0507 0.093 0.11 - - 0.3453 -
a (AU) [predicted] 0.042 0.059 0.083 0.118 0.168 0.238 0.337 0.477
Kepler-33
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
Kepler-33 b c d e f
Orbital period (days)
5.66793
± 0.00012
13.17562
± 1.4 e-04
21.77596
± 1.1 e-04
31.7844
± 0.00039
41.02902
± 0.0004
a (AU) [measured] 0.0677 - 0.1189 0.1662 0.2138 0.2535 -
a (AU) [predicted] 0.07 0.091 0.12 0.157 0.206 0.27 0.354
Apparent Magnitude V
14
Mass
1.291 (+0.063
-0.121) M
Effective Temperature
5904 K
Radius
1.82 (+0.14
-0.18) R
HD 10180
Distance
39.4 (± 1) pc
Spectral Type
G1V
Mass
1.06 (± 0.05) M
Age
4.3 (± 0.5) Gyr
Metallicity [Fe/H]
0.08 (± 0.01)
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
HD 10180 c d e f g h
Orbital period (days) 5.75979
± 0.0001
16.3579
± 0.038
49.745
± 0.022
122.76
± 0.17
601.2
± 8.1
2222
± 91
Eccentricity 0 0.088 0.026 0.135 0.19 0.08
a (AU) [measured] 0.0641 0.1286 0.2699 0.4929 1.422 3.4 -
a (AU) [predicted] 0.058 0.128 0.282 0.621 1.369 3.019 6.655
Kepler-11
Spectral Type
G
Mass
0.95 (± 0.1) M
Age
8 (± 2) Gyr
Radius
1.1 (± 0.1) R
Metallicity [Fe/H]
0 (± 0.1)
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 n = 8
Kepler-11 b c d e f g
Orbital period (days)
10.30375
± 0.00016
13.02502
± 8 e-05
22.68719
± 0.00021
31.9959
± 0.00028
46.68876
± 0.00074
118.37774
± 0.00112
Eccentricity 0 0 0 0 0 0
a (AU) [measured] 0.091 0.106 0.159 0.194 0.25 - 0.462 -
a (AU) [predicted] 0.087 0.114 0.15 0.198 0.26 0.342 0.449 0.591
In summary…
 Exoplanetary systems with 4 observed planets
(with vacancies and extrapolations)
υ And 1 vacancy
n = 2 a = 0.218 AU
n = 6 a = 21.13 AU
KOI-730 0 vacancies
n= 5 a = 0.182 AU
Gliese 581 2 vacancies
n = 4 a = 0.099 AU
n =5 a=0.15 AU**
n= 7 a = 0.63 AU
Gliese 876 2 vacancies
n = 2 a = 0.038 AU
n = 3 a = 0.067 AU
n = 7 a = 0.63 AU
μ Ara 1 vacancy
n = 2 a = 0.263 AU
n = 6 a = 13.507 AU
HR 8799 0 vacancies
n = 5 a = 116.957 AU
 Exoplanetary systems with
5 planets
55 Cancri 1 vacancy
n = 5 a= 2.20 AU
n = 7 a = 21.14 AU
Kepler-20 2 vacancies
n = 5 a = 0.168 AU
n = 6 a = 0.238 AU
n = 8 a = 0.477 AU
Kepler-33 1 vacancy
n = 2 a = 0.091 AU
n = 7 a = 0.354 AU
 Exoplanetary systems with
6 planets
HD 10180 0 vacancies
n = 7 a = 6.655 AU
Kepler-11 1 vacancy
n = 6 a = 0.342 AU
n = 8 a = 0.591 AU
Conclusions
 The results shown here demonstrate that all 11 exoplanetary
systems currently known to harbor four or more planets obey aTB-
like structural relation .
 The two parameters entering the exponential formulation used
here characterize two different aspects of the systems. a0 is
essentially a measure of the overall compactness of the planetary
system. b, on the other hand, characterizes the separation (in units
of a0) between successive planets in the system.
 We find no relation between the value of b and the intrinsic
characteristics (angular momentum, ratio between the stellar and
planetary mass, etc.) of the systems considered here.
 This seems to suggest that the origin of theTB relation is not
related to the formation mechanisms of the systems, but rather to
their subsequent dynamical evolution.
Thank you!
For once pay attention to the widths of the planets from each other
and notice that they are distant from each other almost in a
proportion as their bodily heights increase. Given the distance from
the Sun to Saturn as 100 units, then Mercury is distant 4 such units
from the Sun,Venus 4+3=7 of the same; the Earth 4+6=10; Mars
4+12=16. But see, from Mars to Jupiter there comes forth a
departure from this so exact progression.
From Mars follows a place of 4+24=28 such units, where at the
present neither a chief nor a neighboring planet is to be seen. And
shall the Builder have left this place empty? Never! Let us
confidently wager that, without doubt, this place belongs to the as
yet still undiscovered satellites of Mars; let us add that perhaps
Jupiter also has several around itself that until now have not been
seen with any glass. Above this, to us unrevelead, position ariases
Jupiter’s domain of 4+48=52; and Saturn’s at 4+96=100 units.What
a praiseworthy relation!
Titius-Bode Relation in the
Solar System
Titius-Bode Relation in
Exoplanetary Systems

More Related Content

Similar to On the structural law of exoplanetary systems.pptx

6. galaxy article.pdf
6. galaxy article.pdf6. galaxy article.pdf
6. galaxy article.pdf
BRNSS Publication Hub
 
Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"
Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"
Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"
James Smith
 
How fast do the planets move?
How fast do the planets move?How fast do the planets move?
How fast do the planets move?
DanielPearcy
 
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Sérgio Sacani
 
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Sérgio Sacani
 
Eso1438a
Eso1438aEso1438a
Eso1438a
GOASA
 
Alignment of quasar_polarizations_with_large_scale_structures
Alignment of quasar_polarizations_with_large_scale_structuresAlignment of quasar_polarizations_with_large_scale_structures
Alignment of quasar_polarizations_with_large_scale_structures
Sérgio Sacani
 
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...
Sérgio Sacani
 
Solar system
Solar systemSolar system
Solar system
Malith Niluka
 
Igcse 16-astronomy
Igcse 16-astronomyIgcse 16-astronomy
Igcse 16-astronomy
Bhavana Binu
 
02 distances and scaling
02 distances and scaling02 distances and scaling
02 distances and scaling
mrtangextrahelp
 
Astronomy.ppt
Astronomy.pptAstronomy.ppt
Astronomy.ppt
noman21
 
IGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptx
IGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptxIGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptx
IGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptx
ssuser0836e6
 
Tejeday vargas1996
Tejeday vargas1996Tejeday vargas1996
Tejeday vargas1996
botello05
 
Polarimetric Study of emission nebulea Stock 8 in Auriga
Polarimetric Study of emission nebulea Stock 8 in AurigaPolarimetric Study of emission nebulea Stock 8 in Auriga
Polarimetric Study of emission nebulea Stock 8 in Auriga
rahulporuri
 
Quadrantideos origens
Quadrantideos origensQuadrantideos origens
Quadrantideos origens
Sérgio Sacani
 
4th Year Project
4th Year Project4th Year Project
4th Year Project
Tariqul Dipu
 
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...
Sérgio Sacani
 
The solar system
The solar systemThe solar system
The solar system
Hati Mata
 
There are relativistic effects in the solar group (proves)
There are relativistic effects in the solar group (proves)There are relativistic effects in the solar group (proves)
There are relativistic effects in the solar group (proves)
Gerges francis
 

Similar to On the structural law of exoplanetary systems.pptx (20)

6. galaxy article.pdf
6. galaxy article.pdf6. galaxy article.pdf
6. galaxy article.pdf
 
Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"
Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"
Kepler and Newton vs. Geocentrism, Flat Earth, and the "Vortex"
 
How fast do the planets move?
How fast do the planets move?How fast do the planets move?
How fast do the planets move?
 
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
 
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
Direct imaging and_spectroscopy_of_a_young_extrasolar_kuiper_belt_in_the_near...
 
Eso1438a
Eso1438aEso1438a
Eso1438a
 
Alignment of quasar_polarizations_with_large_scale_structures
Alignment of quasar_polarizations_with_large_scale_structuresAlignment of quasar_polarizations_with_large_scale_structures
Alignment of quasar_polarizations_with_large_scale_structures
 
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...
 
Solar system
Solar systemSolar system
Solar system
 
Igcse 16-astronomy
Igcse 16-astronomyIgcse 16-astronomy
Igcse 16-astronomy
 
02 distances and scaling
02 distances and scaling02 distances and scaling
02 distances and scaling
 
Astronomy.ppt
Astronomy.pptAstronomy.ppt
Astronomy.ppt
 
IGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptx
IGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptxIGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptx
IGCSE-16-Astronomydjdjjdjdjdjjdjjjdjdkd.pptx
 
Tejeday vargas1996
Tejeday vargas1996Tejeday vargas1996
Tejeday vargas1996
 
Polarimetric Study of emission nebulea Stock 8 in Auriga
Polarimetric Study of emission nebulea Stock 8 in AurigaPolarimetric Study of emission nebulea Stock 8 in Auriga
Polarimetric Study of emission nebulea Stock 8 in Auriga
 
Quadrantideos origens
Quadrantideos origensQuadrantideos origens
Quadrantideos origens
 
4th Year Project
4th Year Project4th Year Project
4th Year Project
 
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...
 
The solar system
The solar systemThe solar system
The solar system
 
There are relativistic effects in the solar group (proves)
There are relativistic effects in the solar group (proves)There are relativistic effects in the solar group (proves)
There are relativistic effects in the solar group (proves)
 

Recently uploaded

Simulations of pulsed overpressure jets: formation of bellows and ripples in ...
Simulations of pulsed overpressure jets: formation of bellows and ripples in ...Simulations of pulsed overpressure jets: formation of bellows and ripples in ...
Simulations of pulsed overpressure jets: formation of bellows and ripples in ...
Sérgio Sacani
 
Composting blue materials - Joshua Cabell
Composting blue materials - Joshua CabellComposting blue materials - Joshua Cabell
Composting blue materials - Joshua Cabell
Faculty of Applied Chemistry and Materials Science
 
Bacteria l classification(sperical).pptx
Bacteria l classification(sperical).pptxBacteria l classification(sperical).pptx
Bacteria l classification(sperical).pptx
shubhamve111yadav
 
Complementary interstellar detections from the heliotail
Complementary interstellar detections from the heliotailComplementary interstellar detections from the heliotail
Complementary interstellar detections from the heliotail
Sérgio Sacani
 
Ancient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , BiogenesisAncient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , Biogenesis
SoniaBajaj10
 
How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?
How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?
How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?
Christian Birchler
 
Shoot apex organization and its theories
Shoot apex organization and its theoriesShoot apex organization and its theories
Shoot apex organization and its theories
MEGHASHREE A M
 
MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)
MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)
MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)
Steffi Friedrichs
 
A hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbitA hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbit
Sérgio Sacani
 
From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...
From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...
From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...
Sérgio Sacani
 
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
Faculty of Applied Chemistry and Materials Science
 
Post RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) MetabolismPost RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) Metabolism
Areesha Ahmad
 
Potential of Marine Renewable and Non renewable energy.pptx
Potential of Marine Renewable and Non renewable energy.pptxPotential of Marine Renewable and Non renewable energy.pptx
Potential of Marine Renewable and Non renewable energy.pptx
J. Bovas Joel BFSc
 
Synopsis: Analysis of a Metallic Specimen
Synopsis: Analysis of a Metallic SpecimenSynopsis: Analysis of a Metallic Specimen
Synopsis: Analysis of a Metallic Specimen
Sérgio Sacani
 
Traditional, current and future use of fish and seaweed for fertilisation - ...
Traditional, current and future use of fish and seaweed for fertilisation -  ...Traditional, current and future use of fish and seaweed for fertilisation -  ...
Traditional, current and future use of fish and seaweed for fertilisation - ...
Faculty of Applied Chemistry and Materials Science
 
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
marigreenproject
 
Animal biotechnology Cattle breeds....pptx
Animal biotechnology Cattle breeds....pptxAnimal biotechnology Cattle breeds....pptx
Animal biotechnology Cattle breeds....pptx
Ritesh Chavan
 
Biochar impregnation as slow release fertilizer - Violeta Alexandra Ion
Biochar impregnation as slow release fertilizer - Violeta Alexandra IonBiochar impregnation as slow release fertilizer - Violeta Alexandra Ion
Biochar impregnation as slow release fertilizer - Violeta Alexandra Ion
Faculty of Applied Chemistry and Materials Science
 
Classification and role of plant nutrients - Roxana Madjar
Classification and role of plant nutrients - Roxana MadjarClassification and role of plant nutrients - Roxana Madjar
Classification and role of plant nutrients - Roxana Madjar
Faculty of Applied Chemistry and Materials Science
 
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
Dr. Lenin Kumar Bompalli
 

Recently uploaded (20)

Simulations of pulsed overpressure jets: formation of bellows and ripples in ...
Simulations of pulsed overpressure jets: formation of bellows and ripples in ...Simulations of pulsed overpressure jets: formation of bellows and ripples in ...
Simulations of pulsed overpressure jets: formation of bellows and ripples in ...
 
Composting blue materials - Joshua Cabell
Composting blue materials - Joshua CabellComposting blue materials - Joshua Cabell
Composting blue materials - Joshua Cabell
 
Bacteria l classification(sperical).pptx
Bacteria l classification(sperical).pptxBacteria l classification(sperical).pptx
Bacteria l classification(sperical).pptx
 
Complementary interstellar detections from the heliotail
Complementary interstellar detections from the heliotailComplementary interstellar detections from the heliotail
Complementary interstellar detections from the heliotail
 
Ancient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , BiogenesisAncient Theory, Abiogenesis , Biogenesis
Ancient Theory, Abiogenesis , Biogenesis
 
How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?
How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?
How Does Simulation-Based Testing for Self-Driving Cars Match Human Perception?
 
Shoot apex organization and its theories
Shoot apex organization and its theoriesShoot apex organization and its theories
Shoot apex organization and its theories
 
MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)
MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)
MACRAMÉ ChIPs @Behoerdenklausur 2024 (Berlin)
 
A hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbitA hot-Jupiter progenitor on a super-eccentric retrograde orbit
A hot-Jupiter progenitor on a super-eccentric retrograde orbit
 
From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...
From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...
From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairi...
 
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
End of pipe treatment: Unlocking the potential of RAS waste - Carlos Octavio ...
 
Post RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) MetabolismPost RN - Biochemistry (Unit 7) Metabolism
Post RN - Biochemistry (Unit 7) Metabolism
 
Potential of Marine Renewable and Non renewable energy.pptx
Potential of Marine Renewable and Non renewable energy.pptxPotential of Marine Renewable and Non renewable energy.pptx
Potential of Marine Renewable and Non renewable energy.pptx
 
Synopsis: Analysis of a Metallic Specimen
Synopsis: Analysis of a Metallic SpecimenSynopsis: Analysis of a Metallic Specimen
Synopsis: Analysis of a Metallic Specimen
 
Traditional, current and future use of fish and seaweed for fertilisation - ...
Traditional, current and future use of fish and seaweed for fertilisation -  ...Traditional, current and future use of fish and seaweed for fertilisation -  ...
Traditional, current and future use of fish and seaweed for fertilisation - ...
 
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
17. 20240529_Ingrid Olesen_MariGreen summer school.pdf
 
Animal biotechnology Cattle breeds....pptx
Animal biotechnology Cattle breeds....pptxAnimal biotechnology Cattle breeds....pptx
Animal biotechnology Cattle breeds....pptx
 
Biochar impregnation as slow release fertilizer - Violeta Alexandra Ion
Biochar impregnation as slow release fertilizer - Violeta Alexandra IonBiochar impregnation as slow release fertilizer - Violeta Alexandra Ion
Biochar impregnation as slow release fertilizer - Violeta Alexandra Ion
 
Classification and role of plant nutrients - Roxana Madjar
Classification and role of plant nutrients - Roxana MadjarClassification and role of plant nutrients - Roxana Madjar
Classification and role of plant nutrients - Roxana Madjar
 
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
The Next-Gen Innovative Therapeutic Potential of Probiotics: Insights into Gu...
 

On the structural law of exoplanetary systems.pptx

  • 1. ON THE STRUCTURAL LAW OF EXOPLANETARY SYSTEMS Patricia Lara, Arcadio Poveda & Christine Allen Instituto de Astronomía, UNAM ICNAAM 2012 Kos, Greece 19-25 September 2012
  • 2. Titius-Bode Relation n a 2 3 . 0 4 . 0    donde n = -∞ (Mercury), 0 (Venus),1 (Earth), 2,…
  • 5. Titius-Bode Relation (TBR) Original TBR where n = 0, 3, 6,12 .. Classic TBR (modern formulation) where n = -∞ , 0, 1, 2, … 10 4   n a n a 2 3 . 0 4 . 0    Exponential TBR where n = 1, 2, 3, … n n k P P   0 Dermott´s law where n = 0, 1, 2, … bn n n e a C a a 0 0   
  • 6. TBR in the Solar System Sistema Solar a = 0.1912e0.5594n R 2 = 0.992 0 5 10 15 20 25 30 35 0 1 2 3 4 5 6 7 8 9 10 n a (AU) Poveda &Lara, 2008 Solar System
  • 8. 55 Cancri Distance 12.34 (± 0.4) pc Spectral Type K0IV-V Mass 0.905 (± 0.015) M Age 10.2 (± 2.5) Gyr Radius 0.943 (± 0.01) R Metallicity [Fe/H] 0.31 (± 0.04) n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 55 Cnc e b c f d Orbital period (days) 0.7365449 ± 5e-06 14.651262 ± 0.0008 44.3446 ± 0.007 260.7 ± 1.1 5218 ± 230 Eccentricity 0.057 0.0159 0.053 a (AU) [measured] 0.0156 0.1148 0.2403 0.781 - 5.76 - a (AU) [predicted] 0.0239 0.074 0.2292 0.7103 2.2011 6.8214 21.14 exoplanet.eu
  • 9. υ Andromeda Distance 13.47 (± 0.13) pc Spectral Type F8 V Mass 1.27 (± 0.06) M Age 3.8 (± 1) Gyr Radius 1.631 (± 0.014) R Metallicity [Fe/H] 0.09 (± 0.06) n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 Ups And b c d e Orbital period (days) 4.6171 ± 4.7e-05 237.7 ± 0.2 1302.61 3848.86 ± 0.74 Eccentricity 0.013 0.24 0.274 0.00536 a (AU) [measured] 0.059 - 0.861 2.55 5.2456 - a (AU) [predicted] 0.069 0.218 0.683 2.145 6.732 21.13
  • 10. μ Ara Distance 15.3 pc Spectral Type G3 IV-V Mass 1.08 (± 0.05) M Age 6.41 Gyr Radius 1.245 (± 0.255) R Metallicity [Fe/H] 0.28 (± 0.04) n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 mu Ara c d b e Orbital period (days) 9.6386 ± 0.0015 310.55 ± 0.83 643.25 ± 0.9 4205.8 ± 758.9 Eccentricity 0.172 0.0666 0.128 0.0985 a (AU) [measured] 0.09094 - 0.921 1.5 5.235 - a (AU) [predicted] 0.098 0.263 0.704 1.885 5.046 13.507
  • 11. Gliese 876 Distance 4.7 (± 0.01) pc Spectral Type M4 V Mass 0.334 (± 0.03) M Age 2.5 (+2.5 -2.4) Gyr Radius 0.36 R Metallicity [Fe/H] 0.05 (± 0.2) n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 Gliese 876 d c b e Orbital period (days) 1.93778 ± 2.0e-05 30.0881 ± 0.0082 61.1166 ± 0.0086 124.26 ± 0.7 Eccentricity 0.207 0.25591 0.0324 0.055 a (AU) [measured] 0.020807 - - 0.12959 0.208317 0.3343 a (AU) [predicted] 0.022 0.038 0.067 0.117 0.205 0.36 0.63
  • 12. KOI-730 Apparent Magnitude V 15 Mass 1.07 M Effective Temperature 5590 K Radius 1.1 R n = 1 n = 2 n = 3 n = 4 n = 5 KOI-730 e c b d Orbital period (days) 7.3831 ± 4.0e-04 9.8499 ± 3.0e-04 14.7903 ± 0.0002 19.7216 ± 0.0004 a (AU) [measured] 0.076 0.092 0.12 0.145 - a (AU) [predicted] 0.075 0.094 0.117 0.146 0.182
  • 13. HR 8799 Distance 39.4 (± 0.1) pc Spectral Type A5V Mass 1.56 M Age 0.06 (+0.1 -0.03) Gyr Radius 1.5 (± 0.3) R Metallicity [Fe/H] -0.47 n = 1 n = 2 n = 3 n = 4 n = 5 HR 8799 e d c b Orbital period (days) 18000 41 054 82 145 164 250 a (AU) [measured] 14.5 27 42.9 68 - a (AU) [predicted] 15.214 25.333 42.183 70.239 116.957
  • 14. Gliese 581 Distance 6.21 (± 0.1) pc Spectral Type M2.5 V Mass 0.31 (± 0.02) M Age 8 (+3 -1) Gyr Radius 0.3 (± 0.01) R Metallicity [Fe/H] -0.135 n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 Gliese 581 e b c d Orbital period (days) 3.14945 ± 1.7e-04 5.36865 ± 9e-05 12.9182 ± 0.0022 66.64 ± 0.14 Eccentricity 0.32 0.031 0.07 a (AU) [measured] 0.028 0.041 0.073 - - 0.22 - a (AU) [predicted] 0.029 0.043 0.066 0.099 0.15 0.227 0.344
  • 15. Kepler-20 Distance 290 (± 30) pc Spectral Type G8 Mass 0.912 (± 0.035) M Age 8.8 (+4.7 -2.7) Gyr Radius 0.944 (+0.06 -0.095)R Metallicity [Fe/H] 0.02 (± 0.04) n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 n = 8 Kepler-20 b e c f d Orbital period (days) 3.6961219 6.098493 ± 6.5 e-05 10.85092 ± 1.3 e-05 19.57706 ± 0.00052 77.61185 Eccentricity < 0.32 - < 0.4 0.09 < 0.6 a (AU) [measured] 0.04537 0.0507 0.093 0.11 - - 0.3453 - a (AU) [predicted] 0.042 0.059 0.083 0.118 0.168 0.238 0.337 0.477
  • 16. Kepler-33 n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 Kepler-33 b c d e f Orbital period (days) 5.66793 ± 0.00012 13.17562 ± 1.4 e-04 21.77596 ± 1.1 e-04 31.7844 ± 0.00039 41.02902 ± 0.0004 a (AU) [measured] 0.0677 - 0.1189 0.1662 0.2138 0.2535 - a (AU) [predicted] 0.07 0.091 0.12 0.157 0.206 0.27 0.354 Apparent Magnitude V 14 Mass 1.291 (+0.063 -0.121) M Effective Temperature 5904 K Radius 1.82 (+0.14 -0.18) R
  • 17. HD 10180 Distance 39.4 (± 1) pc Spectral Type G1V Mass 1.06 (± 0.05) M Age 4.3 (± 0.5) Gyr Metallicity [Fe/H] 0.08 (± 0.01) n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 HD 10180 c d e f g h Orbital period (days) 5.75979 ± 0.0001 16.3579 ± 0.038 49.745 ± 0.022 122.76 ± 0.17 601.2 ± 8.1 2222 ± 91 Eccentricity 0 0.088 0.026 0.135 0.19 0.08 a (AU) [measured] 0.0641 0.1286 0.2699 0.4929 1.422 3.4 - a (AU) [predicted] 0.058 0.128 0.282 0.621 1.369 3.019 6.655
  • 18. Kepler-11 Spectral Type G Mass 0.95 (± 0.1) M Age 8 (± 2) Gyr Radius 1.1 (± 0.1) R Metallicity [Fe/H] 0 (± 0.1) n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 n = 8 Kepler-11 b c d e f g Orbital period (days) 10.30375 ± 0.00016 13.02502 ± 8 e-05 22.68719 ± 0.00021 31.9959 ± 0.00028 46.68876 ± 0.00074 118.37774 ± 0.00112 Eccentricity 0 0 0 0 0 0 a (AU) [measured] 0.091 0.106 0.159 0.194 0.25 - 0.462 - a (AU) [predicted] 0.087 0.114 0.15 0.198 0.26 0.342 0.449 0.591
  • 19. In summary…  Exoplanetary systems with 4 observed planets (with vacancies and extrapolations) υ And 1 vacancy n = 2 a = 0.218 AU n = 6 a = 21.13 AU KOI-730 0 vacancies n= 5 a = 0.182 AU Gliese 581 2 vacancies n = 4 a = 0.099 AU n =5 a=0.15 AU** n= 7 a = 0.63 AU Gliese 876 2 vacancies n = 2 a = 0.038 AU n = 3 a = 0.067 AU n = 7 a = 0.63 AU μ Ara 1 vacancy n = 2 a = 0.263 AU n = 6 a = 13.507 AU HR 8799 0 vacancies n = 5 a = 116.957 AU
  • 20.  Exoplanetary systems with 5 planets 55 Cancri 1 vacancy n = 5 a= 2.20 AU n = 7 a = 21.14 AU Kepler-20 2 vacancies n = 5 a = 0.168 AU n = 6 a = 0.238 AU n = 8 a = 0.477 AU Kepler-33 1 vacancy n = 2 a = 0.091 AU n = 7 a = 0.354 AU  Exoplanetary systems with 6 planets HD 10180 0 vacancies n = 7 a = 6.655 AU Kepler-11 1 vacancy n = 6 a = 0.342 AU n = 8 a = 0.591 AU
  • 21. Conclusions  The results shown here demonstrate that all 11 exoplanetary systems currently known to harbor four or more planets obey aTB- like structural relation .  The two parameters entering the exponential formulation used here characterize two different aspects of the systems. a0 is essentially a measure of the overall compactness of the planetary system. b, on the other hand, characterizes the separation (in units of a0) between successive planets in the system.  We find no relation between the value of b and the intrinsic characteristics (angular momentum, ratio between the stellar and planetary mass, etc.) of the systems considered here.  This seems to suggest that the origin of theTB relation is not related to the formation mechanisms of the systems, but rather to their subsequent dynamical evolution.
  • 23. For once pay attention to the widths of the planets from each other and notice that they are distant from each other almost in a proportion as their bodily heights increase. Given the distance from the Sun to Saturn as 100 units, then Mercury is distant 4 such units from the Sun,Venus 4+3=7 of the same; the Earth 4+6=10; Mars 4+12=16. But see, from Mars to Jupiter there comes forth a departure from this so exact progression. From Mars follows a place of 4+24=28 such units, where at the present neither a chief nor a neighboring planet is to be seen. And shall the Builder have left this place empty? Never! Let us confidently wager that, without doubt, this place belongs to the as yet still undiscovered satellites of Mars; let us add that perhaps Jupiter also has several around itself that until now have not been seen with any glass. Above this, to us unrevelead, position ariases Jupiter’s domain of 4+48=52; and Saturn’s at 4+96=100 units.What a praiseworthy relation!
  • 24. Titius-Bode Relation in the Solar System

Editor's Notes

  1. First I would like thank yo the organizing comitte for invite me to this event I´m here to present my work that I being doing with my advisors Dr. Arcadio Poveda and Mrs Christine Allen The title of this talk is On the structural law fo exoplanetary systems Well What is it about?
  2. The major semi-axes of the Solar System obey a simple geometric progression know the Titius-Bode Law. The Titius-Bode Law is not really a law in the physical sense but rather a numerical relation. SO because of that we will call it Titius-Bode relation or TBR. Here is the mathematical relation for the Solar system where “a” gives the distance in astronomical units for the corresponding orbital number. The TBR was born and prevale until our days because of two astronomers: Johann Daniel Titius and Johann Elert Bode Titius was the first to declare it and Bode using his fame and prestige promote it every time that he has oportunity.
  3. The discovery of the fith planet in 55 cancri (THAT AT THE TIME WAS THE EXOPLANETARY SYSTEM WITH MOST PLANETS OBSERVED) Who motivated us to try TBR to this exoplanetary system. Here we will show that the others 10 systems to harbor four or more planets also obey a structural law.
  4. If we put in a mathematical form what Titius state orally, the ecuation will be like this… We can see that Titius scaleated the distance from the Sun to the Earth to 10 units so the orbital number follow this progression where for Mercury is 0, 3 for Venus, 6 to the Earth. Through the years the Original TBR suffer modifications for the Solar System in the orbital number, here we can observed that for Mercury correspond –infinity, 0 for Venus, 1 for the Earth and so on. In 1968, Dermott et al shown that the major satellite of Jupiter, Saturn and Uranus obey a similar progression of… For Keplerian orbits Dermorr’s law will obey a similar law like this….. And the two parameters to stablish in this exponential relation is Ao and B.
  5. For the porpuose that TBR could be a structural law for planetary systems, it has to be a generalized relation. So we applied to the solar system. Here I show the fit to the Solar system where in the horizontal axis is the orbital number and in the vertical axis is the distances in astronomic units, and looks very well and this fit along with 55 cancri was published in paper of Poveda and Lara, for 55 Cancri we will see later his fit
  6. Also we apply TBR to the major satellite of Jupiter, Saturn and Uranus. And every fit looks good and here we have to pay attention to the Gallilean Satellite. Io, Europe and Ganimedes are in resonance know as the Laplacian resonance (1:2:4) and this system is an exemplar example of the TBR.
  7. This the fit for 55 Cancri, and here we observed the orbital parameters and the observed distances. In the paper of Poveda and Lara, 55 Cancri e has a major semi-axes of 0.038 but in 2010 Dawson et al argued that the major semi-axis of 55 Cancri is 0.0156. Because of that I show the fit with the corrected distance. This fit show a vacancy in the orbital 5, and we predict a planet as yet to be found at 2.2 AU. Also we extrapolate to the orbital 7 and with less ceartanty we predict a planet in the orbital 7 with a major semi-axis of 21.14
  8. Now we start to analize the exoplanetary systems with 4 planets. We see the the exoplanetary system of Upsilon Andromeda. Also we the observed and predicted distances by TBR. TBR fir show a vacancy in the orbital 2 with a major semi-axis of