tides on earth, in the solar system and beyond….....rosetta_cd\pr\what_is_rs.ppt, 10.06.2011...
TRANSCRIPT
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483rd WE-Heraeus SeminarExtrasolar Planets:
Towards Comparative Planetology beyond the Solar System
Tideson Earth,
in the Solar System and Beyond…..
Martin Pätzold Rheinisches Institut für Umweltforschung
an der Universität zu KölnAbteilung Planetenforschung
Köln
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tide levels for Hamburg, Sankt Pauli:
Tuesday, 7th June 2011 (CEST)
Low tide 04:03 0.3 m
High tide 09:07 3.9 m
Low tide 16:07 0.4 m
High tide 21:16 4.3 m
Bundesamt für Seeschifffahrt und Hydrographie
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Mont St. Michel, Bretagne
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, 11 The tidal force is a differenced force!
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, 12 The formation of the tidal bulge is
usually known as the (high) tide
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Revolution without rotation
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Revolution without rotation But the Earth rotates!
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• The Earth rotates faster than the Moon revolves
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• The Earth rotates faster than the Moon revolves
• The tidal bulge is advancing the direct LOS
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• The Earth rotates faster than the Moon revolves
• The tidal bulge is advancing the direct LOS
• Torques try to pull the tidal bulge back into LOS
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• The Earth rotates faster than the Moon revolves
• The tidal bulge is advancing the direct LOS
• Torques try to pull the tidal bulge back into LOS
• Consequence is a slow down of Earth rotation (tidal friction)
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chan
gein
LO
D re
lativ
e to
864
00 s
average change in LOD due to lunar tides:2.3 ms/cy
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• The Earth rotates faster than the Moon revolves
• The tidal bulge is advancing the direct LOS
• Torques try to pull the tidal bulge back into LOS
• Consequence is a slow down of Earth rotation (tidal friction)
• another consequence from conservation of angular momentum: the Moon recedes from the Earth
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The first extraterrestrial applied space geophysicist
seismometer Lunar Laser RangingReflector
Buzz Aldrin, Apollo 11, 1969
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Lunar Laser Ranging
Apollo 15 reflector
Wettzell Lunar Laser Station
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Lunar Laser Ranging
Apollo 15 reflector
Wettzell Lunar Laser Station
The Moon recedes from Earth by 4m/cy
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• The Earth rotates faster than the Moon revolves
• The tidal bulge is advancing the direct LOS by 3°
• Earth rotates below the tidal bulge
• A location on the surface experiences periodically high and low tides
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Ocean tides are the directly visiblemanifestation of tidal forces
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• The Earth rotates faster than the Moon revolves
• The tidal bulge is advancing the direct LOS
• Torques try to pull the tidal bulge back into LOS
• Consequence is a slow down of Earth rotation (tidal friction)
• another consequence from conservation of angular momentum: the Moon recedes from the Earth
Is there a case in the solar system wherea moon revolves faster than the planet rotates?
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• The Earth rotates faster than the Moon revolves
• The tidal bulge is advancing the direct LOS
• Torques try to pull the tidal bulge back into LOS
• Consequence is a slow down of Earth rotation (tidal friction)
• another consequence from conservation of angular momentum: the Moon recedes from the Earth
Is there a case in the solar system wherea moon revolves faster than the planet rotates?
YES, there is!
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The Mars/Phobos case
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The Mars/Phobos case
Phobossize : 26 x 22 x 18 kmperiod : 7 h 39 mdistance : 9,378 km
Deimossize : 15 x 12 x 10 kmperiod : 30 h 17 mdistance : 23,459 km
Marsradius : 3,990 km period : 24 h 37 m
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The Mars/Phobos case
Phobossize : 26 x 22 x 18 kmperiod : 7 h 39 mdistance : 9,378 km
Deimossize : 15 x 12 x 10 kmperiod : 30 h 17 mdistance : 23,459 km
synchronous orbit:planetary rotation = moon revolution
Mars24 h 37 m
21,000 km distancePhobos: inside
Deimos: outside
Marsradius : 3,990 km period : 24 h 37 m
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The Mars/Phobos case
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The Mars/Phobos case
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The Mars/Phobos case
The orbit of Phobos decays until the Roche limit is reached.
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P PR S P
S S
Ma cR cRM
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The Mars/Phobos case
The orbit of Phobos decays until the Roche limit is reached.
Roche limit:
Proportionality factor c depends on the nature of thesecondary: fluid c = 2.44 => aR = 10,500 km
solid c = 1.26 => aR = 5,500 km rubble pile c = 1.54 => aR = 6,700 km
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P PR S P
S S
Ma cR cRM
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The Mars/Phobos case
The orbit of Phobos decays until the Roche limit is reached.
Roche limit:
Proportionality factor c depends on the nature of thesecondary: fluid c = 2.44 => aR = 10,500 km
solid c = 1.26 => aR = 5,500 km rubble pile c = 1.54 => aR = 6,700 km
Phobos is highly porous => „rubble pile“ (Andert et al., 2010)
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P PR S P
S S
Ma cR cRM
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When will Phobos reach the Roche limit?
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R
RocheMars Ph
Mars MarsMars Mars
a a
k M R GMQ M
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When will Phobos reach the Roche limit?
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R
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When will Phobos reach the Roche limit?
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Other tidal phenomena in the solar system
• forcing Mercury in a 3/2 resonance• forcing all moons in the solar system into synchronous
rotation• deforming the Jupiter moon Io periodically => tidal
heating => volcanic activity• and the non-plus-ultra:
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Other tidal phenomena in the solar system
• forcing Mercury in a 3/2 resonance• forcing all moons in the solar system into synchronous
rotation• deforming the Jupiter moon Io periodically => tidal
heating => volcanic activity• and the non-plus-ultra: synchronizing the Pluto system
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Tides in extrasolar systems
• studying tides in extrasolar planetary systems requires the knowledge of mass and size of the planet and the star
• feasible with transiting planets combined with radial velocity observations and spectroscopy
• orbital decay => survivability• stellar spin-up• spin-orbit coupling => synchronization of rotation and revolution• circularization => e -> 0
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The tidal potential or the Doodson constant
two tidal potentials:a)The primary acting on the secondaryb) The secondary acting on the primary
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pps s
GMD R
a 2
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sp pGMD Ra
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The tidal potential or the Doodson constant
two tidal potentials:a) The primary acting on the secondaryb) The secondary acting on the primary
Earth/Moon system:Earth on Moon Moon on EarthDps = 20.9 m2/s2 Dsp = 3.5 m2/s2
Sun on EarthDsp = 1.6 m2/s2
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When will the planet reach the stellar Roche limit?
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star starstar star
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When will the planet reach the stellar Roche limit?
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Rochestar P
star starstar star
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stellar property factor
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When will the planet reach the stellar Roche limit?
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• tidal forces affect the evolution of extrasolar planetary systems
• if a < 0.1 AU• if Mp is large• may force orbits towards e -> 0• may lead to the loss of companions• may force massive companions into double-
synchronous rotation• but the companion is not safe….
• may spin-up stellar rotation (look for old fast rotating stars)
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…book your next boat tour when the tide is in!