Tidal Forces Tides Generate a Tidal Bulge Along the Equator

Home , Orbital resonance, Tidal heating

Lattimer, AST 301, Tidal Lecture – p.1/18 ] nd pulling of the planetary 2 rotates, the bulge is ) g the Moon away. 2 ocked, the rotation of the r force that changes angular . ) r 3 r − 4 R + 2 R ) ( R r ( − 2 + ) 2 r GMm ) GMm R r ( − = + − R 4 ( R 2 Rr ( R ) 4 [ r − GMm R ( GMm GMm = = ≈ t F

Tidal Forces Tides generate a tidal bulge along the equator. As the object momentum). The strong tides have synchronized, or tidally l dragged around the object oppositematerial to generates the frictional spin. heat The and pushing produces a a torque (a Moon with its orbital period, 28 Earth days. Tides are pushin 1 orbital Lattimer, AST 301, Tidal Lecture – p.2/18 , even causing rdment and sulted in tidal lt and/or the nd maintains a may have d in small integer esimals. e tidal bulge is pulled stabilized an eccentric orbit the cts become synchronized An extreme case is theresonance Io, that Europa makes and Io Ganymede tremendously system volcanically in active a a 4:2: This could have pushed Uranusthem and to Neptune change into places. larger orbits Coincident with expulsion of objects from an early Kuiper be liquid shell under Europa’s icy crust. asteroid belt that could have explained the Late Heavy Bomba also formed Jupiter’s Trojan asteroids.

Effects of Tidal Forces • • • back and forth; the friction heats the interior. orbital speed varies with separation (Kepler’s 2nd Law). Th developed due to weak gravitational encounters with planet heating and some surface features now visible. Tides or tidal bulges: changing sea levels Rotational Resonances: spins of bodies become synchronize Orbital resonances: orbital stabilization of 2 or more obje Tidal heating: Satellites rotate at a constant speed, but in A past 2:1 resonance between the orbits of Jupiter and Saturn An early 2:3 resonance between Dione and Tethys could have re ratios with frequencies in small integer ratios, or orbits can be de • • • • • • Lattimer, AST 301, Tidal Lecture – p.3/18 6 resonances others locked to r

Spin Resonances Saturn Mercury in a 3:2 rotation:orbit resonance Moon locked to Earth; a 1:1 rotation:orbitPhobos & resonance Deimos locked to Mars Io, Europa, Ganymede, Callisto and 4 othersMimam, locked Enceladus, to Tethys, Dione, Jupite Rhea, Titan, Iapetus and 8 Miranda, Ariel, Umbriel and Titania locked toProteus Uranus and Titania locked to Neptune Charon and Pluto locked to each other;Tau Bootis Nix locked & to Hydra an in orbiting 1:4 giant andGliese planet 1: 581 b and c locked to parent star Gliece 581 a • • • • • • • • • • Lattimer, AST 301, Tidal Lecture – p.4/18 th Pan and with Jupiter) nces (Hilda family, Hyperion (4:3) with Neptune nance with Mimas ung away. ting. al periods. nce ’pumps’ the eccentricity bodies exchange momentum . Resonances involve a ratio of al inﬂuence on each other.

Orbital Resonances Daphnis Thule family and Trojans) Kirkwood gaps within 3.5 AU (1:3, 2:5,Cassini 3:7 Division and between 1:2 Saturn’s resonances A and BEncke rings and from Keeler 2:1 gaps reso in Saturn’s A ring from 1:1 resonance wi Outer edge of A ring in a 7:6 resonance with Janus Io, Europa and Ganymede in a 4:2:1Mimas orbital and frequency Tethys (2:1), lock Enceladus and DionePluto (2:1), and Titan many and Kuiper Belt Objects inClumps a in 3:2 asteroid orbital belt resonance beyond 3.5 AU: 3:2, 4:3 and 1:1 resona Gliese 581 b, c and e are in a 1:2:4 orbital resonance • • • • • • • • • number of orbits in aMost given often, time this rather results than in theand an ratio shift unstable of orbits interaction orbit until in the which until resonance a disappears. body The approaches resona a planet too closely and the body is sl Two orbiting objects exert a regular,Orbital periodic frequencies gravitation related by a ratio of two small integers In some cases, the resonant system is stable and self-correc • Roche limit: Minimum distance from a planet that a solid satellite can orbit without tides pulling it asunder. Equate tidal force and self-gravity of 2 moonlets of mass m and radius r:

2 1/3 4r m 4/3 M GMm 3 = G 2 , or RR = 2 r . RR 4r „ m «

3 Planet’s average density is ρ⊕ = 3M⊕/(4πR⊕) 3 moon’s average density is ρm = 3m/(4πr ) Implies that the Roche limit is

1/3 4/3 ρ⊕ RR = 2 R⊕ ≈ 2.5 − 3R⊕. „ ρm «

• Rings and satellites: Large satellites must orbit outside the Roche Limit. Rings can extend to the Roche Limit. • All the Jovian planets have rings; Outer edge of Saturn’s A ring is at 2.3RY • Eventual loss of prograde satellites: Frictional loss of angular momentum leads to expanding orbits. • Destruction of retrograde satellites: Retrograde satellites have shrinking or decaying orbits and will eventually fall within the Roche Limit and be destroyed. • Triton will be destroyed in 100 Myr to 1 Gyr. Lattimer, AST 301, Tidal Lecture – p.5/18 Lattimer, AST 301, Tidal Lecture – p.6/18 ken rocks and dust n on the far side, 2240

The Moon The moon is in synchronous rotation Only 1 side of moon visible fromBright Earth regions are heavily cratered highlands Dark regions, called mare, are lava-ﬂooded lowlands Near side of moon is 31% mare;Craters far due side to is impact; 2% largest mare is the South-Pole Aitken basi The moon is surface, called the regiolith, is composed of bro km diameter and 13 km deep – the largest crater in solar system • • • • • • • Lattimer, AST 301, Tidal Lecture – p.7/18 time-variable rotation)

Lunar Interior Crust—50 km thick solid magma ocean Mantle—to depths of about 800 km Core—small, semi-liquid or plastic (as indicated by moon’s Wikipedia • • • Seismometry determines lunar structure: Lattimer, AST 301, Tidal Lecture – p.8/18 (discovered by ion of a small amount cks s (Ni, Mn, ...) in lunar

Lunar Surface Composition No sedimentary rocks (limestone, shale) on theAll Moon lunar rocks are igneous (cooling lava) Nearly complete lack of water in lunar rocks, with the except General lack of volatile elements (Hg, Na,General K, lack ...) of iron and in iron-loving lunar (siderophile) ro element of water hidden in deep craters at lunar north and south poles rocks. Clementine and Lunar Prospector) • • • • • iles. Also Lattimer, AST 301, Tidal Lecture – p.9/18 ains lack of opic similarity to to occur 30-50 million th-moon system. ies of other chemical and , or ﬁssion. Needs too much spin, cannot explain lack of volat of a Mars-sized object (called Theia) with early Earth. Expl theory. Difﬁcult to make regular orbit, cannot explain isot , or co-accretion. Cannot explain lack of iron.

Theories of Moon's Origin volatiles and iron, preserves other similarities. Thought Daughter Sister Capture Collision years after Earth’s formation. Earth. Statistically improbable. predicts moon should orbit in equatorial plane of Earth. • • • • isotopic properties; also the large angular momentum of Ear Must explain lack of iron and lack of volatiles and similarit . Lattimer, AST 301, Tidal Lecture – p.10/18 lunar mare arth (?) exception of the nt; oldest surviving ve meteoroid ﬂows from interior wind, cosmic rays and iquid is shrinking and is egions reaching depths

Lunar Chronology rocks date to 4.3 Byrs. Moon formed 4.4–4.5 Byrs ago, by impactOriginal of rocks minor obliterated planet by with extreme E meteoroid bombardme Highland regions are oldest and provide evidence of extensi Radioactive heating melted interior of Moon, semi-liquid r Last large impacts fractured crust, producing massive lava Moon has been geologically quiet since 3.1 Byrs ago, with the bombardment until 3.9 Byrs ago. of 200 km 3–3.5 Byrs ago. which ﬁlled large impact basins 3–3.5 Byrs ago. This created alterations caused by occasional meteoroid impacts, solar human spacecraft. The portion ofalmost the gone interior now. that is semi-l • • • • • • = 19 8 0 . 2 m sE R ω m 2 E Lattimer, AST 301, Tidal Lecture – p.11/18 sE 77] = 3 R M . ω 5 2 , a/a E – 2 E – 5 . 2 2 M R / 64[0 / , 5 2 . 1 s 1 E s 2 E ” ” L ω ≃ = 57 M 0 R 0 a s a a + ) 5 2 a I E E “ “ + M sm = =1+3 orb − 5 2 − ω s L – 1 1 2 L m 2 orb » = » / = ω R 1 s 2 orb 0 1 P ” m a s orb , a/R spin 0 2 ω L a m M a 81 π/ω 2 « / “ + M + « , I E 0 a − = 2 = 2 E E R = 1 a sE a 1 orb 0 R „ ω orb, » E ω E 2 „ 2 E 2 L sE a E m M ω R « orb /M m E m I M M 2 E E + , P E m a M M 2 M 2 5 R E = R M / 3 2 m a ( 5 2 E 3 a ≃ a + „ ) 2 5 E 0 1 M m orb + 2 E orb m M − 5 2 L 1 sE M ) ω ,M M sE M a/a P = E + ( = ω 28 0 m = / )= sE P = /M orb a P 0 orb m ω 0 m orb, I m = 1 5 2 1 M ω sE = M sE M 2 0 P + ω 0 a /P m E sE (1 + orb, =1+ M 2 M P ω ( a 0 G m sE sE P M P =

The Earth and Moon and Angular Momentum orb I Angular Momentum: orbital Moment of Inertia: Center of Mass: Kepler: Rotational Angular Momentum: Total Angular Momentum Conserved: Kepler : Currently: Lattimer, AST 301, Tidal Lecture – p.12/18 1.77 7.15 3.55 16.69 (days) Period 0.63 0.67 0.43 0.22 Albedo ) 65 120 200 150 g Mass ( 0.183 0.134 0.146 0.126 (% Moon) Gravity 90 105 150 140 3.53 3.01 1.94 1.83 Density Diameter (% Moon) (% water)

Jupiter's Galilean Satellites Io Io Name Name Europa Europa Callisto Callisto Ganymede Ganymede Lattimer, AST 301, Tidal Lecture – p.13/18 Tvashtar Paterae

Io O, boiled away eons ago 2 Similar to Moon in mass andTidally size locked in 1:2:4 orbitalwith resonance Europa and Ganymede, causes extensive interior heating Most volcanically active object inSystem, Solar silicate or sodium volcanos, liquid sulfur lakes Less volatile matter, including H Highest density of Galilean satellites • • • • • • No impact craters, new crust grows at rate of 10 cm/yr • Volcanos blast matter into space; it becomes ionized and trapped in Jupiter’s magnetosphere. Io acts as a giant generator (400,000 V, 3,000,000 amps) and creates extensive radio noise.

South polar region

Lattimer, AST 301, Tidal Lecture – p.14/18 Lattimer, AST 301, Tidal Lecture – p.15/18

Europa Half the mass and 90% ofSurface size extremely of ﬂat Io and icy, with ﬁlled-in cracks and few craters Surface resembles sea ice or pack ice. Tidal heated like Io Heating may produce watery 100-kmocean thick 10–30 km under icy crust Are there hydrothermal vents and life? • • • • • • Lattimer, AST 301, Tidal Lecture – p.16/18

Evidence of Water Youngest fractures due to tidal stresses Older fractures due to fasterrotation surface compared to subsurface ocean Induced magnetic ﬁeld suggests presencesubsurface of conductive layer like salty water Dark steaks are rich inacid salts hydrates or deposited sulfuric by evaporating water from within NASA halted funding for allEuropa missions in to favor of spaceMars, station, etc. manned Politics: afraid of what they will ﬁnd? • • • • • Lattimer, AST 301, Tidal Lecture – p.17/18

Ice Floes? Lattimer, AST 301, Tidal Lecture – p.18/18