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Lecture 10. Roche Limit / Comets Thursday, December 20, 12 Lecture 10. Roche Limit / Comets Thursday, December 20, 12 Outline • Roche limit • One word on Pluto • Comets - why they are interesting? - latest results from sample return mission - 2 Thursday, December 20, 12 Roche limit • Roche limit is the closest distance an object can come to another object without being pulled apart by tidal forces. • Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. • Notable examples : - Saturn rings - Shoemaker - Levy 9 comet breakup • Notable exceptions - Mars’ moon Phobos - Jupiter’s moon Metis - held together by their internal strength. 3 Thursday, December 20, 12 Roche limit • Roche limit is the closest distance an object can come to another object without being pulled apart by tidal forces. • Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. • Notable examples : - Saturn rings - Shoemaker - Levy 9 comet breakup • Notable exceptions - Mars’ moon Phobos - Jupiter’s moon Metis - held together by their internal strength. 3 Thursday, December 20, 12 Roche limit • Roche limit is the closest distance an object can come to another object without being pulled apart by tidal forces. • Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. • Notable examples : - Saturn rings - Shoemaker - Levy 9 comet breakup • Notable exceptions - Mars’ moon Phobos - Jupiter’s moon Metis - held together by their internal strength. 3 Thursday, December 20, 12 Roche limit • Roche limit is the closest distance an object can come to another object without being pulled apart by tidal forces. • Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. • Notable examples : - Saturn rings - Shoemaker - Levy 9 comet breakup • Notable exceptions - Mars’ moon Phobos - Jupiter’s moon Metis - held together by their internal strength. 3 Thursday, December 20, 12 Roche limit • Roche limit is the closest distance an object can come to another object without being pulled apart by tidal forces. • Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. • Notable examples : - Saturn rings - Shoemaker - Levy 9 comet breakup • Notable exceptions - Mars’ moon Phobos - Jupiter’s moon Metis - held together by their internal strength. 3 Thursday, December 20, 12 Roche limit • Roche limit is the closest distance an object can come to another object without being pulled apart by tidal forces. • Inside the Roche limit, orbiting material will tend to disperse and form rings, while outside the limit, material will tend to coalesce. • Notable examples : - Saturn rings - Shoemaker - Levy 9 comet breakup • Notable exceptions - Mars’ moon Phobos - Jupiter’s moon Metis - held together by their internal strength. 3 Thursday, December 20, 12 Tidal force (repeat) ˆr - is a unit vector from M to m G - gravitational constant M, m - masses of two bodies R - distance between the two Consider a small particle at a distance of Δr use series to expand acceleration first term is gravity at the center of mass on Earth tides are to pulls by both Sun (0.54x10-7g) and the Moon (1.1x10-7g) 4 Thursday, December 20, 12 Tidal force (repeat) ˆr - is a unit vector from M to m G - gravitational constant M, m - masses of two bodies R - distance between the two Consider a small particle at a distance of Δr use series to expand acceleration first term is gravity at the center of mass on Earth tides are to pulls by both Sun (0.54x10-7g) and the Moon (1.1x10-7g) 4 Thursday, December 20, 12 Roche limit (2) • Roche limit - gravitational and tidal forces 2!"#! !! = ! !! !"# !! = ! ! ! ! - gravitational force equals tidal force !! = !! ! - simple derivation and expression in terms of diameter ! 2!! = ! ! !! ! !"# 2!"#! ! ! = ! ! !! 2! !=! ! ! ! ! 4!!! !! ! where ! = 3 2!! !=! !! ! ! ! 5 Thursday, December 20, 12 Roche limit (3) • Rigid satellites 2!! !=! !! ! ! ! - where R - radius of the primary body, ρM - density of the primary body and ρm - density of the satellite • Fluid satellites (more accurate!) ⎛ ρ M ⎞ d ≈ 2.44R ⎜ ⎝ ρ ⎟⎠ m 1 3 Body Satellite Roche limit (rigid) Distance (km) Earth Moon Earth average Comet Sun R Roche limit (fluid) Distance (km) R 9,496 1.49 18,261 2.86 17,880 2.80 34,390 5.39 Earth 554,400 0.80 1,066,300 1.53 Sun Jupiter 890,700 1.28 1,713,000 2.46 Sun Moon 655,300 0.94 1,260,300 1.81 Sun average Comet 1,234,000 1.78 2,374,000 3.42 6 Thursday, December 20, 12 Another explanation of Saturn’s ring formation NATURE | LETTER Origin of Saturn’s rings and inner moons by mass removal from a lost Titan-sized satellite Robin M. Canup Nature (2010) doi:10.1038/nature09661 Received 24 May 2010 Accepted 05 November 2010 online 12 December 2010 Published The origin of Saturn’s rings has not been adequately explained. The current rings are more than 90 to 95 per cent water ice1, which implies that initially they were almost pure ice because they are continually polluted by rocky meteoroids2. In contrast, a half-rock, half-ice mixture (similar to the composition of many of the satellites in the outer Solar System) would generally be expected. Previous ring origin theories invoke the collisional disruption of a small moon3, 4, or the tidal disruption of a comet during a close passage by Saturn5. These models are improbable and/or struggle to account for basic properties of the rings, including their icy composition. Saturn has only one large satellite, Titan, whereas Jupiter has four large satellites; additional large satellites probably existed originally but were lost as they spiralled into Saturn6. Here I report numerical simulations of the tidal removal of mass from a differentiated, Titan-sized satellite as it migrates inward towards Saturn. Planetary tidal forces preferentially strip material from the satellite’s outer icy layers, while its rocky core remains intact and is lost to collision with the planet. The result is a pure ice ring much more massive than Saturn’s current rings. As the ring evolves, its mass decreases and icy moons are spawned from its outer edge7 with estimated masses consistent with Saturn’s ice-rich moons interior to and including Tethys. 7 Thursday, December 20, 12 Why Pluto is now a dwarf planet. • Was considered a planet from 1930 to 2006 - it’s existence was predicted from perturbations to the Neptune’s orbit • Why not a planet any more. - Percival Lowell looked for this planet (Planet X), but with advances in our understanding of Neptune’s orbit the need for Planet X disappeared. - In the last decade many other similar objects were discovered ‣ 2060 Chiron ‣ Eris (MEris ≈1.28 x Mpluto) - Highly inclined orbit crosses Neptune’s orbit • Exploration - New Horizons mission - closest approach with Pluto in 2015 Original plates from Clyde Tombaugh's discovery of Pluto. (Apparent magnitude +15.1) 8 Credit: Lowell Observatory Archives, from [1]. Thursday, December 20, 12 Comets • Comet is a small solar system body which has a body and a tail • In general comets consist of - Nucleus ‣ mostly ice and gas with some dust and other matter relatively solid and stable - Coma ‣ carbon dioxide and other gases from the nucleus in a dense cloud of water - Dust Tail ‣ the most-visible part of a comet smoke-sized dust particles up to 10 million km long driven off the nucleus by escaping gases - Ion Tail ‣ plasma laced with rays and streamers up to 100 million km long caused by interactions with the solar wind - Hydrogen Cloud ‣ huge sparse envelope of neutral hydrogen millions of km in diameter • Where do comets come from - short period comets originate from Kuiper Belt (beyond orbit of Neptune) - long period comets come from Oort Cloud (far beyond Kuiper Belt) 9 Thursday, December 20, 12 Comets • Comet is a small solar system body which has a body and a tail • In general comets consist of - Nucleus ‣ mostly ice and gas with some dust and other matter relatively solid and stable - Coma ‣ carbon dioxide and other gases from the nucleus in a dense cloud of water - Dust Tail ‣ the most-visible part of a comet smoke-sized dust particles up to 10 million km long driven off the nucleus by escaping gases - Ion Tail ‣ plasma laced with rays and streamers up to 100 million km long caused by interactions with the solar wind - Hydrogen Cloud ‣ huge sparse envelope of neutral hydrogen millions of km in diameter • Where do comets come from - short period comets originate from Kuiper Belt (beyond orbit of Neptune) - long period comets come from Oort Cloud (far beyond Kuiper Belt) 9 Thursday, December 20, 12 Comets • Comet is a small solar system body which has a body and a tail • In general comets consist of - Nucleus ‣ mostly ice and gas with some dust and other matter relatively solid and stable - Coma ‣ carbon dioxide and other gases from the nucleus in a dense cloud of water - Dust Tail ‣ the most-visible part of a comet smoke-sized dust particles up to 10 million km long driven off the nucleus by escaping gases - Ion Tail ‣ plasma laced with rays and streamers up to 100 million km long caused by interactions with the solar wind - Hydrogen Cloud ‣ huge sparse envelope of neutral hydrogen millions of km in diameter • Where do comets come from - short period comets originate from Kuiper Belt (beyond orbit of Neptune) - long period comets come from Oort Cloud (far beyond Kuiper Belt) 9 Thursday, December 20, 12 Comets in History Woodcut showing destructive influence of a fourth century comet from Stanilaus Lubienietski's Theatrum Cometicum (Amsterdam, 1668). Click on image for larger view. Image credit: NASA/JPL The Mawangdui silk, a 'textbook' of cometary forms and the various disasters associated with them, was compiled sometime around 300 B.C. Click on image for larger view. Image credit: NASA/JPL Types of cometary forms, illustrations from Johannes Hevelius' Cometographia (Danzig, 1668) Click on image for larger view. Image credit: NASA/ JPL 10 Thursday, December 20, 12 Why study comets • May be the oldest, most primitive bodies in the solar system preserving the earliest record of material from the nebula which formed the sun and the planets. • Bring volatile light elements to the planets, playing a role in forming oceans and atmospheres. • Are the most organic-rich bodies in the solar system providing ready-formed molecules possibly involved in the origin of life on Earth. • Impact the Earth and other planets at hypervelocities, causing major changes in climate and dramatically affecting the ecological balance, possibly including the extinction of the Dinosaurs. • Are the building blocks of planetary systems around other stars. 11 Thursday, December 20, 12 Exploration Deep Impact – NASA Flyby (2005–2006) - Tempel I Stardust – NASA Sample Return (1999–2006) - Wild 2 Deep Space 1 (1998–2001) - Borelly Galileo – NASA Shoemaker-Levy 1994 flyby (1995–2003) Giotto – ESA flyby (1985–1992) Sakigake – ISAS flyby (1985–1998) Suisei – ISAS flyby (1985–1998) Vega 1– (Venera-Halley 1) Soviet Comet Halley flyby (1984–1986) Vega 2 (Venera-Halley 2) Soviet Comet Halley flyby (1984–1986) Source: Lunar and Planetary Institute 12 Thursday, December 20, 12 Shoemaker Levy 9 comet and impact Source: University of Washington Thursday, December 20, 12 13 SL9 impact into Jupiter First (far left) and consequent impacts of SL9 fragments into Jupiter. All signs have of breakup have soon disappeared. An enigmatic crater chain on Ganymede, which may have formed due to a comet breakup when it came near Jupiter 14 Thursday, December 20, 12 Recently visited comets Cometary nuclei visited in the last decade: (left) Tempel 1 (NASA, University of Maryland, and Deep Impact Team), (middle) Borrelly [NASA, Jet Propulsion Laboratory (JPL), and Deep Space 1 Team], and (right) Wild 2 (NASA, JPL, and Stardust Team). The longest dimensions are 8 km for Borrelly, 6 km for Tempel 1, and 5.5 km for Wild 2. Note the differences in overall shape, even though all are comparable in size. The smooth areas on Tempel 1 are low, whereas the only smooth area on Borrelly is topographically high. On Wild 2, the smooth areas are at the bottoms of circular depressions. The circular features on Wild 2 have a morphology that is very different from those on Tempel . Source: A’Hearn, Whence Comets?, Science, Dec 2006. 15 Thursday, December 20, 12 Comets to scale Images at the same scale for all cometary nuclei observed by spacecraft. Differences in overall shape are dramatic, as are the differences in contrast between the nuclei and their associated jets, which are brighter than the nucleus at Halley and Hartley 2 and much fainter than the nucleus at other comets. Credit: Science/ AAAS. 16 Thursday, December 20, 12 Halley comet Tapestry of Bayeux (Normandy) with Halley's comet. Text reads ISTI MIRANT STELLA: "These (people) are looking in wonder at the star." Venera - Halley spacecraft (Венера Галлей). Vega 1 made its closest approach on March 6, around 8,890 km from the nucleus, and Vega 2 made its closest approach on March 9 at 8,030 km. The data intensive examination of the comet covered only the three hours around closest approach. The nucleus of Halley's Comet, imaged by the Giotto probe in 1986. The dark colouration of the nucleus can be observed, as well as the jets of dust and gas erupting from its surface. 17 Thursday, December 20, 12 Stardust sample return • Sample return from comet Wild/2 - sample collected in an aerogel This image and diagram show the comet Wild 2, which NASA's Stardust spacecraft flew by on Jan. 2, 2004. The picture on the left is the closest short exposure of the comet. The listed names on the right are those used by the Stardust team to identify features. "Basin" does not imply an impact origin. Image credit: NASA/JPLCaltech. Thursday, December 20, 12 This is an artist's concept depicting a view of comet Wild 2 as seen from NASA's Stardust spacecraft during its flyby on Jan. 2, 2004. Image credit: NASA/JPL-Caltech. 18 Stardust • Deep Impact - Tempel 1 in July 2005 - launched a probe to look at impact results • Schedule - encounter with Wild 2 : Jan 2 2004 - Capsule returns to Earth, Jan 19, 2006 - 2007 - retargeting Tempel 1 as Stardust Next - Encounter - February 14, 2011 ‣ distance 178km ‣ best resolution : 12 m/ pixel • Key conclusions - surface albedo ~ 4%, no exposed ice - globally layered - small outbursts occur 19 Thursday, December 20, 12 Comet surface features Key to examples of surface features on Tempel 1. (A) Composite of ITS frames with examples of types of features (B) Topographic regions of Tempel 1. Unit names from (A) with generalized physical descriptions. (C) Portion of MRI frame MV173728497 showing smooth areas near terminator and associated complex topography. (D) Definition of “facets.” (E) Strongly stretched portion of the ITS composite image; arrows denote scarp bounding smooth unit. From Thomas et. al (2007), Icarus, Deep Impact Mission to Comet 9P/Tempel 1 20 Thursday, December 20, 12 EPOXI flyby of Hartley 2 • Flyby - November 4, 2010 • Discovered that not only water is emitted by the comet but CO2 jets as well. • Emits snow-ball size chunks of ice. • The comet acts differently than others we know. 21 Thursday, December 20, 12 EPOXI flyby of Hartley 2 • Flyby - November 4, 2010 • Discovered that not only water is emitted by the comet but CO2 jets as well. • Emits snow-ball size chunks of ice. • The comet acts differently than others we know. 21 Thursday, December 20, 12 EPOXI flyby of Hartley 2 • Flyby - November 4, 2010 • Discovered that not only water is emitted by the comet but CO2 jets as well. • Emits snow-ball size chunks of ice. • The comet acts differently than others we know. 21 Thursday, December 20, 12 Stardust results • First, they found tiny flecks of once-molten minerals--material very different from the raw, primordial dust they expected to see. Such unaltered, so-called presolar material was the prime ingredient of the rocky planets and was thought to abound in icy comets. • Before Stardust's return, cosmochemists thought of comets as vaults where the primitive ingredients of the planetary recipe had been locked up. - Their best look at the likely ingredients list came from the study of certain meteoritic particles collected in Earth's stratosphere by retired spy planes. Because of their exotic isotopic composition, these particular interplanetary dust particles (IDPs) looked as though they might be comet dust. - Presumably, such primitive dust fell into the cold, outer reaches of the nebula that gave rise to the planets and combined with nebular ices to form comets, in which the dust has been preserved ever since. • Wild 2 is more like an asteroid than a primitive comet - Rather than preserving the original ingredients of planets, comets--or at least Wild 2--seem to be loaded with materials first altered by the great heat near the young sun, - no one is at all sure where the solar system's lingering primitive materials might reside. 22 Thursday, December 20, 12 Stardust latest results • Found tiny flecks of once-molten minerals - material very different from the raw, primordial dust they expected to see. - Such unaltered, so-called presolar material was the prime ingredient of the rocky planets and was thought to abound in icy comets. • Before Stardust's return, cosmochemists thought of comets as vaults where the primitive ingredients of the planetary recipe had been locked up. - Because of their exotic isotopic composition, these particular interplanetary dust particles (IDPs) looked as though they might be comet dust. Presumably, such primitive dust fell into the cold, outer reaches of the nebula that gave rise to the planets and combined with nebular ices to form comets, in which the dust has been preserved ever since. • Wild 2 is more like an asteroid than a primitive comet - Rather than preserving the original ingredients of plants, comets--or at least Wild 2--seem to be loaded with materials first altered by the great heat near the young sun, - It is not clear where the solar system's lingering primitive materials might reside. • EPOXI - role of CO2 has to be clarified Source:Kerr, Where Has All the Stardust Gone? Science 25 January 2008 23 Thursday, December 20, 12 Linear regression (1) • Taken from Numerical Recipes, Third Edition, http://www.nr.com - pages 788 through 783, Fitting data to a Straight Line • We are trying to model our data using simple linear regression ! ! = ! + !" ! • We use chi-square merit function, which is - if the measurement is errors are normally distributed then this merit function will give maximum likelihood parameter estimations of a and b !!! ! ! !, ! = !!! !! − ! − !!! !! ! ! • Chi-square merit function is minimized w.r.t to a and b 0= !! ! !" !!! = −2 !!! !! − ! − !!! !! ! ! 0= !! ! !" !!! = −2 !!! !! − ! − !!! !! !! ! ! 24 Thursday, December 20, 12 Linear regression (3) • Define Sums !!! !≡ !!! 1 !!!!!!!! ≡ !! ! !!! !!! !! !!!!!! ≡ !! ! !!! !!! !! !! !! ! !!! !!!! ≡ !!! !!! !!!!!!" ≡ !! ! !!! !!! !! !! ! !! ! • Then solution of equations are ∆≡ !!!!! − !! !! !!! !! − !! !!" != !! ∆ ! !!! − !! !! != !! ∆ • In case where measurements are unweighted (our case, σi=1) define 1 !! !! = ! − !!!! !! ! ! ! 1 ! ! !!! = 1+ ! !!!!! !!! and !!! ! !!! ≡ !!! !!! 1 = ! !!! ! where σa and σb are error estimates for our regression coefficients 25 Thursday, December 20, 12