Astronomy 111, Fall November 2011

Transcription

1 Astonomy 111, Fall Novembe 2011 Today in Astonomy 111: Jupite s moons Stuctue and composition of the Jovian satellites Tidal toques Obital evolution in satellite systems Obital esonances and longlived tidal heating Volcanoes on Io Liquid wate oceans on Euopa Two of Io s volcanoes, in euption (Galileo/JPL/NASA) 10 Novembe 2011 Astonomy 111, Fall All fou, posing with the Moon (Galileo/JPL/NASA) Jupite s egula (Galilean) satellites Io Euopa Ganymede Callisto Obital semimajo axis (cm) Obital eccenticity Sideeal evolution peiod (days) Radius (cm) Mass (gm) Geometic albedo Moment of inetia ( MR ) Aveage density (gm cm ) Stong lowode obital esonances Icy sufaces Rocky inteios 10 Novembe 2011 Astonomy 111, Fall Stuctue and composition of the Galilean moons Density and moment of inetia indicate that all fou Galilean moons ae diffeentiated. Io, Euopa and Ganymede have have ion coes; Callisto does not. Ganymede has its own magnetic field: liquid coe. Tend of aveage density Inteio stuctue of the Galilean moons (Galileo/JPL/NASA). (deceasing outwad fom Jupite) matches that of faction of mass in the fom of ice (inceasing outwad fom Jupite). Most mass in the fom of silicates. 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 1

2 Astonomy 111, Fall Novembe 2011 Stuctue and composition of the Galilean moons (continued) Lage albedoes indicate that all fou have icy sufaces. Euopa is completely coveed in wate ice. Io s yellow colo is fom volcanic SO 2, fosting the wate ice. Sufaces ae not heavily cateed. Flying low ove Ganymede (Voyage/JPL/NASA) To some extent, this is expected fom thei position outside the asteoid belt. Howeve, Euopa has fa fewe cates than the othe two, and Io has no impact cates at all. They must have been esufaced ecently. (Think luna maia vs luna highlands.) 10 Novembe 2011 Astonomy 111, Fall Stuctue and composition of the Galilean moons (continued) In Io s case, the esufacing mechanism is clea: Io is the most volcanic object in the Sola system. It must theefoe have a paticulaly hot mantle. Volcanism is also esponsible fo the SO 2 fost, fozen fom gas eleased duing euptions. Galileo/JPL/NASA 10 Novembe 2011 Astonomy 111, Fall Stuctue and composition of the Galilean moons (continued) In Euopa s case, the esufacing may be elated to widespead liquid wate oceans undeneath its fozen suface. Euopa s suface looks like teestial, oceanic pack ice. Jupite has a stong ba-magnet- like magnetic field. Rocks and ice ae electical insulatos, and they do not affect extenally-applied magnetic fields. Most moons (like ous) behave this way in thei planet s field. Galileo/JPL/NASA 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 2

3 Astonomy 111, Fall Novembe 2011 Stuctue and composition of the Galilean moons (continued) But magnetic-field measuements made duing close flybys have shown Euopa to epel Jupite s magnetic field, in the way an electically-conducting suface would do. A salt-wate ocean unde the ice, coveing most of the moon, would have the ight electical conductivity to epel the field as obseved. Insulato Magnetization measuements also indicate that Ganymede and Callisto might also have sub-suface oceans, though not as extensive as Euopa s. Conducting shell 10 Novembe 2011 Astonomy 111, Fall The iegula satellites of Jupite The lesse satellites tend to be in lage, eccentic, highly inclined obits, many of which ae etogade (evolution opposite to Jupite s otation). Key: Callisto innemost iegula pogade satellite, Themisto. 5 iegula satellites in the pogade goup know befoe etogade satellites discoveed in peviously known etogade satellites. Obits of the iegula Jovian satellites (as of 2002), fom Scott Sheppad s Satellites page. 10 Novembe 2011 Astonomy 111, Fall The iegula satellites of Jupite (continued) Thei shapes ae iegula too, and they tend to be dak, esembling asteoids. Thus most of us think that they ae captued asteoids, athe than leftoves fom the fomation of Jupite like the Galilean moons. (Even the ing shepheds!) Metis, Adastea, Amalthea, and Thebe, by Galileo (JPL/NASA) 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 3

4 Astonomy 111, Fall Novembe 2011 Tides and obital enegy Jupite is vey massive, and exets lage tidal foces on neaby moons. If the oientations o stength of the tidal foces change, then pats of the moon s inteio elax, and othe pats ae stetched anew. Oientation ti changes continuously if the moon otates t at a diffeent angula velocity than it evolves. Tidal-foce stength changes continuously if the moon is in an eccentic obit. Repeated stetching and elaxing ceates heat, which leaks away in the fom of blackbody adiation. Whence comes the heat? What s losing enegy? 10 Novembe 2011 Astonomy 111, Fall Tides and obital enegy (continued) Only one souce: the kinetic enegy of obital motion. The heat fom tidal stetching and elaxing comes fom the obital enegy of the moon elative to Jupite. So, as enegy is lost due to heat and subsequent adiation, the moon s obit changes. It will continue to change until it otates synchonously with its evolution, and evolves in a cicula obit. But it takes toque to change angula velocities. (That is, p and L ae conseved, too.) What is the oigin of the toques that cause these obit changes to be made? Fom the tidal bulges aised on the planet and moon by each othe, as follows 10 Novembe 2011 Astonomy 111, Fall Reminde (?) about toque Linea momentum is to Foce, as Angula momentum is to Toque. N F p mv dp F ma dt L p I dl N F I dt F sinnˆ Fnˆ N is pependicula to the plane of and F, in the diection given by the ighthand ule. 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 4

5 Astonomy 111, Fall Novembe 2011 Tidal toque Tidal bulges don t geneally line up pefectly with the moon that aised them. Enegy is dissipated in making the tidal bulge, and the otation and evolution ates ae diffeent in geneal. So the bulge can lead o lag the location of the moon. Paent otation Tidal lead Satellite evolution Sizes of bulges, bodies geatly exaggeated. 10 Novembe 2011 Astonomy 111, Fall Tidal toque (continued) Let s calculate the toque. Fist, satellite-bulge distances, using the law of cosines: n R 2Rcos f R 2Rcos R 2Rcos R n f 10 Novembe 2011 Astonomy 111, Fall Tidal toque (continued) Usually the obital adius is a good deal lage than the planetay adius R. So these ae good appoximations: 2 R R R 1 a b... 1 a n R R 1a 1na You will lean why the latte is tue, in the fist math couse which deals with infinite seies. Only the toques on the bulges matte: toque cancels out fo the (mio-symmetic) est of the planet. 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 5

6 Astonomy 111, Fall Novembe 2011 Tidal toque (continued) The magnitude of the foce on the bulge neaest the satellite: GMm GMm Fn R 2Rcos n GMm 1 GMm 2R 1 cos cos R R M F n m M F f 10 Novembe 2011 Astonomy 111, Fall Tidal toque (continued) And similaly the magnitude of the foce on the othe bulge: GMm GMm 2R Ff 1 cos 2 2 f M F n m M F f 10 Novembe 2011 Astonomy 111, Fall Tidal toque (continued) Now the toque on the paent body fom F n : sin sin sin sin n 2 2 R 2Rcos sin 1Rcossin 1 2 R cos (using the law of sines) n 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 6

7 Astonomy 111, Fall Novembe 2011 Tidal toque (continued) GMm 2R R Nn RFnsin R 1 cos 1 cos sin 2 GMmRsin 3R 1 cos 2 Diection: into page, p g by y ight-hand g ule, if 0. R N n F n 10 Novembe 2011 Astonomy 111, Fall Tidal toque (continued) Similaly, GMmRsin 3R N f 1 cos 2 diected out of the page. N R f F f 10 Novembe 2011 Astonomy 111, Fall Tidal toque (continued) Thus the net toque exeted by the satellite on the paent is GMmRsin 3R 3R Ns-p Nn Nf 1 cos 1 cos ˆ 2 z 2 2 6GMmR 3GMmR sin coszˆ sin 2 zˆ N 3 3 p-s. by Paent Satellite Newton s otation evolution thid law N s-p 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 7

8 Astonomy 111, Fall Novembe 2011 Tidal toque (continued) We have so fa consideed the paent to be tidally distoted and the satellite to be a point mass. Thus, with a tidal lead (0 2) and the coesponding diection of toque, the spin of the planet deceases with time (day lengthens) the obital angula momentum of the satellite, L m GM, inceases ( inceases). ) Paent Satellite otation evolution N s-p 10 Novembe 2011 Astonomy 111, Fall Tidal toque (continued) By the same token, the paent body aises tides on the satellite, and if the bulge leads the paent s evolution, the toque exeted on the bulge will also decease the satellites spin, and incease the paent s obital angula momentum (i.e. the obital distance ). Paent evolution (in satellite s est fame) Tidal lead N p-s Satellite otation 10 Novembe 2011 Astonomy 111, Fall Obital evolution of satellites If satellites fom fom planetay leftoves, thei spin peiods ae geneally less than thei obital peiods. In this situation, the tidal bulges lead evolution: the faste otation tends to dag the bulge away fom the paentsatellite line pecisely the setup we just consideed. And thus the tidal toques decease otational ti angula momentum (the bodies spin down) and incease obital angula momentum (the obital distance inceases). Fo eccentic obits: since toques ae lage, the close the moon is to the planet, moe angula momentum is tansfeed fom otation the obit nea peiapse. So as the obit gets lage, the eccenticity deceases (obit gets moe cicula). 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 8

9 Astonomy 111, Fall Novembe 2011 Obital evolution of satellites (continued) But two conditions can poduce a lag ( 2 0): Satellite obits pogade (evolution same diection as otation) but faste than paent otation Satellite obits etogade (evolution opposite otation) and the bodies spin up and decease thei distance, eventually meging. Tidal lag 10 Novembe 2011 Astonomy 111, Fall Obital evolution of the Galilean satellites When Jupite was fomed, the Galilean moons wee pobably fomed fom the leftoves, and pobably in obits smalle than they have now, otating apidly. The tidal inteaction between Jupite and all fou satellites quickly slowed thei otation; all ae now otating synchonously. And by the same token, they difted away fom Jupite as thei obital angula momentum inceased As Io difted outwads, it captued Euopa a 2:1 meanmotion esonance. Likewise Euopa captued Ganymede, also in a 2:1 esonance. 10 Novembe 2011 Astonomy 111, Fall Obital evolution of the Galilean satellites (continued) The gavitational inteaction of Io with Euopa, and Euopa with Ganymede, at thei obital esonances, keep pulling the obits of these moons slightly out of cicula shape. And thus the tidal foce fom Jupite s gavity changes though the obit, pemitting a neve ending cycle of stetching and elaxing: tidal heating, again. And this has pobably been the case since vey ealy in the Sola system s histoy: the moons have been heated like this fo about 4.5 Gy. The tidal heating on Io is most sevee. Thus, as Stan Peale pedicted befoe the Voyages got thee to discove it, Io s inteio is molten, and the moon is quite volcanic. 10 Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 9

10 Astonomy 111, Fall Novembe 2011 Euopa, wate, and life. Next on the tidal heating scale is Euopa, fo which the heating is pobably enough to keep the inteio wam. Not wam enough fo the ocks cuently to be molten, but enough fo the lowe pats of the 140 km thick wate cust to be liquid. This is consistent with the pack-ice appeaance and aity of impact cates on Euopa s suface, and with the magnetic-field measuements which indicate salt-wate oceans beneath the ice. Thus the conditions unde the ice pack on Euopa may esemble those in the Eath s Actic Ocean, and have been that way fo billions of yeas making Euopa the extateestial sola-system site most likely to suppot life. 10 Novembe 2011 Astonomy 111, Fall At by Michael Caoll Coming soon to a Sola system nea you: the Euopa Jupite System Mission (EJSM) Two satellites, with 21 complementay instuments between them, will be deployed by NASA and ESA on a mission of detailed exploation of the Jovian system, especially Euopa and Ganymede. Look fo launches in 2020, aival in late 2025 and ealy Novembe 2011 Astonomy 111, Fall (c) Univesity of Rocheste 10