Astronomy HOMEWORK Chapter 5 - 9Th Edition
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Constructing the Secular Architecture of the Solar System I: the Giant Planets
Astronomy & Astrophysics manuscript no. secular c ESO 2018 May 29, 2018 Constructing the secular architecture of the solar system I: The giant planets A. Morbidelli1, R. Brasser1, K. Tsiganis2, R. Gomes3, and H. F. Levison4 1 Dep. Cassiopee, University of Nice - Sophia Antipolis, CNRS, Observatoire de la Cˆote d’Azur; Nice, France 2 Department of Physics, Aristotle University of Thessaloniki; Thessaloniki, Greece 3 Observat´orio Nacional; Rio de Janeiro, RJ, Brasil 4 Southwest Research Institute; Boulder, CO, USA submitted: 13 July 2009; accepted: 31 August 2009 ABSTRACT Using numerical simulations, we show that smooth migration of the giant planets through a planetesimal disk leads to an orbital architecture that is inconsistent with the current one: the resulting eccentricities and inclinations of their orbits are too small. The crossing of mutual mean motion resonances by the planets would excite their orbital eccentricities but not their orbital inclinations. Moreover, the amplitudes of the eigenmodes characterising the current secular evolution of the eccentricities of Jupiter and Saturn would not be reproduced correctly; only one eigenmode is excited by resonance-crossing. We show that, at the very least, encounters between Saturn and one of the ice giants (Uranus or Neptune) need to have occurred, in order to reproduce the current secular properties of the giant planets, in particular the amplitude of the two strongest eigenmodes in the eccentricities of Jupiter and Saturn. Key words. Solar System: formation 1. Introduction Snellgrove (2001). The top panel shows the evolution of the semi major axes, where Saturn’ semi-major axis is depicted The formation and evolution of the solar system is a longstand- by the upper curve and that of Jupiter is the lower trajectory. -
Trans-Neptunian Objects a Brief History, Dynamical Structure, and Characteristics of Its Inhabitants
Trans-Neptunian Objects A Brief history, Dynamical Structure, and Characteristics of its Inhabitants John Stansberry Space Telescope Science Institute IAC Winter School 2016 IAC Winter School 2016 -- Kuiper Belt Overview -- J. Stansberry 1 The Solar System beyond Neptune: History • 1930: Pluto discovered – Photographic survey for Planet X • Directed by Percival Lowell (Lowell Observatory, Flagstaff, Arizona) • Efforts from 1905 – 1929 were fruitless • discovered by Clyde Tombaugh, Feb. 1930 (33 cm refractor) – Survey continued into 1943 • Kuiper, or Edgeworth-Kuiper, Belt? – 1950’s: Pluto represented (K.E.), or had scattered (G.K.) a primordial, population of small bodies – thus KBOs or EKBOs – J. Fernandez (1980, MNRAS 192) did pretty clearly predict something similar to the trans-Neptunian belt of objects – Trans-Neptunian Objects (TNOs), trans-Neptunian region best? – See http://www2.ess.ucla.edu/~jewitt/kb/gerard.html IAC Winter School 2016 -- Kuiper Belt Overview -- J. Stansberry 2 The Solar System beyond Neptune: History • 1978: Pluto’s moon, Charon, discovered – Photographic astrometry survey • 61” (155 cm) reflector • James Christy (Naval Observatory, Flagstaff) – Technologically, discovery was possible decades earlier • Saturation of Pluto images masked the presence of Charon • 1988: Discovery of Pluto’s atmosphere – Stellar occultation • Kuiper airborne observatory (KAO: 90 cm) + 7 sites • Measured atmospheric refractivity vs. height • Spectroscopy suggested N2 would dominate P(z), T(z) • 1992: Pluto’s orbit explained • Outward migration by Neptune results in capture into 3:2 resonance • Pluto’s inclination implies Neptune migrated outward ~5 AU IAC Winter School 2016 -- Kuiper Belt Overview -- J. Stansberry 3 The Solar System beyond Neptune: History • 1992: Discovery of 2nd TNO • 1976 – 92: Multiple dedicated surveys for small (mV > 20) TNOs • Fall 1992: Jewitt and Luu discover 1992 QB1 – Orbit confirmed as ~circular, trans-Neptunian in 1993 • 1993 – 4: 5 more TNOs discovered • c. -
Dynamical Evolution of Planetary Systems
Dynamical Evolution of Planetary Systems Alessandro Morbidelli Abstract Planetary systems can evolve dynamically even after the full growth of the planets themselves. There is actually circumstantial evidence that most plane- tary systems become unstable after the disappearance of gas from the protoplanetary disk. These instabilities can be due to the original system being too crowded and too closely packed or to external perturbations such as tides, planetesimal scattering, or torques from distant stellar companions. The Solar System was not exceptional in this sense. In its inner part, a crowded system of planetary embryos became un- stable, leading to a series of mutual impacts that built the terrestrial planets on a timescale of ∼ 100My. In its outer part, the giant planets became temporarily unsta- ble and their orbital configuration expanded under the effect of mutual encounters. A planet might have been ejected in this phase. Thus, the orbital distributions of planetary systems that we observe today, both solar and extrasolar ones, can be dif- ferent from the those emerging from the formation process and it is important to consider possible long-term evolutionary effects to connect the two. Introduction This chapter concerns the dynamical evolution of planetary systems after the re- moval of gas from the proto-planetary disk. Most massive planets are expected to form within the lifetime of the gas component of protoplanetary disks (see chapters by D’Angelo and Lissauer for the giant planets and by Schlichting for Super-Earths) and, while they form, they are expected to evolve dynamically due to gravitational interactions with the gas (see chapter by Nelson on planet migration). -
1 on the Origin of the Pluto System Robin M. Canup Southwest Research Institute Kaitlin M. Kratter University of Arizona Marc Ne
On the Origin of the Pluto System Robin M. Canup Southwest Research Institute Kaitlin M. Kratter University of Arizona Marc Neveu NASA Goddard Space Flight Center / University of Maryland The goal of this chapter is to review hypotheses for the origin of the Pluto system in light of observational constraints that have been considerably refined over the 85-year interval between the discovery of Pluto and its exploration by spacecraft. We focus on the giant impact hypothesis currently understood as the likeliest origin for the Pluto-Charon binary, and devote particular attention to new models of planet formation and migration in the outer Solar System. We discuss the origins conundrum posed by the system’s four small moons. We also elaborate on implications of these scenarios for the dynamical environment of the early transneptunian disk, the likelihood of finding a Pluto collisional family, and the origin of other binary systems in the Kuiper belt. Finally, we highlight outstanding open issues regarding the origin of the Pluto system and suggest areas of future progress. 1. INTRODUCTION For six decades following its discovery, Pluto was the only known Sun-orbiting world in the dynamical vicinity of Neptune. An early origin concept postulated that Neptune originally had two large moons – Pluto and Neptune’s current moon, Triton – and that a dynamical event had both reversed the sense of Triton’s orbit relative to Neptune’s rotation and ejected Pluto onto its current heliocentric orbit (Lyttleton, 1936). This scenario remained in contention following the discovery of Charon, as it was then established that Pluto’s mass was similar to that of a large giant planet moon (Christy and Harrington, 1978). -
Evidence from the Asteroid Belt for a Violent Past Evolution of Jupiter's Orbit
Evidence from the asteroid belt for a violent past evolution of Jupiter's orbit Alessandro Morbidelli Departement Cassiop´ee: Universite de Nice - Sophia Antipolis, Observatoire de la Cˆote d’Azur, CNRS 4, 06304 Nice, France Ramon Brasser Departement Cassiop´ee: Universite de Nice - Sophia Antipolis, Observatoire de la Cˆote d’Azur, CNRS 4, 06304 Nice, France Rodney Gomes Observatrio Nacional, Rua General Jos Cristino 77, CEP 20921-400, Rio de Janeiro, RJ, Brazil Harold F. Levison Southwest Research Institute, 1050 Walnut St, Suite 300, Boulder, CO 80302, USA and Kleomenis Tsiganis Department of Physics, Aristotle University of Thessaloniki, 54 124 Thessaloniki, Greece Received by AJ, on may 24, 2010; accepted by AJ, on Sept 8, 2010 arXiv:1009.1521v1 [astro-ph.EP] 8 Sep 2010 –2– ABSTRACT We use the current orbital structure of large (> 50 km) asteroids in the main as- teroid belt to constrain the evolution of the giant planets when they migrated from their primordial orbits to their current ones. Minton & Malhotra (2009) showed that the orbital distribution of large asteroids in the main belt can be reproduced by an exponentially-decaying migration of the giant planets on a time scale of τ ∼ 0.5 My. However, self-consistent numerical simulations show that the planetesimal-driven mi- gration of the giant planets is inconsistent with an exponential change in their semi major axes on such a short time scale (Hahn & Malhotra, 1999). In fact, the typical time scale is τ ≥ 5 My. When giant planet migration on this time scale is appliedto the asteroid belt, the resulting orbital distribution is incompatible with the observed one. -
Capture of Irregular Satellites During Planetary Encounters
The Astronomical Journal, 133:1962Y1976, 2007 May # 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A. CAPTURE OF IRREGULAR SATELLITES DURING PLANETARY ENCOUNTERS David Nesvorny´,1 David Vokrouhlicky´,1,2 and Alessandro Morbidelli3 Received 2006 November 23; accepted 2007 January 17 ABSTRACT More than 90 irregular moons of the Jovian planets have recently been discovered. These moons are an enig- matic part of the solar system inventory. Their origin, which is intimately linked with the origin of the planets them- selves, has yet to be adequately explained. Here we investigate the possibility that the irregular moons were captured from the circumsolar planetesimal disk by three-body gravitational reactions. These reactions may have been a fre- quent occurrence during the time when the outer planets migrated within the planetesimal disk. We propose a new model for the origin of irregular satellites in which these objects are captured from the planetesimal disk during en- counters between the outer planets themselves in the model for outer planet migration advocated by Tsiganis and collaborators. Through a series of numerical simulations we show that nearby planetesimals can be deflected into planet-bound orbits during close encounters between planets, and that the overall efficiency of this capture process is large enough to produce populations of observed irregular satellites at Saturn, Uranus, and Neptune. The orbits of captured objects are broadly similar to those of known distant satellites. Jupiter, which typically does not have close encounters with other planets in the model of Tsiganis and coworkers, must have acquired its irregular satellites by a different mechanism. -
Lecture Star Formation 2. Pptx.Pptx
Lecture Star Formaon History 2 Prof. George F. Smoot Star Formaon 2 1 Star Formaon, H II Regions, and the Interstellar Medium Star Formaon 2 2 Introduc-on • Baryonic maer: Maer composed of protons and neutrons • Interstellar Medium (ISM): Consists of molecular, atomic, and ionized gas with large ranges of densi-es and temperatures, as well as dust • New Stars form from molecular, gas-phase maer • ISM releases stellar energy by means of physical processes that are dis-nct from star and stellar formaon Star Formaon 2 3 What to Expect • Focus on the ISM in star-forming regions • Briefly survey star forming environments • Proper-es of young stellar populaons • Physical processes that operate in the ISM around newly formed stars and the observable conseQuences of those processes Star Formaon 2 4 5.1 Cloud Collapse and Star Formaon • Stars form in molecular clouds, which are one component of ISM • Clouds are randomly shaped agglomeraons composed of molecular hydrogen 2 5 • Typical mass of 10 -10 MSun • Sizes of hundreds of parsecs • Densies of 108-1010 m-3 (mostly hydrogen) • Temperature between ~ 10–100 K Star Formaon 2 5 Molecular Clouds • Clouds are largest, most massive, gravitaonally bound objects in ISM • Densi-es of clouds are among highest found in ISM • Nearest giant molecular clouds are in the Orion star- forming region, ~500 pc away Star Formaon 2 6 7 Cloud in Orion Molecular hp://www.outerspaceuniverse.org/media/orion-molecular-cloud.jpg Star Formaon 2 Molecular Clouds • Mean mass density in stars are ~103 kg/m3 and par-cle density -
Planet Formation
Planet Formation A Major Qualifying Project Report: Submitted to the Faculty of Worcester Polytechnic Institute In partial fulfillment of the requirements for the Degree of Bachelor of Science By Peter Dowling Advised by Professor Mayer Humi Peter Dowling Table of Contents Abstract .......................................................................................................................................................... 4 Executive Summary ........................................................................................................................................ 5 Introduction ................................................................................................................................................... 7 Background .................................................................................................................................................... 7 Stellar Formation ........................................................................................................................................ 8 Jeans Instability ...................................................................................................................................... 8 History of Solar System Formation Theories............................................................................................ 10 Tidal Theory .......................................................................................................................................... 11 The Chamberlin-Moulton model ......................................................................................................... -
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A&A 564, A44 (2014) Astronomy DOI: 10.1051/0004-6361/201322041 & c ESO 2014 Astrophysics Dynamical formation of detached trans-Neptunian objects close to the 2:5 and 1:3 mean motion resonances with Neptune P. I. O. Brasil1,R.S.Gomes2, and J. S. Soares2 1 Instituto Nacional de Pesquisas Espaciais (INPE), ETE/DMC, Av. dos Astronautas, 1758 São José dos Campos, Brazil e-mail: [email protected] 2 Observatório Nacional (ON), GPA, Rua General José Cristino, 77, 20921-400 Rio de Janeiro, Brazil e-mail: [email protected] Received 7 June 2013 / Accepted 29 January 2014 ABSTRACT Aims. It is widely accepted that the past dynamical history of the solar system included a scattering of planetesimals from a primordial disk by the major planets. The primordial scattered population is likely the origin of the current scaterring disk and possibly the detached objects. In particular, an important argument has been presented for the case of 2004XR190 as having an origin in the primordial scattered disk through a mechanism including the 3:8 mean motion resonance (MMR) with Neptune. Here we aim at developing a similar study for the cases of the 1:3 and 2:5 resonances that are stronger than the 3:8 resonance. Methods. Through a semi-analytic approach of the Kozai resonance inside an MMR, we show phase diagrams (e,ω) that suggest the possibility of a scattered particle, after being captured in an MMR with Neptune, to become a detached object. We ran several numerical integrations with thousands of particles perturbed by the four major planets, and there are cases with and without Neptune’s residual migration. -
Lecture 15: Stars
Matthew Schwartz Statistical Mechanics, Spring 2019 Lecture 15: Stars 1 Introduction There are at least 100 billion stars in the Milky Way. Not everything in the night sky is a star there are also planets and moons as well as nebula (cloudy objects including distant galaxies, clusters of stars, and regions of gas) but it's mostly stars. These stars are almost all just points with no apparent angular size even when zoomed in with our best telescopes. An exception is Betelgeuse (Orion's shoulder). Betelgeuse is a red supergiant 1000 times wider than the sun. Even it only has an angular size of 50 milliarcseconds: the size of an ant on the Prudential Building as seen from Harvard square. So stars are basically points and everything we know about them experimentally comes from measuring light coming in from those points. Since stars are pointlike, there is not too much we can determine about them from direct measurement. Stars are hot and emit light consistent with a blackbody spectrum from which we can extract their surface temperature Ts. We can also measure how bright the star is, as viewed from earth . For many stars (but not all), we can also gure out how far away they are by a variety of means, such as parallax measurements.1 Correcting the brightness as viewed from earth by the distance gives the intrinsic luminosity, L, which is the same as the power emitted in photons by the star. We cannot easily measure the mass of a star in isolation. However, stars often come close enough to another star that they orbit each other. -
The Terrestrial Planets R
A&A 507, 1053–1065 (2009) Astronomy DOI: 10.1051/0004-6361/200912878 & c ESO 2009 Astrophysics Constructing the secular architecture of the solar system II: the terrestrial planets R. Brasser1, A. Morbidelli1,R.Gomes2,K.Tsiganis3, and H. F. Levison4 1 Dep. Cassiopee, University of Nice – Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, 06304 Nice, France e-mail: [email protected] 2 Observatório Nacional, Rio de Janeiro, RJ, Brazil 3 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 4 Southwest Research Institute, Boulder, CO, USA Received 13 July 2009 / Accepted 31 August 2009 ABSTRACT We investigate the dynamical evolution of the terrestrial planets during the planetesimal-driven migration of the giant planets. A basic assumption of this work is that giant planet migration occurred after the completion of terrestrial planet formation, such as in the models that link the former to the origin of the late heavy bombardment. The divergent migration of Jupiter and Saturn causes the g5 eigenfrequency to cross resonances of the form g5 = gk with k ranging from 1 to 4. Consequently these secular resonances cause large-amplitude responses in the eccentricities of the terrestrial planets if the amplitude of the g5 mode in Jupiter is similar to the current one. We show that the resonances g5 = g4 and g5 = g3 do not pose a problem if Jupiter and Saturn have a fast approach and departure from their mutual 2:1 mean motion resonance. On the other hand, the resonance crossings g5 = g2 and g5 = g1 aremoreofa concern: they tend to yield a terrestrial system incompatible with the current one, with amplitudes of the g1 and g2 modes that are too large. -
WHERE DID CERES ACCRETE? William B. Mckinnon, Department Of
Asteroids, Comets, Meteors (2012) 6475.pdf WHERE DID CERES ACCRETE? William B. McKinnon, Department of Earth and Planetary Sciences and the McDonnell Center for the Space Sciences, Washington University, Saint Louis, MO 63130 ([email protected]). Introduction: Ceres is an unusual asteroid. Com- models where Jupiter reverses migration direction at prising ~1/3 of the total mass of the present asteroid 1.5 AU, the primordial asteroid belt is simply emptied, belt, it resides deep in the Main belt at a semimajor but then repopulated with bodies from both the inner axis of 2.77 AU, at the center of the broad distribution and outer solar system. At Ceres’ distance the major- of C type asteroids [1]. But it is not a C-type as usu- ity of icy, outer solar system bodies derive from be- ally considered. It is likely a differentiated dwarf tween the giant planets (out to ~8 AU in the initial planet, whose ice-rich composition indicates a kinship compact configuration). The new belt is also a dy- with bodies farther out in the solar system [2]. Here I namically hot belt, and (if it lasts) requires e and i re- explore Ceres’ place of origin, either in situ in the as- shuffling during the Nice-model LHB [16]. teroid belt, farther out among the giant planets, or even Transneptunian Refugee: In 2008, I proposed in the primordial transneptunian belt. As the next tar- that Ceres was dynamically scattered inwards during a get of the Dawn mission, I also address whether any of Nice-model like reorganization of the outer solar sys- these formation scenarios can be tested.