Transneptunian Objects and Centaurs from Light Curves
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Hydrostatic Shapes
7 Hydrostatic shapes It is primarily the interplay between gravity and contact forces that shapes the macroscopic world around us. The seas, the air, planets and stars all owe their shape to gravity, and even our own bodies bear witness to the strength of gravity at the surface of our massive planet. What physics principles determine the shape of the surface of the sea? The sea is obviously horizontal at short distances, but bends below the horizon at larger distances following the planet’s curvature. The Earth as a whole is spherical and so is the sea, but that is only the first approximation. The Moon’s gravity tugs at the water in the seas and raises tides, and even the massive Earth itself is flattened by the centrifugal forces of its own rotation. Disregarding surface tension, the simple answer is that in hydrostatic equi- librium with gravity, an interface between two fluids of different densities, for example the sea and the atmosphere, must coincide with a surface of constant ¡A potential, an equipotential surface. Otherwise, if an interface crosses an equipo- ¡ A ¡ A tential surface, there will arise a tangential component of gravity which can only ¡ ©¼AAA be balanced by shear contact forces that a fluid at rest is unable to supply. An ¡ AAA ¡ g AUA iceberg rising out of the sea does not obey this principle because it is solid, not ¡ ? A fluid. But if you try to build a little local “waterberg”, it quickly subsides back into the sea again, conforming to an equipotential surface. Hydrostatic balance in a gravitational field also implies that surfaces of con- A triangular “waterberg” in the sea. -
" Tnos Are Cool": a Survey of the Trans-Neptunian Region VI. Herschel
Astronomy & Astrophysics manuscript no. classicalTNOsManuscript c ESO 2012 April 4, 2012 “TNOs are Cool”: A survey of the trans-Neptunian region VI. Herschel⋆/PACS observations and thermal modeling of 19 classical Kuiper belt objects E. Vilenius1, C. Kiss2, M. Mommert3, T. M¨uller1, P. Santos-Sanz4, A. Pal2, J. Stansberry5, M. Mueller6,7, N. Peixinho8,9 S. Fornasier4,10, E. Lellouch4, A. Delsanti11, A. Thirouin12, J. L. Ortiz12, R. Duffard12, D. Perna13,14, N. Szalai2, S. Protopapa15, F. Henry4, D. Hestroffer16, M. Rengel17, E. Dotto13, and P. Hartogh17 1 Max-Planck-Institut f¨ur extraterrestrische Physik, Postfach 1312, Giessenbachstr., 85741 Garching, Germany e-mail: [email protected] 2 Konkoly Observatory of the Hungarian Academy of Sciences, 1525 Budapest, PO Box 67, Hungary 3 Deutsches Zentrum f¨ur Luft- und Raumfahrt e.V., Institute of Planetary Research, Rutherfordstr. 2, 12489 Berlin, Germany 4 LESIA-Observatoire de Paris, CNRS, UPMC Univ. Paris 06, Univ. Paris-Diderot, France 5 Stewart Observatory, The University of Arizona, Tucson AZ 85721, USA 6 SRON LEA / HIFI ICC, Postbus 800, 9700AV Groningen, Netherlands 7 UNS-CNRS-Observatoire de la Cˆote d’Azur, Laboratoire Cassiope´e, BP 4229, 06304 Nice Cedex 04, France 8 Center for Geophysics of the University of Coimbra, Av. Dr. Dias da Silva, 3000-134 Coimbra, Portugal 9 Astronomical Observatory of the University of Coimbra, Almas de Freire, 3040-04 Coimbra, Portugal 10 Univ. Paris Diderot, Sorbonne Paris Cit´e, 4 rue Elsa Morante, 75205 Paris, France 11 Laboratoire d’Astrophysique de Marseille, CNRS & Universit´ede Provence, 38 rue Fr´ed´eric Joliot-Curie, 13388 Marseille Cedex 13, France 12 Instituto de Astrof´ısica de Andaluc´ıa (CSIC), Camino Bajo de Hu´etor 50, 18008 Granada, Spain 13 INAF – Osservatorio Astronomico di Roma, via di Frascati, 33, 00040 Monte Porzio Catone, Italy 14 INAF - Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 Napoli, Italy 15 University of Maryland, College Park, MD 20742, USA 16 IMCCE, Observatoire de Paris, 77 av. -
Astronomy 201 Review 2 Answers What Is Hydrostatic Equilibrium? How Does Hydrostatic Equilibrium Maintain the Su
Astronomy 201 Review 2 Answers What is hydrostatic equilibrium? How does hydrostatic equilibrium maintain the Sun©s stable size? Hydrostatic equilibrium, also known as gravitational equilibrium, describes a balance between gravity and pressure. Gravity works to contract while pressure works to expand. Hydrostatic equilibrium is the state where the force of gravity pulling inward is balanced by pressure pushing outward. In the core of the Sun, hydrogen is being fused into helium via nuclear fusion. This creates a large amount of energy flowing from the core which effectively creates an outward-pushing pressure. Gravity, on the other hand, is working to contract the Sun towards its center. The outward pressure of hot gas is balanced by the inward force of gravity, and not just in the core, but at every point within the Sun. What is the Sun composed of? Explain how the Sun formed from a cloud of gas. Why wasn©t the contracting cloud of gas in hydrostatic equilibrium until fusion began? The Sun is primarily composed of hydrogen (70%) and helium (28%) with the remaining mass in the form of heavier elements (2%). The Sun was formed from a collapsing cloud of interstellar gas. Gravity contracted the cloud of gas and in doing so the interior temperature of the cloud increased because the contraction converted gravitational potential energy into thermal energy (contraction leads to heating). The cloud of gas was not in hydrostatic equilibrium because although the contraction produced heat, it did not produce enough heat (pressure) to counter the gravitational collapse and the cloud continued to collapse. -
STARS in HYDROSTATIC EQUILIBRIUM Gravitational Energy
STARS IN HYDROSTATIC EQUILIBRIUM Gravitational energy and hydrostatic equilibrium We shall consider stars in a hydrostatic equilibrium, but not necessarily in a thermal equilibrium. Let us define some terms: U = kinetic, or in general internal energy density [ erg cm −3], (eql.1a) U u ≡ erg g −1 , (eql.1b) ρ R M 2 Eth ≡ U4πr dr = u dMr = thermal energy of a star, [erg], (eql.1c) Z Z 0 0 M GM dM Ω= − r r = gravitational energy of a star, [erg], (eql.1d) Z r 0 Etot = Eth +Ω = total energy of a star , [erg] . (eql.1e) We shall use the equation of hydrostatic equilibrium dP GM = − r ρ, (eql.2) dr r and the relation between the mass and radius dM r =4πr2ρ, (eql.3) dr to find a relations between thermal and gravitational energy of a star. As we shall be changing variables many times we shall adopt a convention of using ”c” as a symbol of a stellar center and the lower limit of an integral, and ”s” as a symbol of a stellar surface and the upper limit of an integral. We shall be transforming an integral formula (eql.1d) so, as to relate it to (eql.1c) : s s s GM dM GM GM ρ Ω= − r r = − r 4πr2ρdr = − r 4πr3dr = (eql.4) Z r Z r Z r2 c c c s s s dP s 4πr3dr = 4πr3dP =4πr3P − 12πr2P dr = Z dr Z c Z c c c s −3 P 4πr2dr =Ω. Z c Our final result: gravitational energy of a star in a hydrostatic equilibrium is equal to three times the integral of pressure within the star over its entire volume. -
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Five New and Three Improved Mutual Orbits of Transneptunian Binaries W.M. Grundya, K.S. Nollb, F. Nimmoc, H.G. Roea, M.W. Buied, S.B. Portera, S.D. Benecchie,f, D.C. Stephensg, H.F. Levisond, and J.A. Stansberryh a. Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff AZ 86001. b. Space Telescope Science Institute, 3700 San Martin Dr., Baltimore MD 21218. c. Department of Earth and Planetary Sciences, University of California, Santa Cruz CA 95064. d. Southwest Research Institute, 1050 Walnut St. #300, Boulder CO 80302. e. Planetary Science Institute, 1700 E. Fort Lowell, Suite 106, Tucson AZ 85719. f. Carnegie Institution of Washington, Department of Terrestrial Magnetism, 5241 Broad Branch Rd. NW, Washington DC 20015. g. Dept. of Physics and Astronomy, Brigham Young University, N283 ESC Provo UT 84602. h. Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson AZ 85721. — Published in 2011: Icarus 213, 678-692. — doi:10.1016/j.icarus.2011.03.012 ABSTRACT We present three improved and five new mutual orbits of transneptunian binary systems (58534) Logos-Zoe, (66652) Borasisi-Pabu, (88611) Teharonhiawako-Sawiskera, (123509) 2000 WK183, (149780) Altjira, 2001 QY297, 2003 QW111, and 2003 QY90 based on Hubble Space Tele- scope and Keck II laser guide star adaptive optics observations. Combining the five new orbit solutions with 17 previously known orbits yields a sample of 22 mutual orbits for which the period P, semimajor axis a, and eccentricity e have been determined. These orbits have mutual periods ranging from 5 to over 800 days, semimajor axes ranging from 1,600 to 37,000 km, ec- centricities ranging from 0 to 0.8, and system masses ranging from 2 × 1017 to 2 × 1022 kg. -
Thermal Measurements
Physical characterization of Kuiper belt objects from stellar occultations and thermal measurements Pablo Santos-Sanz & the SBNAF team [email protected] Stellar occultations Simple method to: -Obtain high precision sizes/shapes (unc. ~km) -Detect/characterize atmospheres/rings… -Obtain albedo, density… -Improve the orbit of the body …this looks like very nice but...the reality is harder (at least for TNOs and Centaurs) EPSC2017, Riga, Latvia, 20 Sep. 2017 Stellar occultations Titan 10 mas Quaoar 0.033 arsec Diameter of 1 Euro (33 mas) Pluto coin at 140 km Eris Charon Makemake Pablo Santos-Sanz EPSC2017, Riga, Latvia, 20 Sep. 2017 Stellar occultations ~25 occultations by 15 TNOs (+ Pluto/Charon + Chariklo + Chiron + 2002 GZ32) Namaka Dysnomia Ixion Hi’iaka Pluto Haumea Eris Chiron 2007 UK126 Chariklo Vanth 2014 MU69 2002 GZ32 2003 VS2 2002 KX14 2002 TX300 2003 AZ84 2005 TV189 Stellar occultations: Eris & Chariklo Eris: 6 November 2010 Chariklo: 3 June 2014 • Size ~ Plutón • It has rings! • Albedo= 96% 3 • Density= 2.5 g/cm Danish 1.54-m telescope (La Silla) • Atmosphere < 1nbar (10-4 x Pluto) Eris’ radius Pluto’s radius 1163±6 km 1188.3±1.6 km (Nimmo et al. 2016) Braga-Ribas et al. 2014 (Nature) Sicardy et al. 2011 (Nature) EPSC2017, Riga, Latvia, 20 Sep. 2017 Stellar occultations: Makemake 23 April 2011 Geometric Albedo = 77% (betwen Pluto and Eris) Possible local atmosphere! Ortiz et al. 2012 (Nature) EPSC2017, Riga, Latvia, 20 Sep. 2017 Stellar occultations: latest “catches” 2007 UK : 15 November 2014 2003 AZ84: 8 Jan. 2011 single, 3 Feb. 126 2012 multi, 2 Dec. -
Journal Pre-Proof
Journal Pre-proof A statistical review of light curves and the prevalence of contact binaries in the Kuiper Belt Mark R. Showalter, Susan D. Benecchi, Marc W. Buie, William M. Grundy, James T. Keane, Carey M. Lisse, Cathy B. Olkin, Simon B. Porter, Stuart J. Robbins, Kelsi N. Singer, Anne J. Verbiscer, Harold A. Weaver, Amanda M. Zangari, Douglas P. Hamilton, David E. Kaufmann, Tod R. Lauer, D.S. Mehoke, T.S. Mehoke, J.R. Spencer, H.B. Throop, J.W. Parker, S. Alan Stern, the New Horizons Geology, Geophysics, and Imaging Team PII: S0019-1035(20)30444-9 DOI: https://doi.org/10.1016/j.icarus.2020.114098 Reference: YICAR 114098 To appear in: Icarus Received date: 25 November 2019 Revised date: 30 August 2020 Accepted date: 1 September 2020 Please cite this article as: M.R. Showalter, S.D. Benecchi, M.W. Buie, et al., A statistical review of light curves and the prevalence of contact binaries in the Kuiper Belt, Icarus (2020), https://doi.org/10.1016/j.icarus.2020.114098 This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. -
1. A) the Sun Is in Hydrostatic Equilibrium. What Does
AST 301 Test #3 Friday Nov. 12 Name:___________________________________ 1. a) The Sun is in hydrostatic equilibrium. What does this mean? What is the definition of hydrostatic equilibrium as we apply it to the Sun? Pressure inside the star pushing it apart balances gravity pulling it together. So it doesn’t change its size. 1. a) The Sun is in thermal equilibrium. What does this mean? What is the definition of thermal equilibrium as we apply it to the Sun? Energy generation by nuclear fusion inside the star balances energy radiated from the surface of the star. So it doesn’t change its temperature. b) Give an example of an equilibrium (not necessarily an astronomical example) different from hydrostatic and thermal equilibrium. Water flowing into a bucket balances water flowing out through a hole. When supply and demand are equal the price is stable. The floor pushes me up to balance gravity pulling me down. 2. If I want to use the Doppler technique to search for a planet orbiting around a star, what measurements or observations do I have to make? I would measure the Doppler shift in the spectrum of the star caused by the pull of the planet’s gravity on the star. 2. If I want to use the transit (or eclipse) technique to search for a planet orbiting around a star, what measurements or observations do I have to make? I would observe the dimming of the star’s light when the planet passes in front of the star. If I find evidence of a planet this way, describe some information my measurements give me about the planet. -
" Tnos Are Cool": a Survey of the Transneptunian Region IV. Size
Astronomy & Astrophysics manuscript no. SDOs˙Herschel˙Santos-Sanz˙2012 c ESO 2012 February 8, 2012 “TNOs are Cool”: A Survey of the Transneptunian Region IV Size/albedo characterization of 15 scattered disk and detached objects observed with Herschel Space Observatory-PACS? P. Santos-Sanz1, E. Lellouch1, S. Fornasier1;2, C. Kiss3, A. Pal3, T.G. Muller¨ 4, E. Vilenius4, J. Stansberry5, M. Mommert6, A. Delsanti1;7, M. Mueller8;9, N. Peixinho10;11, F. Henry1, J.L. Ortiz12, A. Thirouin12, S. Protopapa13, R. Duffard12, N. Szalai3, T. Lim14, C. Ejeta15, P. Hartogh15, A.W. Harris6, and M. Rengel15 1 LESIA-Observatoire de Paris, CNRS, UPMC Univ. Paris 6, Univ. Paris-Diderot, 5 Place J. Janssen, 92195 Meudon Cedex, France. e-mail: [email protected] 2 Univ. Paris Diderot, Sorbonne Paris Cite,´ 4 rue Elsa Morante, 75205 Paris, France. 3 Konkoly Observatory of the Hungarian Academy of Sciences, Budapest, Hungary. 4 Max–Planck–Institut fur¨ extraterrestrische Physik (MPE), Garching, Germany. 5 University of Arizona, Tucson, USA. 6 Deutsches Zentrum fur¨ Luft- und Raumfahrt (DLR), Institute of Planetary Research, Berlin, Germany. 7 Laboratoire d’Astrophysique de Marseille, CNRS & Universite´ de Provence, Marseille. 8 SRON LEA / HIFI ICC, Postbus 800, 9700AV Groningen, Netherlands. 9 UNS-CNRS-Observatoire de la Coteˆ d0Azur, Laboratoire Cassiopee,´ BP 4229, 06304 Nice Cedex 04, France. 10 Center for Geophysics of the University of Coimbra, Av. Dr. Dias da Silva, 3000-134 Coimbra, Portugal 11 Astronomical Observatory, University of Coimbra, Almas de Freire, 3040-004 Coimbra, Portugal 12 Instituto de Astrof´ısica de Andaluc´ıa (CSIC), Granada, Spain. 13 University of Maryland, USA. -
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A&A 564, A35 (2014) Astronomy DOI: 10.1051/0004-6361/201322416 & c ESO 2014 Astrophysics “TNOs are Cool”: A survey of the trans-Neptunian region X. Analysis of classical Kuiper belt objects from Herschel and Spitzer observations E. Vilenius1,C.Kiss2, T. Müller1, M. Mommert3,4, P. Santos-Sanz5,6,A.Pál2, J. Stansberry7, M. Mueller8,9, N. Peixinho10,11,E.Lellouch6, S. Fornasier6,12, A. Delsanti6,13, A. Thirouin5, J. L. Ortiz5,R.Duffard5, D. Perna6, and F. Henry6 1 Max-Planck-Institut für extraterrestrische Physik, Postfach 1312, Giessenbachstr., 85741 Garching, Germany e-mail: [email protected] 2 Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Konkoly Thege 15-17, 1121 Budapest, Hungary 3 Deutsches Zentrum für Luft- und Raumfahrt e.V., Institute of Planetary Research, Rutherfordstr. 2, 12489 Berlin, Germany 4 Northern Arizona University, Department of Physics and Astronomy, PO Box 6010, Flagstaff AZ 86011, USA 5 Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía s/n, 18008-Granada, Spain 6 LESIA-Observatoire de Paris, CNRS, UPMC Univ. Paris 06, Univ. Paris-Diderot, France 7 Stewart Observatory, The University of Arizona, Tucson AZ 85721, USA 8 SRON Netherlands Institute for Space Research, Postbus 800, 9700 AV Groningen, The Netherlands 9 UNS-CNRS-Observatoire de la Côte d’Azur, Laboratoire Cassiopée, BP 4229, 06304 Nice Cedex 04, France 10 Center for Geophysics of the University of Coimbra, Geophysical and Astronomical Observatory of the University of Coimbra, Almas de Freire, 3040-004 Coimbra, Portugal 11 Unidad de Astronomía, Facultad de Ciencias Básicas, Universidad de Antofagasta, 601 avenida Angamos, Antofagasta, Chile 12 Univ. -
Astronomy 241: Review Questions #1 Distributed: September 20, 2012 Review the Questions Below, and Be Prepared to Discuss Them I
Astronomy 241: Review Questions #1 Distributed: September 20, 2012 Review the questions below, and be prepared to discuss them in class on Sep. 25. Modified versions of some of these questions will be used in the midterm exam on Sep. 27. 1. State Kepler’s three laws, and give an example of how each is used. 2. You are in a rocket in a circular low Earth orbit (orbital radius aleo =6600km).Whatve- 1 locity change ∆v do you need to escape Earth’s gravity with a final velocity v =2.8kms− ? ∞ Assume your rocket delivers a brief burst of thrust, and ignore the gravity of the Moon or other solar system objects. 3. Consider a airless, rapidly-spinning planet whose axis of rotation is perpendicular to the plane of its orbit around the Sun. How will the local equilibrium surface temperature temperature T depend on latitude ! (measured, as always, in degrees from the planet’s equator)? You may neglect heat conduction and internal heat sources. 3 4. Given that the density of seawater is 1025 kg m− ,howdeepdoyouneedtodivebefore the total pressure (ocean plus atmosphere) is 2P0,wherethetypicalpressureattheEarth’s 5 1 2 surface is P =1.013 10 kg m− s− ? 0 × 5. An asteroid of mass m M approaches the Earth on a hyperbolic trajectory as shown " E in Fig. 1. This figure also defines the initial velocity v0 and “impact parameter” b.Ignore the gravity of the Moon or other solar system objects. (a) What are the energy E and angular momentum L of this orbit? (Hint: one is easily evaluated when the asteroid is far away, the other when it makes its closest approach.) (b) Find the orbital eccentricity e in terms of ME, E, L,andm (note that e>1). -
Colours of Minor Bodies in the Outer Solar System II - a Statistical Analysis, Revisited
Astronomy & Astrophysics manuscript no. MBOSS2 c ESO 2012 April 26, 2012 Colours of Minor Bodies in the Outer Solar System II - A Statistical Analysis, Revisited O. R. Hainaut1, H. Boehnhardt2, and S. Protopapa3 1 European Southern Observatory (ESO), Karl Schwarzschild Straße, 85 748 Garching bei M¨unchen, Germany e-mail: [email protected] 2 Max-Planck-Institut f¨ur Sonnensystemforschung, Max-Planck Straße 2, 37 191 Katlenburg- Lindau, Germany 3 Department of Astronomy, University of Maryland, College Park, MD 20 742-2421, USA Received —; accepted — ABSTRACT We present an update of the visible and near-infrared colour database of Minor Bodies in the outer Solar System (MBOSSes), now including over 2000 measurement epochs of 555 objects, extracted from 100 articles. The list is fairly complete as of December 2011. The database is now large enough that dataset with a high dispersion can be safely identified and rejected from the analysis. The method used is safe for individual outliers. Most of the rejected papers were from the early days of MBOSS photometry. The individual measurements were combined so not to include possible rotational artefacts. The spectral gradient over the visible range is derived from the colours, as well as the R absolute magnitude M(1, 1). The average colours, absolute magnitude, spectral gradient are listed for each object, as well as their physico-dynamical classes using a classification adapted from Gladman et al., 2008. Colour-colour diagrams, histograms and various other plots are presented to illustrate and in- vestigate class characteristics and trends with other parameters, whose significance are evaluated using standard statistical tests.