DOCUMENT RESUME ED 161 705 SE 025 159 TITLE Minicourses in Astrophysics, Modular Approach, Vol. I. INSTITUTION Illinois Univ., Chicago. SPONS AGENCY National Science Foundation, Washington, D.C. BURtAU NO SED-'5-21297 PUB DATE 77 NOTE 144p.; For r-elated document, see SE 025 =160; Contains occasional light'and broken type EDRS PRICE MF-$0.4113 HC-$7.35 Plus Postage. DESCRIPTORS *Astronomy; *Curriculum Guides; Evolution; Graduate Study; *Higher Education; *Instructional Materials; Light; Mathematics; Nuclear Physics; *Physids; Radiation; Relativity; Science Education; *Short Courses; Space Sciences IDEN1fIFIERS *Astrophysics r. ABSTRACT This is the first volume of a two-volume minicourse in astrophysics. It contains chapters on the following topics; planetary atmospheres; r-ray astronomy; radio astrophysics; molecular astrophysics; and, gamma-ray astrophysics. Each chapter gives much technical discussion, mathematical treatment, diagrams, and exavples. References are included with each chapter. (BB) , ******************************************h***************************-- * -Reproductions supplied by EDRS are the best that can be made. *. from the original document. .* ********************************************************************** U.S. DEPARTMENT OF 1!EALTH, EOUCATION & WELFARE NATIONAL INSTITUTE OF EOUCATION THIS DOCUMENT HAS BEEN REPRO: DICED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN ATING IT POINTS OF VIEW OR OPINIONS STATED DO' NOT NECESSARILY REPRE SENT OFFICIAL NATIONAL INSTITUTE OF EDUCATION POSITION OR POLICY L.L.1 el . MINICOURSES IN ASTROPHYSICS MODULAR APPROACH VOL, I DEVELOPED AT THE UNfVERSITY*OF ILLINOIS AT CHICPGO 1977 v. C SUPPORTED BY NATIONAL SCIENCE FOUNDATION DIRECTOR:N SUNDARAM ASSOCIATE DIRECTOR: J. BURNS DEPARTMENT PHYSICS DEPARTMENT OF PHYSICS AND SPACE UNIVERSITY oF ILLINWS SCIENCES , ul LHICAGO, ILLINOIS 60680 FLORIDA-INSTITUTE OF TECHNOLOGY a MELBOURNE, FLORIDA 32901 40 PLANETARY ATMOSPHERES 1.Introduction The study of the planets and the solarsystem is one of themost important and oldest of the various branchesof astrophysics.With renewed interest on the part of the scientists'and engineers during the sixties and the earlyseventies on variousspace programs, this study ---of_solar_system ancl the exploration of the possible.existence of lifeon other planets besides earth has occupied themajor thrust of allprograms. As we know, theprograms are still continuing andwith more and more sophisticated instrumentation,the healthy competitionand cooperation between the U.S. andU.S.S.R. can be hopedto further our understand- ing of the solar systemin detail. Let us begin our discussion with the general ideasconcerning the formation of the planets and the evolution of planetaryatmospheres. Beginning with the "Big Bang"of our expandinguniverse some nearly itten billion years ago, the cont. us burning of hydrogen hasyielded the helium in theuniverse and hydrogenas well as helium a.re'by far the most abundant elements in the universe.In the interiors Of the stars, the continuous' burning besides yielding heliumalso leads ,to the final nuclear reactions in the last stages ofnuclear burning when the 9n temperature rises to -,10-K. .The final nuclearreactions take place so fast that the resulting explosion ejects a major part of thestar into . interstellar space thus leading.to the enrichmentof heavy elements in the galactic matter. The solar system which is approximately five billionyears old traces its origin to the nebula 'andthe vastly enhancedsolar wind in the earlystages of sun's life must have influenced thenature of the gaseous matter in the planets.The inner planets of Mercury, Venus, Earth, and Mars have only a small fraction of their total initialmassand very little of hydrogen and helium whereas theouter planets of Jupiter, Saturn, Uranus, and Neptune are muchmore massive and retain a composition very similar to the initial nebula.In this evolutionary process from the .primordial nebula, it is interesting to note how the analysis of ancient rocks on earth gifesus clues to the beginnings of life on earth.The early atmosphere of earth was mainly H2, CH4,N2, NH3, CN, CO, and H2O. Aminoacids and organic substanceswere formed from these constituents.The organic chemicals at the bottoms of the lakes and oceans through different reactions formedDNA, RNA and others like the various .enzymes and thus leadingto photosynthesis with the vitally needed oxygen as a by-product.- Finally, theprotective ozone also. was formed from oxygen.In-the next section, we shall review very briefly the gravitational escape ofgases from planets and then the general nature of their atmospheres. 2,Es cape of Atmospheric Gases from Planets The history of the atmosphere of a planet and the atmosphere 3 etained by the planet will depend on the rates of escape of the various s from the gravitational field of the planet.The minimum velocity . capeof a particle is governed by its total energy reaching a value The total energy is given by the sum of the kinetic energy and 42: the gi,...vitational potential energy.It is 2 heIMG. 2 R (1) where hi is the mass of the particle with velocity V, and mG are the mass, gravitational constant, and radius of theplanet res- pectively.The minimum velocity which allows-the particle to escape from the gravitational field is called the "escape-velocity" ve giyen by (2) Or, v (2 9 II. 3FiS kw% /Sec (3) M and R-are a e the mass and radius of the planet in terms of the mass and radius of earth.Thus compared to the value of 3 km/sec P4= 0.108 andR = 0.53, the escape velocity on earth, for Marq with 8 t works out-to %es 5 km/sec. Similar calculations would give 2.3, 4.3, and 61 km/sec as the escape velocities for the planets-moon, mercury,° and jupiter respectively.Table I gives the various planetary para- meters and-escape velocities. Table I.Planetary Parameters and Escape Velocities...... Name Radius Mass Gravity Esc. Vel. in Ro in Mo in .m/s2 in km/s Mercury 0.38 0.054 3.6 4.2 Venus 0.96 0.815 8.7 10.3 Earth 1.00 1.000 9.8 11.2 Mars 0.53 0.108 3.8 5.0 Jupiter 11.19 317,8 26.0 61.0 Saturn 9.47 95.2 11.2 37.. 0 Uranus 3.v13 14.5 9.4 22.0 Neptune 3.49 17.2 15.0 25.0 Pluto 0,4 0.2 12.3 7.6 The particles can escape from only high altitudes and not only V >V but also they must be moving outwards with low probability for collisions.The region where the probability for ccillisions is very much less than unity is called the exosphere:In the lower atmosphere, the distribUtion of particles is governed by the hydrostatic equilibrium given by cIP P.3dh'. (4) Using gas law, 1 PkT / , =is1 IRT (5) one gets the differential equation for hydrostatic equilibrium as (6) C where H = kT/mg iS the constant parameter called the scale height of .the" atmosphere. Thus Po ex 12c 01 kb)i (7) Felbeing the pressure at a height b .Similar forms of equations will be applicable fdr the density and the number of particles.So we have (11-110)/F1 17-2fo (8) and N = N 01-110)/H]. (9) To calculate the outward flux of particles escaping the exosphere one has the flux as (considering an elementary:volnme) ° 2iT 1i /2 co eifrcosi)f (v) v2cl F=(4-Tr Re2) ) ci (10) 0 0 e where f(v) is the velocity distribution of the particles, Re is the radius of the base of exosphere at which Ne if.1 the atmospheric particle density. Assuming a Maxwellian distribution of velocities for the particles, the flux becomes my: Farr NJ:r a v)-t.[ c m P 214Te Z (1)1 Using the abOve equation and Eq. (9), the time)in which a fraction 1 - e-1 of-the original content is lost by gravitational escape and only a fraction eI remans2is determined.Table II gives such "lifetimes" for the typical constituents of atmospheres in planets. Table Ir.'. Lifetimes in Years for Planetary Atmospheric Constituents' Constituent Moon Mars Earth Venus Jupiter c 2 500 H 10-3, 10 103.5 103 10 . 8 -2 2000. He 10 103. 10 105 10 1 35 l'O 10? JO 1025 2- . 40 N2 10 1017 106° 10 80 Ar 109 1025 1080 10 It must be clearly understood that the nature of the resulting equation for the lifetime is such thata small uncertainty in tempera- , ture causes a huge uncertainty in the lifetime.Probably- only-the exo- sphere temptexature of earth is known within reasonable limitsof uncertainty.For other planets, probably the errorsare between wide 6 limits and this should be taken into account in discussing. theescape of gases from these planets.However, one can still draw some general and interesting conclusions from the foregoing discussion and the results of Table II.Except for small amounts .of hydrogen probably coming from solar wind, all the terrestrial planets must have lost theirhydro- gen.Moon,. Mars,and Venus must also have lost their helium. Moon must have lost all of its atmosphere except Argon andany other heavier gas like xenon.Though not included in Table II, gases like methane and- ammonia might have been dissociated by solar ultraviolet radiation and depleted by losing all the hydrogen. Hence itaccounts for the scarcity of these gases like CH4 and NH3 in terrestrial planets though they 0 might have been present,in the very beginning to account for the early history of the earth and evolution of living organisms.Clearly Jupiter must be retaining the constituents. of its primitive atmosphere including hydrogen and hence may be expected to have CH4, NH3 and 'probably H2O. These have been ctinfirrnea by observations.In the case of earth by a. fortunate circumstance the water has been retained by the.