WELCOME TO AST 111! OVERVIEW OF THE SOLAR SYSTEM

Transcription

1 WELCOME TO AST 111! The Solar System and its Origins 4 September 2018 ASTRONOMY 111, FALL OVERVIEW OF THE SOLAR SYSTEM Contents of the Solar System What can we measure and what can we infer about the contents? How do we know? Initial explanations of four of the most important facts about the solar system The basic collection of solar system facts The eight planets and a moon (NASA, Palomar Observatory, Lowell Observatory) 4 September 2018 ASTRONOMY 111, FALL

2 INVENTORY OF THE SOLAR SYSTEM Q: What would an outside observer see if they were looking at our Solar System? A: The Sun. And that s pretty much it. The luminosity (total power output in the form of light) of the Sun is 3.8x10 26 watts 4x10 8 times as luminous as the second brightest object, Jupiter. The mass of the Sun is about metric tons about 500 times the total mass of everything else in the Solar System. The Solar System is the Sun, plus a little debris. Image by Robert Gendler 4 September 2018 ASTRONOMY 111, FALL ASIDE OBSERVATIONS OF OTHER PLANETARY SYSTEMS In most other stellar (extrasolar) systems, all we know about are the stars, because they are overwhelmingly bright. But planets have been detected around other stars recently, with surprising properties (high eccentricity, small radii from star). This is mostly done by observing the motion of the central star, as we will learn this semester. Our understanding of the Solar System has helped us understand the formation and evolution of planetary and stellar systems. However, what we are finding about extrasolar systems is challenging previous views of solar system formation and evolution. 4 September 2018 ASTRONOMY 111, FALL Artist s conception of AEgir around its star Ran 2

3 COMPONENTS OF THE DEBRIS The Giant planets: mostly gas and liquid The Terrestrial (Earthlike) planets and other planetesimals, some quite small: mostly rock and ice The Heliosphere: widespread, very diffuse plasma Io and Jupiter, seen from Cassini (NASA-JPL) 4 September 2018 ASTRONOMY 111, FALL GIANT PLANETS Jupiter dominates with a mass of 10-3 times that of the Sun (10-3 M ), or 318 times that of the Earth (318 M ) Saturn s mass is 3x10-4 M, or 100 M Neptune and Uranus are about 1/6 the mass of Saturn Giant planets are 5, 10, 20, and 30 times further from the Sun than Earth (a = 5, 10, 20, 30 AU; a is commonly used to denote semi-major axis, covering the possibility of an elliptical orbit) Saturn and Jupiter have roughly Solar type abundances (composition), which means mostly hydrogen and helium. Saturn probably has a rocky core; Jupiter might not. Neptune and Uranus are dominated by water (H2O), ammonia (NH3), and methane (CH4) and have a larger percentage of their mass in rocky/icy cores. Jupiter and Saturn are called gas giants Neptune and Uranus are called ice giants Jupiter, seen from Cassini (NASA-JPL) 4 September 2018 ASTRONOMY 111, FALL

4 TERRESTRIAL PLANETS AND OTHER ROCKY DEBRIS Mercury: R 2500 km, a = 0.4 AU Venus and Earth: radius R 6000 km, a = 0.7, 1.0 AU, respectively Mars: R 3500 km, a = 1.5 AU Asteroid belt: a 2-5 AU Kuiper Belt, including Pluto, at a > 30 AU Oort Cloud, including Sedna, at a 10 4 AU Interplanetary dust Moons and satellites Planetary rings Images from Galileo (NASA-JPL) 4 September 2018 ASTRONOMY 111, FALL THE HELIOSPHERE All planets orbit within the heliosphere, which contains magnetic fields and plasma primarily of solar origin. (Plasma: an ionized gas with electrical conductivity and magnetization much larger than an ideal gas.) The solar wind is a plasma traveling at supersonic speeds. Where the solar wind interacts or merges with the interstellar medium is called the heliopause. Cosmic rays (high energy particles) are affected by the magnetic fields in the heliosphere. 4 September 2018 ASTRONOMY 111, FALL

5 PLANETARY PROPERTIES THAT CAN BE DETERMINED DIRECTLY FROM OBSERVATIONS Orbit Age Mass, mass distribution Size Rotation rate and spin axis Shape Temperature Magnetic field Surface composition Surface structure Atmospheric structure and composition Saturn, Venus, and Mercury, with the European Southern Observatory in the foreground (Stephane Guisard) 4 September 2018 ASTRONOMY 111, FALL OTHER PLANETARY PROPERTIES THAT CAN BE INFERRED OR MODELED FROM OBSERVATIONS Density and temperature of the atmosphere and interior as functions of position Formation Geological history Dynamical history These will be discussed in context with the observations and astrophysical processes as part of this course. Cut-away view of the Sun s convective zone (Elmo Schreder, Aarhus University, Denmark) 4 September 2018 ASTRONOMY 111, FALL

6 HOW DO WE KNOW Note that most of what we will say about the planets this semester is founded upon a lot of very direct evidence, rather than theory or reason-aided handwaving. For example: that the Earth is approximately spherical? Direct observation, of course, and known since about 500 BC. Lunar phases indicate that it shines by reflected sunlight. Therefore, the full moon is nearly on the opposite side of the sky from the Sun. Therefore, lunar eclipses are the Earth s shadow cast on the Moon. The edge of this shadow is always circular; thus, the Earth must be a sphere. Lunar eclipse (16 Aug 2008) sequence photographed by Anthony Ayiomamitis 4 September 2018 ASTRONOMY 111, FALL HOW DO WE KNOW that the planets orbit the Sun, nearly all in the same plane? Also direct observation. The planets and the Sun always lie in a narrow band across the sky: the zodiac. This is a plane, seen edge-on. Distant stars that lie in the direction of the zodiac exhibit narrow features in their spectrum that shift back and forth in wavelength by ±0.01% with periods of one year. No such shift is seen in the stars toward the perpendicular direction, or in the Sun. The shift is a Doppler effect, from which one can infer a periodic velocity change of Earth with respect to the stars in the zodiac by ±30 km/s. Thus, the Earth travels in an approximately circular path at 30 km/s, centered on the Sun. 4 September 2018 ASTRONOMY 111, FALL

7 THE DOPPLER EFFECT Suppose two observers had light emitters and detectors that can measure wavelength very accurately, and move with respect to each other at speed v along the direction between them. If one emits light with a pre-arranged wavelength λ 0, the other one will detect the light at wavelength That is,! =! # 1 + & ' & = '!! #! # where c = x10 10 cm/s is the speed of light. You will learn why this is in your E&M classes. 4 September 2018 ASTRONOMY 111, FALL HOW DO WE KNOW that the Sun lies precisely 1.5x10 13 cm (1 AU) from Earth? Direct observation: It follows from the previous example, but we can measure the same thing more precisely these days by reflecting radar pulses off the Sun or the inner planets, measuring the time between sending the pulse and receiving the reflection, and multiplying by the speed of light. Note that knowing the AU enables one to measure the sizes of everything else one can see in the Solar System. Using Venus or Mercury gives the most accurate results, as the Sun itself does not have a very sharp edge at which the radar pulse is reflected. It works with Venus or Mercury as follows: 4 September 2018 ASTRONOMY 111, FALL

8 MEASURING THE ASTRONOMICAL UNIT (AU) Suppose you were to send a radar pulse at Venus when it appeared to have a first- or third-quarter phase, so that the line-of-sight is perpendicular to the Venus-Sun line. Then Sun! = #$% & 1 AU =! cos + = cm (corrected for planet size and averaged over the orbit) 1 AU Earth θ d Venus 4 September 2018 ASTRONOMY 111, FALL HOW DO WE KNOW that the Solar System is precisely 4.6 billion years old? Direct observation, again, on terrestrial rocks, lunar rocks, and meteorites, nearly all of which originate in the asteroid belt. We will study this in great detail: When rocks melt, the contents homogenize pretty thoroughly. When they cool off, they usually recrystallize into a mixture of several minerals. Each different mineral will incorporate a certain fraction of trace impurities. Those trace impurities that are radioactive will vanish in times that are accurately measured in the lab. Thus, the ratio of the amounts of radioactive trace impurities tell how much of that tracer the rock had when it cooled off, and how long ago that was. The oldest rocks in the Solar System are all billion years old, independent of where they came from, so that s how long ago the Solar System solidified. 4 September 2018 ASTRONOMY 111, FALL

9 THE BASIC FACTS Gravitational constant G = 6.674x10-8 dyn cm 2 g -2 = 6.674x10-11 m 3 kg -1 s -2 Boltzmann s constant k = x10-16 erg K -1 = x10-23 J K -1 Stefan-Boltzmann constant σ = x10-5 erg s -1 cm -2 K -4 = x10-8 J s -1 m -2 K -4 Planck s constant h = x10-27 erg s = x10-34 J s Speed of light c = x10 10 cm s -1 = x10 8 m s -1 Earth mass M = 5.976x10 27 g Astronomical unit AU = 1.496x10 13 cm Solar mass M = 1.989x10 33 g Solar radius R = 6.96x10 10 cm Solar temperature T = 5800 K Solar luminosity L = 3.827x10 33 erg s -1 Solar apparent magnitude m = Light year ly = x10 17 cm Parsec pc = 3.086x10 18 cm = ly Earth radius Solar day Sidereal year R = 6.378x10 8 cm Day = s P = yr = x10 7 s Densities (in g cm -3 ) Water ice: 0.94 Water: Carbonaceous minerals: 2.5 Silicate minerals: 3.5 Iron sulfide: 4.8 Iron: September 2018 ASTRONOMY 111, FALL THE SUN AND OTHER BLACKBODIES A few salient facts about the Sun Nucleosynthesis Blackbody radiation and temperatures of stars The spectrum of blackbodies, and solid angle Wien s Law Three-color X-ray mosaic image of the Sun, made by the NASA TRACE satellite (J. Covington, LMMS) 4 September 2018 ASTRONOMY 111, FALL

10 THE SUN: BASIC FACTS Mass x10 33 grams Luminosity 3.826x10 33 erg sec -1 Radius Surface rotation period, sidereal, at equator Surface temperature Surface pressure Central temperature 6.96x10 10 cm 2.193x10 6 sec (25.38 days) 5800 K 10 dyne cm -2 (10-5 atmospheres) 1.58x10 7 K Central pressure 2.50x10 17 dyne cm -2 Surface composition, by mass H (70.4%), He (28.0%), O (0.76%), C (0.28%), Ne (0.17%), N (0.08%), others (0.32%) Sun, sunspots, and Mercury transit, May 2003, by Dominique Dierick 4 September 2018 ASTRONOMY 111, FALL MUCH MORE LATER One learns a lot more about the Sun and other stars, including the reasons why the Sun has the set of properties that it does, in AST 142 and AST 241. For our purposes, it will suffice to discuss only three of its properties now: its composition, its surface temperature, and its luminosity. UV movie of loop prominence on the Sun s surface, from the NASA SDO satellite 4 September 2018 ASTRONOMY 111, FALL

11 THE SUN S COMPOSITION AND NUCLEOSYNTHESIS The Sun is a sphere of hot ionized gas, obviously boiling at the surface, so one might think that it is well mixed. It is not. The Sun s size is determined by the balance of its weight and its internal pressure. The heat that provides the pressure would leak away (in the form of sunshine) within a few million years if it were not somehow replenished. The replenishment of heat is provided by nuclear fusion reactions taking place at the very center. When atomic nuclei fuse to produce a nucleus light than that of iron (Fe, Z = 26, A = 56), kinetic energy is liberated (the reaction is exothermic) and added as heat to the energy of the surroundings. By the same token, this means that the contents of stars continuously transmute themselves from light elements to heavy elements. 4 September 2018 ASTRONOMY 111, FALL NUCLEOSYNTHESIS Models of the Sun s interior indicate that the composition at the very center is 33.6% H and 64.3% He by mass. Much of the H there has been burned to He, mostly due to the proton-proton reaction chains. The interior of the Sun is so hot that the enough collisions occur to ionize H, resulting in a plasma Individual protons collide, fusing together to form deuterium (fusion); deuterium continues to fuse with other protons in a chain reaction to form He. The alpha particle (He) is less massive than the four protons that combined to make it, so the protonproton chain releases energy equal to the mass difference via! = #$ % In hotter, denser stellar cores, fusion of He (by the triple alpha reaction), C, O, Ne, and even heavier elements can take place at respectable rates and elements heavier than Fe can be made in small quantities in such stars by the endothermic (opposite of exothermic) s-process reactions. 4 September 2018 ASTRONOMY 111, FALL

12 NUCLEOSYNTHESIS The Universe was born (in a fireball we can see, which we call the Big Bang) with hardly any elements heavier than helium. This is because fusion of two normal helium nuclei (! " He) produces an isotope of beryllium ( " % Be) that is quite unstable, dissolving back into helium within sec. Fusion of three normal helium nuclei produces a stable result: 3 "! He *! ) C + - Triple-α process But very high density and temperature are necessary in order to make three He nuclei collide simultaneously, energetically enough to fuse. And by the time the Universe cooled enough for nuclei to condense, the density was too low. 4 September 2018 ASTRONOMY 111, FALL NUCLEOSYNTHESIS In the cores of some stars, temperatures and densities can both be large enough for the triple-α process to proceed. And the carbon produced thereby can react to form other heavier nuclei. Thus the heavy elements that the planets and you are made of were synthesized by nuclear reactions in the cores of stars that lived and died billions of years ago. Stars die before they burn more than about 10% of their total H into He, so the Universe will take a very long time to run out of hydrogen. 4 September 2018 ASTRONOMY 111, FALL

13 THE NUCLEAR- CHEMICAL EVOLUTION OF THE MILKY WAY New stars Younger stars Older stars Number of atoms per hydrogen atom 1.0E E E E E E E E E E E-10 C O Ne Mg Si N Na Al P S Ar Ca Ti Fe Ni Interstellar gas Sun Pop I stars Pop II stars 1.0E Atomic number, Z 4 September 2018 ASTRONOMY 111, FALL THE TEMPERATURE OF THE SUN S SURFACE The Sun is a ball of hot gas; it has no sharp, solid surface. So what do we mean by the surface of the Sun? Usually, we mean the deepest place we can see in the Sun s atmosphere; this is called the photosphere. The absorption of light in the Sun varies with wavelength, though, so the position of the photosphere is different for different parts of the spectrum. The temperature varies with depth within the Sun s atmosphere and interior, so the physical temperature of the surface that we see is different for different wavelengths. So, it is more convenient to characterize the Sun s surface temperature in a way that depends upon the luminosity (total power output), which of course is wavelength-dependent. Effective temperature of the Sun: the temperature that would produce the Sun s observed luminosity, if the Sun were a spherical blackbody with the same radius. You will learn all about blackbodies in PHY 143/123 and PHY 227. We will only list the properties and equations pertaining to blackbodies that we will need to use this semester, and defer the detailed explanations to those courses. 4 September 2018 ASTRONOMY 111, FALL

14 BLACKBODIES AND BLACKBODY RADIATION A blackbody is a body that is perfectly opaque: it absorbs all of the light incident on it. If such a body has a constant temperature, it must therefore also emit light at exactly the same rate as it absorbs light. This is called blackbody radiation. The flux total power emitted in all directions by a blackbody at temperature T per unit area of a blackbody is given by! = #$ % # = erg sec -4 cm -6 K -% = J sec -4 m -6 K -% Stefan s Law Stefan-Boltzmann constant 4 September 2018 ASTRONOMY 111, FALL DEFINITIONS: LUMINOSITY AND FLUX Luminosity is the total power output (in the form of light) emitted in all directions by an object. Units = erg sec -1 The Sun s luminosity, as we listed before, is! = ** erg sec 01 Flux is the total power (in the form of light) per unit area that passes through a (sometimes imaginary) surface. Units = erg sec -1 cm -2 The flux of sunlight at the Sun s surface is! 2 = = ; erg sec 01 cm 07 The flux of sunlight at Earth s orbit (the solar constant) is! 2 = AU 7 = ? erg sec 01 cm 07 4 September 2018 ASTRONOMY 111, FALL

15 THE SUN S EFFECTIVE TEMPERATURE If the Sun were a blackbody with radius equal to that of its visible photosphere (R = 6.96x1010 cm) and luminosity as observed (L = 3.83x1033 erg/s), then its (effective) temperature T e would be given by " = %& = '( ) * 4,-. or ( ) = / * ;< = == erg sec >5 *0?.@A ;< >B erg sec >5 cm >3 K ;< 5D cm = 5770 K Hence the number given above for the surface temperature. This turns out not to be far off from the physical temperature typical of the photospheric region. 4 September 2018 ASTRONOMY 111, FALL THE SPECTRUM OF A BLACKBODY One reason the effective temperature comes so close to the relevant physical temperature is that the spectrum of the Sun resembles the spectrum of a blackbody. 4 September 2018 ASTRONOMY 111, FALL

16 BLACKBODY SPECTRUM The spectrum of blackbody radiation is given by the Planck function:! " = 2h&' 1 ( ) -., + "/0 1 where h = '7 erg sec Planck s constant = = @A erg K 6@ Boltzmann s constant The dimensions of the Planck function may seem confusing at first: they are power per unit area, per unit solid angle, per unit wavelength interval; for example, erg sec -1 cm -2 ster -1 μm -1 4 September 2018 ASTRONOMY 111, FALL SOLID ANGLE? Solid angle is to area what angle is to length. It is usually defined by a differential element in spherical coordinates:!ω = sin '!'!(!'!( Angles in radians Unit of solid angle = steradian For small angles, the solid angle is calculated from the angular widths of the patch in the same manner as plane-geometrical areas. For a rectangle, the two angles ΔΩ = Δ( sin ' Δ' 4 September 2018 ASTRONOMY 111, FALL

17 !, +,, ' #, ', *! = # sin ' cos * + = # sin ' sin *, = # cos '!, # # =! , - ' = tan 12! , * = tan 12 +! + * REMINDER: THE SPHERICAL COORDINATES r, θ, φ 4 September 2018 ASTRONOMY 111, FALL SIMPLE EXAMPLE What is the solid angle of a square patch of sky 15.4 arcminutes on a side? (This is the solid angle covered by the CCD camera you will use on the Mees 24-inch telescope.) 15.4 arcminutes is a small angle (<< 1 radian). Since I did not specify where the z- axis is, we are free to point it through the square s center, so sin $ = 1: ΔΩ = Δ$ Δ) = radians Ω = :; steradians 4 September 2018 ASTRONOMY 111, FALL

18 COMPUTING SOLID ANGLES When the angles are not small, one must integrate the differential element over the range of θ and φ. You will not be doing that in AST 111, but just so you can see how it works The solid angle of the entre sky: %& Ω = # '( # $ $ & Ω = 4/ steradians & sin, ', = 2/ cos, 0 = 2/ 2 $ The solid angle of a cone with an angular radius of π/8 radians: %& & 9 :sin & 9 : Ω = # '( #, ', = 2/ cos, 0 = 2/ $ $ $ Ω = steradians 4 September 2018 ASTRONOMY 111, FALL BLACKBODY SPECTRUM The reason for the funny dimensions of the Planck function is that it has to be integrated over wavelength, solid angle, and area in order to produce a luminosity:! = # $ ( %Ω # %) * +, = # %. # ' - $ ( %Ω # %) * + ' In PHY 227 or AST 241, you will learn how to prove that the power per unit area emitted in all directions by a blackbody is /0 02 /%3! = # %1 # cos 3 # (%) * + = 289 : ; ' ' ' 15> / A; CA ; that is, Stefan s Law follows from the Planck function. 4 September 2018 ASTRONOMY 111, FALL

19 THE PLANCK FUNCTION Note that the higher the temperature, the shorter the wavelength at which the peak occurs. Note also that visible wavelengths do not include much of the luminosity, whatever the temperature. u l (T) (erg sec -1 cm -3 ster -1 ) K Wavelength (µm) 5000 K 2000 K 1000 K Visible light 4 September 2018 ASTRONOMY 111, FALL WIEN S LAW We will not be using the Planck function much, and we certainly will not be integrating it. It appears now because of a useful consequence of the shape of the function. It is fairly easy to convince oneself as you will, in Problem Set 1 that there is a simple relation between the temperature of a blackbody and the wavelength at which it is brightest:! "#$ % = cm K = m K Wien s law The shape of the spectrum tells one what the effective temperature is. This shape is easier to measure accurately than luminosity is. 4 September 2018 ASTRONOMY 111, FALL

20 EXAMPLES At what wavelength do you (T = 98.6 F = 37 C = 310 K) emit the most blackbody radiation?! "#$ = 0.29 cm K - = = cm = 9.4 4m 0.29 cm K 310 K Infrared light Gamma-ray bursters emit most of their light at a wavelength of about cm. If this emission were blackbody radiation, what would be the temperature of the burster? - = 0.29 cm K 0.29 cm K =! "#$ cm = K Pretty hot 4 September 2018 ASTRONOMY 111, FALL