Introduction Inventory of the Solar System Major Characteristics Distances & Timescales Spectroscopy Abundances, Rocks & Minerals Half-Life Some Definitions and Key Equations
Solar System A collection of planets, asteroids, etc that are gravitationally bound to the Sun
Inventory of the Solar System 1 Star 8 Planets + at least 4 dwarf planets 4 Planetary Ring Systems > 60 Natural Satellites (i.e., moons) > 4000 Numbered Asteroids ~ 10 12 comets Zodiacal Dust Cloud Solar Wind / Solar Magnetic Field 70,000 Kuiper Belt Objects (with diameters > 100 km)
Major Characteristics of the Solar System Orbits of planets are co-planar Orbits of planets are nearly circular (exceptions Mercury, Kuiper Belt Objects, & comets) Motion of Planets are prograde Planetary spins are prograde, with periods of 10-20 hours (exceptions Venus, Uranus, and Pluto) Terrestrial planets (Mercury!Mars) have refractory (bits of rocks) compositions, and the Jovian planets are gaseous The Jovian planets resemble mini-solar systems (many satellites) Solar system is transparent (i.e., dust free)
Distances & Timescales Astronomical unit - the average distance between the Earth & Sun. 1 AU = 150 million kilometers or 8.3 light minutes Sun to Pluto ~ 40 AU or 5.5 light hours Sun to Nearest Star ~ 4.2 light years Size of our Galaxy ~ 150,000 light years
Parsec - a commonly used measure of distance in extragalactic astronomy Method: Parallax the apparent displacement of an object caused by the motion of the observer Earth #Sun Distance " = Distance to Star A star with a parallax angle of 1 is at a distance of 1 pc = 3.1x10 16 m (~ 3.25 light years). I.e., D star = D 1AU " = 1AU 1" # 3600" 1 # 180 $ = 3.1%1016 m =1pc
Age of the Universe Hubble Diagram (1926) v (km s -1 ) the Doppler motion "# / # = v / c R (Mpc), where f ~ R -2. So, v ~ R, v = H 0 R
Age of the Universe Hubble Diagram (1926) H 0 = 75 km s -1 Mpc -1 t H = R/v = 1/H 0 = 13.1x10 9 yr ago (~ Age of Universe) Note: We ve ignored acceleration/deceleration for this calculation Present accepted value = 13.7x10 9 yr
Age of the solar system By comparison, we know through radioactive dating of rocks that the solar system is 4.5x10 9 yr old Thus the solar system formed when the Universe was 2/3 its present age
Typical spiral galaxy - Milky Way Number of stars ~ 10 11 Mass ~ 10 12 M sun How many times has the Sun orbited the galactic center? Distance of Sun from galactic center ~ 8.5 kpc Time for one orbit t = 2!R / v = 2! 8.5 kpc / 250 km s -1 = 2x10 8 yr Thus, the Sun has made 4.5x10 9 / 2.0x10 8 ~ 20 turns around the galactic center
How often do stars collide? Volume disk = (thickness)"(radius) 2 = H"R 2 = (3 #10 19 m)"(3#10 20 m) 2 = 8.5 #10 60 m 3 The Number density of stars in the disk is, n = N stars V = 1011 stars 8.5 "10 60 m =1.17 3 "10#50 m #3 The mean cross section, $, of stars is calculated by assuming every star is like the sun, " = #(2R sun ) 2 = 6.08 $10 18 m 2 Mean free path % = 1 n" =1.4 $1028 km
Stellar collisions (continued) Given that v random = 40 km s -1, Stars collide every, t collision ~ I.e., not very often " v random =1#10 19 years Note that considering the gravitational cross section only lowers this time by a factor of 100. Thus, while passing stars may effect the motion of small solar system objects in the outer solar system, collisions are not an important part of the evolution of stars and their associated solar systems
Spectroscopy Determination of object compositions Note that we can only directly observe the exterior layers of astronomical objects Density measurements help us to infer the rest
Photon discrete unit of electromagnetic energy Massless Travels at 2.9979x10 8 m / s (I.e., the speed of light ) Has specific frequency, %, & wavelength, # Energy = h %, where h = 6.63x10-34 J.s Speed of wave, v = % # Of course, v = c for radiation
# & % some examples
Spectroscopy works because different kinds of atoms and molecules emit & absorb different kinds of photons
Emission & Absorption Ionization: the process by which an atom loses electrons Ion: an atom that has become electrically charged due to the loss of one or more electrons. Note that isolated atoms are electronically neutral i.e, they have the same number of protons & neutrons unless they are ionized.
Emission vs. Absorption Lines
Example: Spectrum of the Sun Absorption features are observed I.e., hot radiation from below is absorbed in the cooler outer envelope
Not all wavelengths of radiation reach the ground This is one reason why air/space-borne missions are necessary Modern Examples - Chandra X-ray observatory, XMM, Spitzer Space Telescope
Cosmic Abundances
Cosmic Abundances The abundances were set to ~75% H & ~ 25% He within the first few minutes of the Universe Fusion in stars converts lighter elements into heavier ones, but the relative abundances of H and He have barely changed from the early Universe percentages
Abundances: Sun, star-forming region, & planetary nebula
Abundances - Sun vs. Terrestrial Planets & Life The Sun is primarily Hydrogen & Helium The inner planets are primarily Oxygen, Silicon, Magnesium & Iron (also abundant on Earth - Sodium Calcium, Aluminum, and Nickel) Life is primarily Hydrogen, Oxygen, Carbon, & Nitrogen
Four Types of Matter Gas: what makes up planetary atmospheres Ice (Volatiles): molecules that are liquid or gaseous at moderate temperatures but form solids/crystals at low temperatures (e.g., Water H 2 O, Carbon dioxide CO 2, Methane CH 4 ) Rock: objects such as silicates that can be left behind after ice mixed with heavier elements are heated (e.g., silicates molecules of oxygen combined with either silicon, magnesium, or aluminum) Metal: material, such as iron, nickel, & magnesium that separate out from the rest of the material that make up rock when temperatures get extremely high Heat
Classification of Rocks Igneous: formed directly by cooling from a molten state. 2/3 of the Earth s crust is igneous rock Sedimentary: fragments (which are produced by weathering) that are cemented together (e.g., limestone & sandstone) Metamorphic: Igneous or Sedimentary rock that have been buried & compressed by high pressure & temperature (e.g., marble, material dredged up by continental drift) Primitive rock: rock that is affected only moderately by chemical or physical processes (e.g., meteorites)
Minerals While rocks can be a mixture of different substances, minerals are rocks that are made up of only one substance. Minerals form according to local pressure, temperature, & cooling rate Silicates are the most important & extensive type of mineral - based on SiO 4. Olivine (Mg,Fe) 2 SiO 4 is an example We will talk more about minerals later
Age-Dating Solidification Age: Time since the material became solid Gas Retention Age: A measure of the age of a rock, defined in terms of its ability to retain radioactive argon (which is the daughter product of potassium)
Half-Life Half-Life: Given a quantity of material, the half-life is the time which half the material will have decayed into the daughter product Examples - Radioactive Decay U-238 (92p +,146n)! Pb-206 (82p +,124n) + (10p +,22n) K-40 (19p +,21n)! Ar-40 (18p +,22n) The Decay Rates U-238! 4.5 billion years K-40! 1.25 billion years
Radioactive decay of Potassium-40 to Argon-40
Radioactive Decay Number of radioactive atoms, "N, that will decay within a time interval, "t, is proportional to the number of atoms (which is decreasing), N, present in the sample, I.e., The number of atoms that remain after "t is obtained by integrating over the time interval t = 0! & to get
Radioactive Decay To measure the age of the rock, We first determine # in terms of the half-life time & hl, And thus,
Radioactive Decay The number of `daughter atoms after & is, And thus, The ratio D # / N # can be measured, and # hl is known from laboratory measurements.
Spectral Energy Distribution The energy emitted from a source as a function of wavelength/frequency The whole SED of a source is difficult to measure (Wang et al. 2006, Nature, 440, 772)
Flux Density, Flux Flux density: f $ or f %, measured in units of W m -2 Hz -1 or W m -2 µm -1 (or the equivalent) Flux: measured in units of W m -2 (or the equivalent). To convert flux density to flux,
Luminosity For a source at a distance R & measured flux f, the luminosity is, Luminosity is measured in units of Watts (I.e., J/s) or ergs/s, & it is determined for whatever wavelength/frequency the flux is determined at. Bolometric Luminosity: the luminosity of an object measured over all wavelengths
Useful form of the ideal gas law The common form of the ideal gas law is where P = pressure exerted by the gas (N m -2 ), V = volume occupied by the gas (m 3 ), n = number of moles of gas within V, R = gas constant (8.31 J K -1 mole -1 ), & T = absolute temperature of the gas (K) One mole = one Avogadro s # of atoms (N A = 6.02x10 23 mole -1 ) Mass of one mole = N A µm H, where m H = 1.67x10-27 kg & µ = molecular weight of gas atom. Given that
Ideal gas law (cont) we can make the following substitutions, where k = Boltzmann constant (1.38x10-23 J/K) and & = mass density of the gas (kg m -3 ), to get
Equation of Hydrostatic Equilibrium The Sun and the atmospheres of planets are in hydrostatic equilibrium Consider a slab of the Earth s atmosphere of thickness dh, surface area da, density & (kg m -3 ). The gravitational acceleration of the Earth is g. In equilibrium, the Forces Up = Forces Down. I.e.,
Thus, Hydrostatic Equilibrium (cont)
Motion: Centripetal Acceleration Consider a planet moving in a circular orbit with a speed v & radius r from the center. The change in its angular position '( occurs within a time 't. So, the speed is, The velocity changes because of the change in the direction of motion, "v The acceleration is, r Substituting in 't = r '( / v gives, "' v
Motion The gravitational acceleration experienced by an object which is a distance r from a mass M is, Equating this with the centripetal acceleration gives us,
Motion (cont) Thus, for an object orbiting the Sun at a distance of 1.5x10 11 m (= 1 AU), the velocity is The time it takes to traverse one orbit is Note that the accuracy of this calculation is limited by the accuracy of the number with the least significant digits (I.e., in this calculation, the Sun-Earth distance). TBC.