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

• ~ 1012 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

• A star with a parallax angle

of 1” is at a distance of 1 pc

= 3.1x1016 m (~ 3.25 light

years). I.e.,

!

!

" =Earth#Sun Distance

Distance to Star

!

Dstar

=D1AU

"

=1AU

1"#3600"

1°#180°

$= 3.1%1016m =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 = H0R

Age of the Universe

–

Hubble Diagram

(1926)

• H0 = 75 km s-1 Mpc-1

• tH = R/v = 1/H0 = 13.1x109 yr ago (~ Age of Universe)

• Note: We’ve ignored acceleration/deceleration for this calculation

• Present accepted value = 13.7x109 yr

Age of the solar system

• By comparison, we know through radioactive dating

of rocks that the solar system is 4.5x109 yr old

• Thus the solar system formed when the Universe

was 2/3 its present age

Typical spiral galaxy - Milky Way• Number of stars ~ 1011

• Mass ~ 1012 Msun

• How many times has the Sun orbited the galacticcenter?

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 = 2x108 yr

Thus, the Sun has made 4.5x109 / 2.0x108 ~ 20 turnsaround the galactic center

How often do stars collide?

• The Number density of stars in the disk is,

• The mean cross section, $, of stars is calculated by

assuming every star is like the sun,

!

Volumedisk

= (thickness)" (radius)2 = H"R2

= (3#1019m)" (3#1020m)2 = 8.5 #10

60m3

!

n =N

stars

V=

1011stars

8.5 "1060m3

=1.17 "10#50m

#3

!

" = # (2Rsun )2

= 6.08 $1018m2

Mean freepath % =1

n"=1.4 $10

28km

Stellar collisions (continued)

• Given that vrandom = 40 km s-1,

• Stars collide every,

• I.e., not very often

• 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

!

tcollision ~"

vrandom=1#10

19years

Spectroscopy

• Determination of object compositions

• Note that we can only directly observe the exterior layersof astronomical objects

• Density measurements help us to infer the rest

Photon – discrete unit of

electromagnetic energy• Massless

• Travels at 2.9979x108 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 tothe loss of one or more electrons. Note that isolatedatoms are electronically neutral – i.e, they have thesame number of protons & neutrons – unless they areionized.

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 arenecessary

• 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 – H2O, Carbon dioxide – CO2, Methane – CH4)

• 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 byweathering) that are cemented together (e.g., limestone& sandstone)

• Metamorphic: Igneous or Sedimentary rock that havebeen buried & compressed by high pressure &temperature (e.g., marble, material dredged up bycontinental drift)

• Primitive rock: rock that is affected only moderately bychemical 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 onesubstance.

• Minerals form according to local pressure,

temperature, & cooling rate

• Silicates are the most important & extensive type of

mineral - based on SiO4. Olivine (Mg,Fe)2SiO4 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

• Radioactive Decay

• The Decay Rates

U-238 (92p+,146n) ! Pb-206 (82p+,124n) + (10p+,22n)

K-40 (19p+,21n) ! Ar-40 (18p+,22n)

U-238 ! 4.5 billion years

K-40 ! 1.25 billion years

Examples -

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 (m3), 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 (NA =

6.02x1023 mole-1)

• Mass of one mole = NAµmH, where mH = 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 ofthickness 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.,

Hydrostatic Equilibrium (cont)

• Thus,

Motion: Centripetal Acceleration

• Consider a planet moving in a circular orbit with a

speed v & radius r from the center. The change in itsangular position '( occurs within a time 't.

• So, the speed is,

• The velocity changes because of the change in the

direction of motion,

• The acceleration is,

• Substituting in 't = r '( / v gives,

r"'

v

"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 of1.5x1011 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 theaccuracy of the number with the least significant digits(I.e., in this calculation, the Sun-Earth distance). TBC.