Gravity Galileos observations on gravity led to Newtons

Gravity • Galileo’s observations on gravity led to Newton’s Law of Gravitation and the three Laws of Motion • Objects fall at the same rate regardless of mass because more massive objects have more inertia or resistance to motion • Fgrav = G (m 1 x m 2) / r 2 • Force of gravity between two masses is proportional to the product of masses divided by distance squared ‘inverse square law’

Newton – Three Laws of Motion 1. Inertia 2. F = ma 3. Action = Reaction

Newton’s Laws of Motion • Law of Inertia: A body continues in state of rest or motion unless acted on by an external force; Mass is a measure of inertia • Law of Acceleration: For a given mass m, the acceleration is proportional to the force applied F=ma • Law of Action equals Reaction: For every action there is an equal and opposite reaction; momemtum (mass x velocity) is conserved

Velocity, Speed, Acceleration • Velocity implies both speed and direction; speed may be constant but direction could be changing, and hence accelerating • Acceleration implies change in speed or direction or both • For example, stone on a string being whirled around at constant speed; direction is constantly changing therefore requires force

Ball Swung around on a String: Same Speed, (in uniform circular motion) Changing Direction (swinging around the circle)

Donut Swung around on a String Acceleration Force

Conservation of momemtum: action equal reaction • The momemtum (mv) is conserved before and after an event • Rocket and ignited gases: M(rocket) x V(rocket) = m(gases) x v(gases) • Two billiard balls: m 1 v 1 + m 2 v 2 = m 1 v 1’ + m 2 v 2’ v 1, v 2 – velocities before collision v 1’, v 2’ – velocities after collision • Example – you and your friend (twice as heavy) on ice!

Action = Reaction Equal and Opposite Force from the Table Net Force is Zero, No Net Motion Force = (apple’s mass) (acceleration due to gravity)

Acceleration due to gravity • Acceleration is rate of change of velocity, speed or direction of motion, with time a = v/t • Acceleration due to Earth’s gravity : a g g = 9. 8 m per second, or 32 ft/sec 2 • Speed in free-fall T (sec) v (m/sec) v (ft/sec) 0 0 0 1 9. 8 32 2 19. 6 64 3 29. 4 96 60 mi/hr = 88 ft/sec (between 2 and 3 seconds)

Galileo’s experiment revisited • What is your weight and mass ? • Weight W is the force of gravity acting on a mass m causing acceleration g • Using F = m a, and the Law of Gravitation W = m g = G (m MEarth) /R 2 (R – Radius of the Earth) The mass m of the falling object cancels out and does not matter; therefore all objects fall at the same rate or acceleration g = GM / R 2 i. e. constant acceleration due to gravity 9. 8 m/sec 2

Galileo’s experiment on gravity • Galileo surmised that time differences between freely falling objects may be too small for human eye to discern • Therefore he used inclined planes to slow down the acceleration due to gravity and monitor the time more accurately v Changing the angle of the incline changes the velocity v

‘g’ on the Moon g(Moon) = G M(Moon) / R(Moon)2 G = 6. 67 x 10 -11 newton-meter 2/kg 2 M(Moon) = 7. 349 x 1022 Kg R(Moon) = 1738 Km g (Moon) = 1. 62 m/sec About 1/6 of g(Earth); objects on the Moon fall at a rate six times slower than on the Earth

Escape Velocity and Energy • To escape earth’s gravity an object must have (kinetic) energy equal to the gravitational (potential) energy of the earth • Kinetic energy due to motion K. E. = ½ m v 2 • Potential energy due to position and force P. E. = G m M(Earth) / R (note the similarity with the Law of Gravitation) • Minimum energy needed for escape: K. E. = P. E. ½ m v 2 = G m M / R Note that the mass m cancels out, and • v (esc) = 11 km/sec = 7 mi/sec = 25000 mi/hr The escape velocity is the same for all objects of mass m

Object in orbit Continuous fall ! Object falls towards the earth at the same rate as the earth curves away from it

Angular Momentum Conservation of angular momentum says that product of radius r and momentum mv must be constant radius times rotation rate (number of rotations per second) is constant

Angular Momentum • All rotating objects have angular momentum • L = mvr ; acts perpendicular to the plane of rotation • Examples: helicopter rotor, ice skater, spinning top or wheel (experiment) • Gyroscope (to stabilize spacecrafts) is basically a spinning wheel whose axis maintains its direction; slow precession like the Earth’s axis along the Circle of Precession

Conservation of Angular Momentum • Very important in physical phenomena observed in daily life as well as throughout the Universe. For example, • Varying speeds of planets in elliptical orbits around a star • Jets of extremely high velocity particles, as matter spirals into an accretion disc and falls into a black hole

1 Relativistic Jet “From” Black Hole 1. “Relativistic velocities are close to the speed of light

Quiz 1 • Each quiz sheet has a different 5 -digit symmetric number which must be filled in (as shown on the transparency, but NOT the same one!!!!!) • Please hand in both the exam and the answer sheets with your name on both • Question/answer sheets will be handed back on Wednesday after class • Please remain seated until we begin collecting (20 -25 minutes after start) • Class after quiz

Stars and Galaxies: Galileo to HST • http: //thenextdigit. com/16961/nasa-telescopes-new-panoramic-view-andromeda-resolves-stars/

Why is the sky blue ? The atmosphere scatters the blue light more than red light

Light and Matter • Light is electromagnetic energy, due to interaction of electrical charges • Matter is made of atoms – equal number of positive and negative particles • An atom is the smallest particle of an element; natural element H to U • Atom Nucleus (protons + neutrons), with ‘orbiting’ electrons • No. of protons in nucleus = Atomic Number • Science of light Spectroscopy

Radiation and Spectroscopy • • Light is electromagnetic energy Propagates as both particles and waves Photons – particles of light Wavelength = Velocity / Frequency

Light is electromagnetic wave; Does not require a medium to propagate, unlike water or sound Wavelength is the distance between successive crests or troughs

WAVES: Frequency, Wavelength, Speed Wavelength ( ) Frequency (f) (# waves/second) Speed (c) Frequency ‘f’ is the number of waves passing a point per second Speed = wavelength x frequency c=lf

Units of wavelength and frequency • Frequency is the number of cycles per second • Since speed of light is constant, higher the frequency the shorter the wavelength and viceversa • Wavelengths are measured in Angstroms: 1 A = 1/100, 000 cm = 1/10 nanometer (nm) • The higher the frequency the more energetic the wave • Wavelength (or frequency) defines radiation or color

Prisms disperse light into its component colors: Red-Violet White Light Spectrum Prism

Visible light spectrum: Each color is defined by its wavelength, frequency or energy Red - Blue 7000 - 4000 Angstroms ( 1 nm = 10 A, 1 A = 10 -8 cm) Blue light is more energetic than red light Light also behaves like ‘particles’ called photons Photon energy, frequency, wavelength: E = h f = hc/l Planck’s Law (‘h’ is a number known as Planck’s constant)

Visible Light • Forms a narrow band within the electromagnetic spectrum ranging from gamma rays to radio waves • Human eye is most sensitive to which color? • Yellow. Why?

Light: Electromagnetic Spectrum From Gamma Rays to Radio Waves Gamma X-Ray UV Visible Gamma rays are the most energetic (highest frequency, shortest wavelength), Radio waves are the least energetic.

Decreasing Wavelength OR Increasing Frequency

Matter and Particles of Light: Quantum Theory • Light (energy) and matter in motion behave both as • • • waves and particles Wave-Particle Duality - Quantum Theory Energy particles: quanta or photons: E = hf = hc/l Photons of a specific wavelength may be absorbed or emitted by atoms in matter Matter is made of different natural elements: lightest Hydrogen (1 proton), heaviest Uranium (92 protons) Smallest particle of an element is atom, made up of a nucleus (protons and neutrons), and orbiting electrons Electrons and protons attract as opposite electrical charges, NOT gravitationally like planets and Sun

The simplest atom: Ordinary Hydrogen Resemblance to planets orbiting the Sun is superficial ! Electrons also move both as particles and waves p – positively charged e – negatively “ One proton in the center (nucleus) and one electron in orbits of definite energy; Ordinary H has no neutrons, but ‘heavy hydrogen’ has one neutron in the nucleus

Absorption of a quantum of energy photon by H-atom

Emission of a quantum of energy photon by H-atom photon energy color

Absorption and emission of quanta of energy photons by H-atom An electron may absorb or emit light photons at specific wavelength Wavelength (n = 3 n = 2): 6562 Angstroms (RED Color) Energy of the photon must be exactly equal to the energy difference between the two ‘orbits’

Continuum n= n=5 n=4 Energy Level Diagram of 1 H n=3 (2 nd excited state) n=2 (1 st excited state) n=1 (Ground State)

2 6 2 5 2 4 n=2 3 n=6 n=5 n=4 n=3 (2 nd excited state) n=2 (1 st excited state) Photons of all other energies (wavelengths) are ignored and pass on by unabsorbed. n=1 (Ground State)

6 2 5 2 4 2 n=3 2 n=6 n=5 n=4 n=3 (2 nd excited state) n=2 (1 st excited state) Larger Jump = More Energy = Bluer Wavelength n=1 (Ground State)

Series of spectral lines of Hydrogen

Wavelengths of series of lines from Hydrogen

SPECTRAL SIGNATURE OF ELEMENTS

Continuous, Absorption, and Emission Spectra

Brightness decreases inversely as the square of the distance d=1 B=1 d=2 B=1/4 d=3 B=1/9

Brightness and Temperature • Brightness is related to the total energy emitted, or the luminosity of an object • The energy emitted is related to the temperature of the object • B = s T 4 (s is a constant) Stefan-Boltzmann Law

Color Indicates Temperature and Energy of the Source Blackbody: Perfect absorber and emitter Of radiation at a given Temperature T Surface T (Sun) = 5600 K “ (Mercury) = 800 K Objects generally emit radiation at all wavelengths, but mostly at one peak Wavelength depending on their temperature (e. g. blue – hot, red – cool)

TEMPERATURE SCALES Astronomers usually use the Kelvin Scale Room Temp = 300 K = 27 C = 81 F K = C + 273 C = (F - 32) x 5/9 F = (C x 9/5) + 32 ~ (F - 30) / 2 ~ C x 2 + 30

The Doppler Effect • Why does the “pitch” of a police siren differ when, say, a police car is approaching you, or when you are running away from the police (not recommended) ? • The frequency (the number of sound waves per second) is higher when approaching, and smaller when receding from the source

Doppler Effect in Sound High Pitch (short waves) Low Pitch (long waves)

The Doppler Effect Velocity c = frequency (f) x wavelength (l)

Doppler Shift of Wavelengths • • • What about the wavelength? What about light? Shorter wavelength Blue-shift, Longer wavelength Red-shift We can determine the velocity of astronomical objects, moving away or towards the Earth, by measuring the wavelength of light from the object • Observed red-shift of galaxies all over the sky shows that galaxies are moving away from one another the Universe is expanding (Hubble’s Law)