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 F grav = G (m1 x m2) / 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 = m a 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)

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

Donut Swung around on a String Force Acceleration

Donut Swung around on a String Force Acceleration

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: m1 v1 + m2 v2 = m1 v1’ + m2 v2’ v1,v2 – velocities before collision v1’,v2’ – velocities after collision Example – you and your friend (twice as heavy) on ice!

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: m1 v1 + m2 v2 = m1 v1’ + m2 v2’ v1,v2 – velocities before collision v1’,v2’ – velocities after collision Example – you and your friend (twice as heavy) on ice!

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

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

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 per second, or 32 ft/sec 2 Speed in free-fall T (sec) v (m/sec) v (ft/sec) 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 M Earth ) /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 newton-meter 2 /kg 2 M(Moon) = x Kg R(Moon) = 1738 Km g (Moon) = 1.62 m/sec/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 = mi/hr The escape velocity is the same for all objects of mass m

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 = 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

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

Relativistic 1 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

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

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

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 vice- versa Wavelengths are measured in Angstroms: 1A = 1/100,000,000 cm = 1/10 nanometer (nm) The higher the frequency the more energetic the wave Wavelength (or frequency) defines radiation or color

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

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 rays are the most energetic (highest frequency, shortest wavelength), Radio waves are the least energetic. Gamma X-Ray UV Visible

Decreasing Wavelength OR Increasing Frequency

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

Matter and Particles of Light: Quantum Theory Light (energy) and matter in motion behave both as waves and particles Wave-Particle Duality - Quantum Theory Particles of light are called photons: E = hf = hc/ 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 Hydrogen Atom Electron orbits Discrete energies

Absorption of light (energy) photon by H-atom

Emission of light photon by H-atom photon energy  color

Series of spectral lines of Hydrogen

Wavelengths of series of lines from Hydrogen

SPECTRAL SIGNATURE OF ELEMENTS

Continuous, Absorption, and Emission Spectra

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 =  T 4  is a constant) Stefan-Boltzmann Law

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

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

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)

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

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

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)