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From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. Clicker Question: Why didn’t my hand get crushed by the hammer? A: My bones are actually stronger than steel. B: The plate has a lot of inertia C: The plate is very strong D: The force of gravity kept the plate from moving Newton's Laws of Motion Newton’s Zeroeth Law of Motion Objects are dumb. They do not know the past and they are not good predictors of the future. They only know what forces act on them right now. Newton’s First Law of Motion Every object continues in a state of rest or a state of motion with a constant speed in a straight line unless acted on by an unbalanced force. Newton’s 2nd Law of Motion When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass. a= Fnet m Newton’s Third Law of Motion To every action there is an equal and opposite reaction. Or, when one object exerts a force on a second object, the second exerts an equal and opposite force on first. Gravitational Force on a Planet For an object of mass m at or near the surface of a planet the force of their gravitational attraction is given by: F = mg F is the gravitational force. g is the planetary "gravitational constant". Your "weight" is just the gravitational force between the Earth and you. Newton's Law of Gravity For two objects of mass m1 and m2, separated by a distance R, the force of their gravitational attraction is given by: F= G m1 m2 R2 F is the gravitational force. G is the universal "gravitational constant". An example of an "inverse-square law". Your "weight" is just the gravitational force between the Earth and you. Throwing a ball into Orbit Clicker Question: Suppose Matt weighs 120 lbs on his bathroom scale on Earth, how much will his scale read if he standing on a platform 6400 km high (1 Earth radius above sea-level)? A: 12 lbs B: 30 lbs C: 60 lbs D: 120 lbs E: 240 lbs Newton's Correction to Kepler's First Law The orbit of a planet around the Sun has the common center of mass (instead of the Sun) at one focus. Escape Velocity Velocity needed to completely escape the gravity of a planet. The stronger the gravity, the higher the escape velocity. Examples: Earth Jupiter Deimos (moon of Mars) 11 km/s 60 km/s 7 m/s = 15 miles/hour Timelines of the Big Names Galileo Copernicus 1473-1543 1564-1642 Brahe 1546-1601 Kepler 1571-1630 Newton 1642-1727 Electromagnetic Radiation (How we get most of our information about the cosmos) Examples of electromagnetic radiation: Light Infrared Ultraviolet Microwaves AM radio FM radio TV signals Cell phone signals X-rays Radiation travels as waves. Waves carry information and energy. Properties of a wave wavelength (l) crest amplitude (A) trough velocity (v) l is a distance, so its units are m, cm, or mm, etc. Also, v = l n Period (T): time between crest (or trough) passages Frequency (n): rate of passage of crests (or troughs), n = (units: Hertz or cycles/sec) 1 T = hn Waves Demo: making waves - wave table Demo: slinky waves Radiation travels as Electromagnetic waves. That is, waves of electric and magnetic fields traveling together. Examples of objects with magnetic fields: a magnet the Earth Clusters of galaxies Examples of objects with electric fields: Power lines, electric motors, … Protons (+) "charged" particles that make up atoms. Electrons (-) } Scottish physicist James Clerk Maxwell showed in 1865 that waves of electric and magnetic fields travel together => traveling “electromagnetic” waves. The speed of all electromagnetic waves is the speed of light. c = 3 x 10 8 m / s or c = 3 x 10 10 cm / s or c = 3 x 10 5 km / s light takes 8 minutes Earth Sun c= ln or, bigger l means smaller n The Electromagnetic Spectrum 1 nm = 10 -9 m , 1 Angstrom = 10 -10 m c= ln A Spectrum Demo: white light and a prism Refraction of light All waves bend when they pass through materials of different densities. When you bend light, bending angle depends on wavelength, or color. Clicker Question: Compared to ultraviolet radiation, infrared radiation has greater: A: energy B: amplitude C: frequency D: wavelength Clicker Question: The energy of a photon is proportional to its: A: period B: amplitude C: frequency D: wavelength Clicker Question: A star much colder than the sun would appear: A: red B: yellow C: blue D: smaller E: larger Rainbows rred orange yellow green blue violet What's happening in the cloud? raindrop 42o 40o Double Rainbows We form a "spectrum" by spreading out radiation according to its wavelength (e.g. using a prism for light). What does the spectrum of an astronomical object's radiation look like? Many objects (e.g. stars) have roughly a "Black-body" spectrum: • Asymmetric shape Brightness • Broad range of wavelengths or frequencies • Has a peak Frequency also known as the Planck spectrum or Planck curve. Approximate black-body spectra of astronomical objects demonstrate Wien's Law and Stefan's Law cold dust hotter star (Sun) “cool" star very hot stars frequency increases, wavelength decreases Laws Associated with the Black-body Spectrum Wien's Law: lmax energy a 1 T (wavelength at which most energy is radiated is longer for cooler objects) Stefan's Law: Energy radiated per cm2 of area on surface every second a T 4 (T = temperature at surface) 1 cm2 Betelgeuse Rigel Betelgeuse The total energy radiated from entire surface every second is called the luminosity. Thus Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2) For a sphere, area of surface is 4pR2, where R is the sphere's radius. The "Inverse-Square" Law Applies to Radiation Each square gets 1/4 of the light Each square gets 1/9 of the light apparent brightness a 1 D2 D is the distance between source and observer. The Doppler Effect Applies to all kinds of waves, not just radiation. at rest velocity v1 velocity v2 velocity v1 velocity v1 velocity v3 you encounter more wavecrests per second => higher frequency! fewer wavecrests per second => lower frequency! Doppler Effect Demo: buzzer on a moving arm Demo: The Doppler Ball The frequency or wavelength of a wave depends on the relative motion of the source and the observer. Things that waves do 1. Refraction Waves bend when they pass through material of different densities. air water swimming pool prism air glass air 2. Diffraction Waves bend when they go through a narrow gap or around a corner. 3. Interference QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Waves can interfere with each other QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture.