ASTR 151 Chapter 2
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This 6 page Class Notes was uploaded by Wesley Fowler on Monday February 1, 2016. The Class Notes belongs to ASTR 151 001 at a university taught by Dr. Sean Lindsay in Spring 2016. Since its upload, it has received 46 views.
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Date Created: 02/01/16
Wesley Fowler ASTR Ancient Astronomy Stonehenge: An ancient astronomical observatory of sorts. Helps determine what time of year it is…useful to plan harvesting and planting crops Diurnal Motion: Sun, moon and Stars Annual Motions: The Ecliptic Prograde motion: night-to-night eastward motion -> (rights are pro) Retrogade motion: night-to-night westward motion <- (lefts are retro) Mercury and Venus are “tethered” to the sun Mars, Jupiter, and Saturn exhibit retrograde motion Inferior planets: Between earth and sun Superior planets: Outside earth from sun Opposition occurs at a planet’s closest approach to earth (Inf/superior) Conjunction occurs when a planet appears closest to the sun from the earth’s perspective (etc) Aristotle: Geocentrism. Not an experimentalist at all - The Ptolemaic Universe: Earth at center, perfect orbs and orbits. Circular orbits called epicycles. Lots of problems, planets too close to sun, etc. Copernicus: Heliocentrism (borrowed from Aristarchus) - The Copernican universe: Observed Mar’s orbital motion in comparison to Earth’s, found that Mars had a retrograde motion Retrograde motion: *Point “B” is the opposition. In line with each other 1. Earth is not at the center 2. Center of Earth is the center of the Moon’s orbit 3. All planets revolve around the sun 4. The stars are much farther away than the sun 5. The motion of the stars in the sky is due to Earth’s orbit 6. The motion of the sun in the sky is due to Earth’s orbit 7. Retrogade motion of planets is due to Earth’s motion around the sun - Still believed in perfect orbs and orbits The Team: Heliocentrism’s Establishment Tycho Brahe (1546-1601) The data collector Galileo Galilei (1564-1642) The observer Johannes Kepler (1571-1630) The analyst Galileo Used the pre-invented telescope to observe the heavens. Drew the moon. - Observed craters on the moon. Observed sun spots on the sun. Thus disproving “perfect sphere” theory - Observed phases of Venus - Observed Jupiter’s moons in orbit Tycho Brahe - Took very accurate measurements for decades (~1 arcsec) and preserved them well. - Copper nose, mysterious death. Wesley Fowler ASTR Kepler’s Laws Johannes Kepler - “Acquires” Brahe’s data and creates “Kepler’s Laws of Planetary Motion” 1. Planetary orbits are elliptical. An oval, not circular. The sun is the focus 2. Equal Areas: equal times. Fast when close to sun, slow when far away. 3. The square of the period (P, years) is proportionate to the cube of the semi-axis major (a, astronomical units) P (years) = a (AU)3 st 1 law Elliptical Orbit Perihelion: Closest to sun Aphelion: Farthest from the sun Eccentricity: How “out of circular” the ellipse is (e) Semi-major axis: Radius of major axis (a) nd 2 Law Equal areas, equal times. When plant is farthest away from the sun, it moves the slowest. When it’s closest it moves the fastest. - Fastest at perihelion and slowest at aphelion rd 32 Law 3 P (years) = a (AU) Where (P) is period and (a) is Semilunar Axis AU is defined as the Semilunar axis of Earth The Astronomical Unit Giovanni Cassini measured the earth’s semi major axis via parallax, and was pretty close! One Astronomical Unit is the distance between the Sun and Earth. *1.5 x 10 km is the AU (for this class)* - Force: (N) An influence that tends to change motion - Inertia: (kg*m ) The resistance of an object to change its speed or direction, inertia. - Mass: (kg) The amount of matter - Weight: The gravitational force exerted by an object. How mass is changed by gravity. - Speed: Distance divided by the time it takes to cover it. - Velocity: Speed and direction - Acceleration: (m/(s ))The rate of change of velocity, meters per second per second Newton’s Laws Isaac Newton: Invented Calculus, and fathered Physics. 1. Newton’s first law of motion: An object will maintain constant velocity, or its state of rest (v=0), unless acted upon by an outside force. 2. Newton’s second law of motion: An enacting force is equal to the mass times acceleration of the object it’s pushing against. F = ma - Constant Force: The greater the mass, the harder it is to accelerate the object - Constant Mass: The greater the force applied the larger the acceleration 3. Newton’s third law of motion: When one body exerts a force on the second body, the second body exerts a force equal in magnitude, but opposite in direction of the first body Gravity Th2 acceleration due to gravity’s pull towards the center of Earth: g = 9.8 m/ (s ) F = (Gm m1)/2 2 This is the “Inverse Square Law”. The farther away the object is, the weaker gravity becomes. - The gravitational force is proportional to the product on the two objects mass’s divided by the square of the distance between the two objects (Definition) Gravitational constant (G) = 6.67 x 10 N m /kg 2 2 Planets are constantly being pulled towards the sun by the sun’s gravity Orbiting masses are localized to a common focus, at the center of mass Wesley Fowler ASTR 152 Newtonian Mechanics Planetary Motion Planets don’t shoot strait ahead due to the pull of the sun’s gravity. Thus they orbit. Due to its mass, the sun is the dominant influence over planetary orbit in our solar system. - The earth orbits the sun at a speed of 30km/sec Newton’s corrections to Kepler’s first and third laws: - The earth does not orbit around the center of the sun, but rather around the center of mass between the earth and sun. The “average” position of all the matter. This is the true common focus. This point is still in the sun for the Earth, because it’s so massive. *Mass of sun: 2.0 x 30 kg - P = (a )/(M ) P-orbital period a-semimajor axis M-combined total mass of two objects in solar units Escape Velocity If an object escapes the gravitational pull of an object, then it is unbound. The orbit is no longer an ellipse! Orbital Speed: GM vorb R √ Escape Velocity:
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