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Developing the Science of Astronomy (Chapter 4) Student Learning Objectives • Examine the contributions of ancient and modern astronomy to the understanding of gravity and planetary motion. Identify contributions from the first Astronomers Recall and apply Kepler’s Laws to our solar system Apply Newtonian physics to our solar system Describe gravity and its effects Analyze orbital motion How did early Greek philosophers describe motions in the sky? The Greeks had 3 basic theories for the sky 1. 2. 3. All heavenly bodies spheres that move in circles Heavens unchangeable Earth stationary at center of universe Most Greeks in B.C. times believed in the geocentric model. Aristotle (300 B. C.) Placed Earth at the center of the universe by logic (persisted for 2000 years) Ptolemy (150 A. D.) Developed the epicycle model to explain Mars backwards motion retrograde motion Ptolemy’s Epicycle Model Copernicus (mid-1500’s) Used mathematics to determine the Sun was at the center of the solar system. Heliocentric Model The Early Models Aristotle Stationary Earth Earth at Center Circular Motion Orbital speeds same for all Based on Observation of Apparent Motion Ptolemy Stationary Earth Earth at Center Circular motion Orbital speeds same for all Based on Observation of Apparent Motion Copernicus Rotating Earth Sun at Center Circular motion Orbital speeds depend on distance Based on Mathematics Practice Write a compare and contrast sentence which relates these models. The Transition Tycho Brahe (late-1500’s) Designed and utilized new instruments for measuring precise angles in the sky. Although Tycho Brahe believed in a geocentric system, his measurements were later used to provide proof for the heliocentric system. lol What are Kepler’s Laws? Kepler (1600’s) Used Tycho Brahe’s observations and measurements of planetary positions to develop three laws of planetary motion. Kepler’s 1st Law Planets move in elliptical orbits with the Sun at one focus. (Ellipses) Kepler’s 2nd Law Planets sweep out equal areas of space in equal time intervals. (Equal Areas) Kepler’s 3rd Law The orbital period of a planet is related to the semi-major axis of it’s orbit. P2 = a3 Orbital Period Squared = Semi-major Axis Cubed Practice 1) Which planet has the longer orbital period? Saturn: a = 9.54 AU Jupiter: a = 5.2 AU 2) How do we measure birthdays? http://www.exploratorium.edu/ronh/age/index.html The planets in our solar system follow orbits that are nearly circular. Circles vs Ellipses Eccentricity indicates the elongation of the ellipse. (e = 0 to 1) Galileo Galilei Galileo (1600’s) Used observations to provide visual proof of Copernicus’s Sun centered system. First to use telescope to view sky Planet positions confirmed Moon & Sun not perfect spheres Objects orbiting Jupiter (not Sun or Earth) How are the motions of objects described? Average speed is the amount of distance traveled in some amount of time. (65 mph) s=d t Velocity is speed in a particular direction. (65 mph South) Acceleration Acceleration is the change of velocity in some amount of time. Change in speed or direction All objects on Earth have the same acceleration, downward. 9.81 m/s2 Practice 1) How fast would an object dropped from the tower of Pisa be traveling after 2 seconds, in the absence of air? 2) If the Moon is orbiting at a speed of 1,023 m/s, does the moon experience acceleration? 3) Is the acceleration due to gravity greater on a book or a feather? What are Newton’s Laws of Motion? Newton’s 1st Law An object will remain at rest or maintain a constant velocity unless an unbalanced force causes the object’s motion to change. (Inertia) Inertia is the tendency of an object to maintain its motion. Newton’s 2nd Law of Motion An unbalanced force acting on a mass gives the mass an acceleration in the same direction as the unbalanced force. (F = ma) More push = more acceleration http://www.physicsclassroom.com/mmedia/kinema/stl.cfm Mass vs Weight Mass is a fundamental quantity. Mass is the amount of material contained in an object. Average Man 73 kg Sun 1.989 x 1030 kg Earth 5.972 x 1024 kg more mass more inertia harder to change motion Weight is the gravitational force acting on a mass. W = mg Earth 1kg = 2.2 lbs = 9.8 N http://www.exploratorium.edu/ronh/weight/index.html Practice 1) Mass is often defined in elementary school as “the amount of space an object takes up”. Why is this not correct? 2) Would your mass be different if you were on the moon right now? 3) What would a 75 kg person weigh on Earth? What would this person weigh on Mars where the acceleration due to gravity is 3.72 m/s2? Newton’s 3rd Law of Motion When two objects interact, they create equal and opposite forces on each other. (Action-Reaction) Same Pull Opposite Directions Space X Practice 1) Apply each of Newton's laws to our solar system. 2) If a person weighs 135 pounds, how much force does the floor apply to the person? How much force does the floor apply to a person who weighs 175 pounds, if they stand on the same spot? What is Gravity? Gravity is a property of mass Newton’s Universal Law of Gravitation Every object with mass attracts every other object with mass with a force. Fg = GMm d2 Mutual Force of Attraction Both masses pull the same on each other! Inverse Square Law Force decreases with the square of the distance. Practice 1) Is the gravitational force zero in space? 2) If Earth had twice as much mass, would this change your weight? Would it change your mass? 3) If the distance changes between two objects, does the acceleration due to gravity change? What is Einstein’s description of Gravity? According to Einstein Einstein’s Theory of gravity Every object with mass creates a curvature of space-time. Mass does not create a force Mass changes space Space alters path of objects and light More Mass = More Curvature Image Credit: oneminuteastronomer.com Question to Consider 1) What does gravity effect or cause? Name as many phenomena as you can. 2) How do Newton’s and Einstein’s descriptions of gravity compare and contrast? Effects of Gravity Orbits Orbital Perturbations Atmospheres Synchronous Motion Galaxies Weight Star Formation Tides Shapes of Objects Motion Ocean Tides Changing Systems Our Earth-Moon system is changing. Earth’s rotation is slowing (0.0015 seconds/century) Our Moon is drifting away (3.8 cm/year) The synchronous orbit of the Moon (same face) Weightlessness The feeling of weightlessness occurs when an object and its reference frame accelerate at the same rate. Objects fall together. Image Credit wired.com Practice 1) The Sun's tidal affects are weak compared to the Moon. Why? 2) The astronauts on the space station have no weight. (true or false) 3) Does the moon have weight? What is the physics of orbital motion? Objects move in a straight line, unless an unbalanced force changes the motion. In circular motion, a centripetal force is causing a change in motion. Objects in orbit around the Earth, are falling around Earth. Earth’s escape velocity = 11.2 km/s Earth’s circular velocity = 8 km/s Practice 1) If the force keeping an object in a circular orbit is removed, what will be the path of the orbiting object? 2) What is a geosynchronous orbit? 3) What would be the path of an open orbit? Center of Mass Astronomical objects actually orbit about the center of mass of the system. (Elliptical Orbits) Common Center Of Gravity Conservation Of Energy Elliptical orbits are maintained by conservation of mechanical energy. GPEMax KEMax