Comet 1P Halley Halley s Comet NASA in 1986 Next apparition July 2061 Period 75 3 Years Semi major Axis 17 8 AU Course Announcements Quiz 1 Graded On table in back of room Mean 7 8 10 Median 8 10 Dr Lindsay s General Evaluation Quiz Difficulty Moderate OSIRIS REx spacecraft launches tomorrow 8 Sept from Cape Canaveral at 7 05 pm EDT Launched on an Atlas V rocket Origins Spectral Interpretation Resource IdentificationSecurity Regolith Explorer Will reach Near Earth Asteroid NEA Bennu in August 2018 collect a sample and return the sample to Earth in 2023 Assignments Reading Assignments No new readings Parallel Lectures CC Astronomy Episode 7 Gravity Mastering Astronomy Chapter 2 Homework Due Tuesday 13 Sept at 11 59 PM EDT Metric System Prefixes Most missed question on Quiz 1 Prefix Symbol Number Giga G 109 1 Billion Mega M 106 1 Million Kilo k 103 1 Thousand Centi c 10 2 1 Hundredth Milli m 10 3 1 Thousandth Micro 10 6 1 Millionth Nano n 10 9 1 Billionth Kepler s Laws of Planetary Motion Empirical description of planetary orbits in our Solar System Kepler s Laws of Planetary Motion 1 Planetary orbits around the Sun are elliptical NOT CIRCULAR in shape with the Sun at one focus 2 Equal Areas Equal Times Alternatively Planets travel fastest in their orbits near Perihelion and slowest at Aphelion 3 The square of the period P is proportion to the cube of the semi major axis a P2 a3 where P is in years and a is in AU See Hyperphysics for additional details Kepler s 1 Law st Geometry of an Ellipse Orbits are Elliptical Long axis is the Major Axis Short axis the Minor Axis Half the Major Axis is the Semimajor Axis a Semiminor Axis b focus focus Semimajor Axis a a is used to define planetary orbits e 0 7 Major Axis Eccentricity e describes how out of circular the ellipse is for the curious e2 a2 b2 a2 e is used to define planetary orbits Note Do not confuse Ecliptic with Elliptical Kepler s 1 Law st Elliptical orbits with the Sun at one focus Vocabulary to Know Perihelion Aphelion Perihelion Closest point to Sun Aphelion Farthest point from Sun Pronounced Ap Helion Eccentricity e Semi major axis is the average distance a object is from the Sun Semi major axis a Kepler s 1 Law st All bound orbits are ellipses A circle is a special case of an ellipse Kepler s 2 Law nd Equal Areas in Equal Times Kepler s 2nd Law is NOT Equal Distances in Equal Times Kepler s 2 Law in practice nd Indicates that a planet is moving fastest at perihelion and moving slowest at aphelion Slower far from Sun Faster close to Sun Kepler s 3 Law rd P2 years a3 AU where P is Period and a is Semimajor Axis NOTE Kepler s 3rd Law only applies to objects orbiting our Sun For other orbits we need a bit more physical understanding The Astronomical Unit AU is defined to be the Semimajor Axis of Earth 1 AU 149 597 970 km or 1 5 x 108 km Using Kepler s 3rd Law Kepler s 3rd Law THIS WILL BE ON QUIZZES AND EXAMS Kepler s 3rd Law states that the square of a planet s orbital period P measured in years is equal to the cube of it s semimajor axis a measured in Astronomical Units AU P2 a3 P is in YEARS and a is in AU The further away from the Sun the longer it takes to orbit Algebraic manipulation yields the following If solving for Period P a3 2 Or P square root a3 If solving for semimajor axis Or a cubed root P2 a P2 3 Example 1 Kepler s 3rd Law Kepler s 3rd Law P2 a3 Ex 1 Planet Galileo orbits a star identical to the Sun at a distance of 4 AU a 4 AU What is the orbital period of Galileo A P 8 years Example 2 Kepler s 3rd Law Kepler s 3rd Law P 2 a3 Ex 2 Comet Halley has a semi major axis distance of 17 9 AU a 17 9 AU What is the orbital period of Halley s comet A P 75 6 years Example 3 Kepler s 3rd Law Kepler s 3rd Law P2 a3 Ex 3 Planet Brahe has an orbital period of 0 5 years P 0 5 yr around a star identical to the Sun What is the semimajor axis distance of Brahe A a 0 63 AU Example 4 Kepler s 3rd Law Kepler s 3rd Law P2 a3 Ex 4 Planet Kepler has an orbital period of 125 years P 125 yr around a star identical to the Sun What is the semimajor axis distance of Kepler A a 25 AU Planetary Motion Kepler s Laws are all well and good but we are left with some pretty big questions here Kepler s Three Laws of Planetary Motion are observations and solutions based on mathematics fits to Brahe s data We call such a result an empirical result One that is based on observations and data but doesn t explain the how the physics of why that result occurred So I ask you What is the reason that planets orbit our Sun Or why do Kepler s Three Laws of Planetary Motion work Isaac Newton Newtonian Mechanics Gravity Calculus The mechanism behind Kepler s Laws Newton published all of this in 1687 in Philosphi Naturalis Principia Mathematica Mathematical Principles of Natural Philosophy or simply The Principia Sir Isaac Newton Newton s Laws of Motion Some required Definitions Force F Any influence that tends to change the motion of an object SI Unit Newton N Inertia the resistance of an object to change its speed and direction Weight versus Mass m or M Mass is the amount of matter protons neutrons electrons etc an object contains SI Unit kg Weight is the gravitational force exerted on a object with mass Speed versus Velocity v y v Velocity is the speed and direction with which an object is x traveling Newton s Laws of Motion Some required Definitions Speed v Velocity v meters second m s Speed is just how fast it is going Velocity is the speed and direction with which an object is traveling Acceleration a m s2 m s The rate of change of velocity i e how velocity in speed and direction is changing with time Acceleration is velocity per time or meters per second per second Newtonian Mechanics Newton s 1st Law of Motion Inertia An object will remain in a state of rest or uniform straight line motion constant velocity unless acted upon by an outside force At Rest In straight line motion Acted on by an outside force Newtonian Mechanics Newton s 2nd Law of Motion F ma When a Force F acts on a body of mass m it produces an acceleration a equal to the force divided by the mass a F m F ma The acceleration an object experiences is inversely proportional to the mass …
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