Comet 1P/Halley (Halley’s Comet)Course AnnouncementsAssignmentsMetric System PrefixesKepler’s Laws of Planetary MotionKepler’s 1st LawKepler’s 1st LawKepler’s 1st LawKepler’s 2nd LawKepler’s 2nd Law – in practiceKepler’s 3rd LawUsing Kepler’s 3rd LawExample 1Example 2Example 3Example 4Planetary MotionIsaac NewtonNewton’s Laws of MotionNewton’s Laws of MotionNewtonian MechanicsNewtonian MechanicsNewtonian MechanicsNewtonian GravityNewtonian GravityNewtonian GravityExample Gravity QuestionExample Gravity QuestionExample Gravity QuestionExample Gravity QuestionHard Gravity QuestionHard Gravity QuestionComet 1P/Halley (Halley’s Comet)NASA in 1986Next apparition: July 2061Period = 75.3 YearsSemi-major Axis = 17.8 AUCourse 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 Identification-Security-Regolith Explorer–Will reach Near Earth Asteroid (NEA) Bennu in August 2018, collect a sample, and return the sample to Earth in 2023AssignmentsReading Assignments•No new readingsParallel Lectures•CC Astronomy – Episode 7: GravityMastering Astronomy•Chapter 2 Homework[Due Tuesday, 13 Sept. at 11:59 PM EDT]Metric System PrefixesMost missed question on Quiz 1Prefix Symbol NumberGiga- G 109; 1 BillionMega- M 106; 1 MillionKilo- k 103; 1 ThousandCenti- c 10-2; 1 HundredthMilli- m 10-3; 1 ThousandthMicro- µ 10-6; 1 MillionthNano- n 10-9; 1 BillionthKepler’s Laws of Planetary MotionKepler’s Laws of Planetary Motion1. Planetary orbits around the Sun are elliptical, NOT CIRCULAR, in shape (with the Sun at one focus)2. Equal Areas; Equal TimesAlternatively: 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 AUEmpirical description of planetary orbits in our Solar SystemSee Hyperphysics for additional detailsKepler’s 1st Law•Long axis is the Major Axis,•Short axis the Minor Axis•Half the Major Axis is the Semimajor Axis, a –a is used to define planetary orbitsOrbits are Elliptical•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 EllipticalGeometry of an EllipseMajor AxisSemimajor Axis, afocus focusSemiminor Axis, be = 0.7Kepler’s 1st LawElliptical orbits with the Sun at one focusVocabulary to KnowPerihelion: Closest point to SunAphelion: Farthest point from Sun[PronouncedAp – Helion]Eccentricity (e)Semi-major axis (a)PerihelionAphelionSemi-major axis is the average distance a object is from the SunKepler’s 1st LawAll bound orbits are ellipsesA circle is a special case of an ellipseKepler’s 2nd LawEqual Areas in Equal Times(Kepler’s 2nd Law is NOT Equal Distances in Equal Times)Kepler’s 2nd Law – in practiceIndicates that a planet is moving fastest at perihelion and moving slowest at aphelion.Faster(close to Sun)Slower(far from Sun)Kepler’s 3rd LawP2 (years) = a3 (AU), where P is Period and a is Semimajor AxisNOTE: 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 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 AUThe 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. a = P2/3 •Or a = cubed root ( P2 )Kepler’s 3rd Law – THIS WILL BE ON QUIZZES AND EXAMSExample 1•Kepler’s 3rd LawP2 = a3Ex. 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 yearsKepler’s 3rd LawExample 2•Kepler’s 3rd LawP2 = a3Ex. 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 yearsKepler’s 3rd LawExample 3•Kepler’s 3rd LawP2 = a3Ex. 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 AUKepler’s 3rd LawExample 4•Kepler’s 3rd LawP2 = a3Ex. 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 AUKepler’s 3rd LawPlanetary MotionKepler’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 NewtonNewtonian Mechanics (+ Gravity; + Calculus) :The mechanism behind Kepler’s LawsSir Isaac NewtonNewton published all of this in 1687 in Philosphiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), or simply, “The Principia”Newton’s Laws of Motion•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):–Velocity is the speed and direction with which an object is travelingSome required DefinitionsxyvNewton’s Laws of Motion•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
View Full Document
Unlocking...