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Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 191500 B.C.: Egyptians and Babylonians350 B.C.: Greek ThoughtsSlide 22Slide 23Slide 24Orbit History :Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Types of Orbits:Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Types of Orbits (cont.)Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74Slide 75Slide 76Slide 77Slide 78Slide 79Slide 80Slide 81Slide 82Slide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Announcements:Colorado Space Grant ConsortiumColorado Space Grant ConsortiumGateway To SpaceASEN / ASTR 2500Class #22Gateway To SpaceASEN / ASTR 2500Class #22Announcements…- 16 days to launch- DD C is due one week from today – comments today- No New homework- Not sure what happened to our guest speaker- I doubt we will be able to rescheduleAnnouncements:Announcements:Announcements:Announcements:Announcements:Orbits:A Brief Historical LookEarth, the Moon, Mars, and the Stars BeyondA Brief Discussion on Mission DesignUniversal Gravitation, Applied:Moon VideoUniversal Gravitation, Applied:• When in space why do you float? i.e. WeightlessnessrMGVrMmGrmV22Universal Gravitation, Applied:• How does this apply to orbits?Questions:• How fast can you throw a snowball? - A baseball? - A shot put?- A Subway sandwich out a moving car?• Could you throw any of these in to an orbit? - How fast would it have to be going?Questions:• Let’s figure it out…v GMRv is velocityG is Universal Gravitational ConstantM is mass of planet or satelliteR is radius of planet of satelliteAtmosphere:• How about throwing something into orbit on the moon?golf ballAtmosphere:• Let’s figure it out…v GMRv is velocityG is Universal Gravitational ConstantM is mass of planet or satelliteR is radius of planet of satelliteG 6.67x 1011m3kg s2  MEarth5.974x 1024kg REarth6367000 mMMoon7.350x 1022kg RMoon1738000 mOrbits:A Brief Historical LookArthur C. ClarkeDiscovered This OrbitAncient Orbit History:“ORBIT” from Latin word “orbita” orbitus = circular; orbis = orb• 1800 B.C. Stonehenge - Study of the vernal equinox1500 B.C.: Egyptians and Babylonians •Written evidence of stellar observations•Solar Calendar of 365 days•Time divided into 60 even unitsAristotle•Said earth is center of the universe•Dominated scientific thought for 1800 years Ptolemy•Geocentric (Earth centered) theory 350 B.C.: Greek ThoughtsStart of the Heliocentric Model:350 B.CAristarchus of Samos•Said Geocentric model was B.S•Heliocentric•Figured out distance to sun and moon•Why didn’t objects fly off the spinning Earth?•Why didn’t the motion of the Earth around the sun leave behind the birds flying in the air?Start of the Heliocentric Model:1543 A.D. Nicholas Copernicus•Said Sun-centered rotations•Measurements crude but thinking shifts•Didn’t release findings until the end of his lifeOrbit History :• 1580 A.D. Tycho Brahe•Accurate measurements of planets (Mars) as a function of time•Even though telescope had not been inventedOrbit History :• 1610 A.D. Galileo Galilei•Good friends with Copernicus•Observations with TELESCOPE reinforced•Discovered Venus has phasesOrbit History:• 1600 A.D. Johannes Kepler•Used Tycho’s careful Mars observations to smash Aristotle theories•Presented 3 laws of planetary motion•Basis of understanding of spacecraft motion•However, “Why was not understood”•Calculus?Orbit History:Kepler’s 3 Laws of Planetary Motion:1. All planets move in elliptical orbits, sun at one focusOrbit History:Kepler’s 3 Laws of Planetary Motion:1. All planets move in elliptical orbits, sun at one focusOrbit History:Kepler’s 3 Laws of Planetary Motion:2. A line joining any planet to the sun, sweeps out equal areas in equal timesOrbit History:Kepler’s 3 Laws of Planetary Motion:2. A line joining any planet to the sun, sweeps out equal areas in equal timesOrbit History:Kepler’s 3 Laws of Planetary Motion:2. A line joining any planet to the sun, sweeps out equal areas in equal timesOrbit History:Kepler’s 3 Laws of Planetary Motion:3. The square of the period of any planet about the sun is proportional to the cube of the of the planet’s mean distance from the sun.If you can observe the period of rotation, you can determine the distancePlanet P (yr) a (AU) T2R3Mercury0.24 0.39 0.06 0.06Venus 0.62 0.72 0.39 0.37Earth 1.00 1.00 1.00 1.00Mars 1.88 1.52 3.53 3.51Jupiter 11.9 5.20 142 141Saturn 29.5 9.54 870 868T2 = R3Orbit History:• 1665 A.D. Isaac Newton•At 23, plague while at Cambridge•Went to be one with nature•He studied gravity•Discovered “Newton’s Laws of Motion”•1666, he understood planetary motion•Did zip for 20 years until Edmund HalleyNewton’s Laws:1st Law.....Body at rest stays at rest, a body in motion stay in motion2nd Law....F = m * a3rd Law...For every action, there is an equal and opposite reactionNewton’s Laws: Newton Continued... • 1687, Principia Published• Law of Universal Gravitation (Attraction)221rGmmFNewton’s Laws: Newton Continued... • 1687, Principia Published• Law of Universal Gravitation (Attraction)221rGmmFrVmF22maUniversal Gravitation, Applied:• When in space why do you float? i.e. WeightlessnessrMGVrMmGrmV22Types of Orbits:Orbits are conic sections:• Circle• Ellipse• Parabola• HyperbolaFrom Kepler’s Law, the central body is at a focus of the conic sectionaMGrMGV 2Kepler:Kepler’s Laws...Orbits described by conic sectionsVelocity of an orbit described by following equationFor a circle (a=r):For a ellipse (a>0):For a parabola (a=):v2 raGMv rv2 rav2 rQuestions:• Let’s figure it out…v GMRv is velocityG is Universal Gravitational ConstantM is mass of planet or satelliteR is radius of planet of satelliteEarth, the Moon, Mars, and the Stars BeyondA Brief Discussion on Mission DesignOrbit Introduction:What is an orbit?- The path of a satellite around the Earth (or any central body)What shape is it?- Orbits are


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CU-Boulder ASTR 2500 - Orbits Design

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