Understanding Orbits Orbit Facts Morehead State University Morehead, KY Prof. Bob Twiggs RJTwiggs@gmail.com 1 Understanding Orbits • Longitude • Latitude • Altitude This aircraft is flying across the country. The ground controller radios the pilot and wants to get all of the parameters that determine it’s flight, what are they? • Horizontal velocity • Heading ( north, south, etc.) • Velocity (ascending or descending) SSE-120 2 Page 105-6 Understanding Orbits Understanding Longitude and Latitude SSE-120 3 Understanding Orbits Understanding Longitude and Latitude Greenwich, UK SSE-120 4 Understanding Orbits Understanding Longitude and Latitude Greenwich, UK SSE-120 5 Understanding Orbits Understanding Longitude and Latitude SSE-120 6 Understanding Orbits Understanding Longitude and Latitude Morehead ~= W 840, N 37.50 SSE-120 Page 105-6 7 Understanding Orbits Satellite Launch Ports SSE-120 8 Understanding Orbits Launch directions from launch ports 57.50 Vandenberg AFB ISS 51.60 Cape Kennedy 28.50 Polar Polar French Guiana Polar Near Equatorial SSE-120 9 Understanding Orbits Understanding Longitude and Latitude r = 6378 km What additional orbit launch velocity would be needed to launch to 500 km circular orbit from the equator to the west? SSE-120 What additional orbit launch velocity would be needed to launch to 500 km circular orbit from the equator to the east? 10 Understanding Orbits Understanding Longitude and Latitude r = 6378 km 50 40 30 20 10 q Q = 300 0 r’ r’ = 6378*cos (q) Now can calculate throw velocity at any latitude SSE-120 11 Understanding Orbits What must be the velocity of the launch vehicle to put a spacecraft into a given orbit? Orbital Velocity - v Altitude - h Altitude - h SSE-120 Page 308 12 Understanding Orbits SSE-120 13 Page 273 Understanding Orbits What determines the velocity of spacecraft in a circular orbit? Altitude: given Velocity of spacecraft Fc v Vcir = 631.3481 r-1/2 km/sec r Orbit - is from center of the earth – 6378 + alt km Vesc = 892.8611 r-1/2 km/sec Fg Orbit Period Circumference = 2pr Time to orbit = distance/velocity Orbit Period = Time to orbit (minutes) 14 SSE-120 Page 181 Understanding Orbits Understanding Longitude and Latitude Orbit Calculations Eclipse Time for Noon-Midnight Orbit Orbital Altitude Velocity km 300 350 400 450 500 550 600 650 700 750 800 SSE-120 km/sec 7.726 7.697 7.669 7.641 7.613 7.585 7.558 7.531 7.504 7.478 7.452 Circum Period Eclipse Time km Min Min 41958 42272 42586 42900 43214 43529 43843 44157 44471 44785 45099 90.51 91.53 92.55 93.58 94.61 95.64 96.68 97.72 98.77 99.82 100.87 36.59 36.33 36.11 35.92 35.75 35.61 35.49 35.38 35.28 35.20 35.13 Vcir = 631.3481(r+h)-1/2 km/sec % Eclipse 40.4% 39.7% 39.0% 38.4% 37.8% 37.2% 36.7% 36.2% 35.7% 35.3% 34.8% r = 6378 km h = altitude Circumference = 2pi(r+h) Period = (Circum/velocity)/60 Eclipse time = (2*(90-ACOS(r/(r+h))*(180/3.1415))/360)*Period 15 Understanding Orbits Eccentricity e = 2c/2a Relationship between conic sections Conic Sections Eccentricity Circle e=0 Ellipse 0<e<1 Parabola e =1 Hyperbola e >1 SSE-120 16 Page 157 Understanding Orbits Spacecraft orbit definition • Orbital size, use the semimajor axis, a • Orbital shape, is defined by eccentricity, e • Orientation of the plane in space, uses inclination, i right ascension of the ascending node, Ω X X• Orientation of the orbit within the plane is defined by the argument of perigee, v X• Spacecraft’s location in the orbit is represented by true anomaly, u SSE-120 17 Page 155-156 Understanding Orbits SSE-120 18 Page 155-156 Understanding Orbits X X X 19 Understanding Orbits Classic Orbital Elements (COEs) Checklist • Orbit’s size • Orbit’s shape • Orbit’s orientation Orbit plane in space Orbit within the plane • Spacecraft’s location SSE-120 20 Page 159 Understanding Orbits SSE-120 21 Page 164 Understanding Orbits SSE-120 22 Page 273 Understanding Orbits SSE-120 23 Page 179 Understanding Orbits SSE-120 24 Page 180 Understanding Orbits SSE-120 Page 184 25 Understanding Orbits SSE-120 Page 184 26 Understanding Orbits SSE-120 Page 203 27 Understanding Orbits SSE-120 Page 315 28 Understanding Orbits For a zenith pass. A d B 1. What is the distance d in km? 2. What is the time it takes the spacecraft to go from A to B? r h SSE-120 29 Understanding Orbits What is maximum latitude that a geostationary spacecraft can be seen? SSE-120 30 Understanding Orbits Assessment Time SSE-120 31