The Basic Science and Mathematics of Satellites ETPsatellitebasics02
The Basic Science and Mathematics of Satellites ETP_satellite_basics_02 1
“Satellite” Word History A satellite is something small or less powerful that orbits around something bigger. It often describes a body in space, such as an artificial satellite that orbits the Earth and beams down signals that power devices like cell phones. The word satellite was first used to describe a follower of someone in a superior position. The word's meaning later broadened to describe anything small that's dependent on something larger. The small satellite circles around the more powerful force, like a moon orbiting a planet. Satellite can describe a small country — a satellite country — controlled by a larger one, or a large organization that has a small office — a satellite office — in another location. https: //www. vocabulary. com/dictionary/satellite ETP_satellite_basics_02 2
Vocabulary 1. artificial satellite - An artificial satellite is a manufactured object that continuously orbits Earth or some other body in space. 2. attitude - Attitude describes the position of a spacecraft relative to the direction of motion. 7. inclination - Inclination is the angle between a reference plane and another plane or axis of direction. For an artificial satellite, the reference plane is the Equator. The inclination of a satellite's orbit is the angle that the orbit crosses the Equator. If a satellite has a 0° inclination then it would be orbiting over the Equator. If a satellite has a 90° inclination, then its orbit is perpendicular to the Equator and it would pass over the poles. 3. Earth Orbiting System - The Earth Orbiting System, 8. low-Earth orbit – Low-Earth orbit (LEO) is the path in which a spacecraft or satellite moves around the Earth. This path may be or EOS, is a series of satellites that orbit Earth and between 320 and 800 kilometers (200 -500 miles) above the collect various types of data. Earth’s surface. 4. engineers - Engineers use math and science to design 9. medium-Earth orbit – Medium-Earth orbit (MEO) is the path new tools and devices to solve practical problems. in which a spacecraft or satellite moves around the Earth. This 5. geosynchronous orbit - A geosynchronous orbit is path may be between 800 and 35800 kilometers (500 -22, 240 miles) above the Earth’s surface. a satellite orbit at approximately 35, 800 kilometers above the Equator in which objects travel at the same 10. orbit - An orbit is the path of a celestial body or an speed as Earth. Objects in this orbit remain stationary artificial satellite as it revolves around another body. in reference to Earth. (geostationary) 11. orbital period - Orbital period is the time it takes a satellite to complete one orbit. 6. gravity - Gravity is a force between objects based on their masses and the distance between the objects. The 12. apogee-the point in the orbit where the satellite is farthest from the earth. force of gravity on the moon is less than the force of 13. perigee-the point in the orbit where the satellite is nearest gravity on Earth because the moon has only 1/6 the earth. mass of Earth's gravity is described as 1 g. ETP_satellite_basics_02 3
Do the MATH-What you should know to do Calculations in this Unit y=mx + b m= y 2 -y 1 x 2 -x 1 Y=ax^2+bx+c SOHCAHTOA y=sin x y=cos x y=tan x y=arcsin x y=arccos x y=arctan x y=e^x y=ln x X^2 + y^2=r^2 *substitution property of equality *composites of functions ETP_satellite_basics_02 4
Source: http: //apod. nasa. gov/apod/ap 090406. html ETP_satellite_basics_02 5
Objectives The student will be able to: • Describe orbital inclination • Define satellite orbit orientation • Describe and sketch satellite ground tracks • Summarize orbital altitudes • Describe Lagrange points and their usefulness in space telescopes. ETP_satellite_basics_02 6
Orbital Information - 1 Ө Source: ETP_satellite_basics_02 7
Definitions Geocentric – a satellite that orbits earth (e. g. moon, artificial satellites) with the following characteristics Type of Orbit Characteristics Polar θ = 90° Equatorial θ = 0° Inclined 0° < θ < 90° ETP_satellite_basics_02 8
Definitions - 2 Orbit Characteristic Low earth orbit (LEO) Up to 1240 miles Medium earth orbit (MEO) Between 1240 miles and just below 22, 240 miles Geosynchronous At 22, 240 miles High earth orbit > 22, 240 miles ETP_satellite_basics_02 9
Orbital altitudes “Various earth orbits to scale; cyan represents low earth orbit, yellow represents medium earth orbit, the black dashed line represents geosynchronous orbit, the green dash-dot line the orbit of Global Positioning System (GPS) satellites, and the red dotted line the orbit of the International Space Station (ISS). ” Source: http: //en. wikipedia. org/wiki/Satellite ETP_satellite_basics_02 10
Lagrange points “Lagrange points are locations in space where gravitational forces and the orbital motion of a body balance each other. They were discovered by French mathematician Louis Lagrange in 1772 in his gravitational studies of the ‘Three body problem’: how a third, small body would orbit around two orbiting large ones. There are five Lagrangian points in the Sun -Earth system and such points also exist in the Earth-Moon system. ” Source: European Space Agency, http: //www. esa. int/esa. SC/SEMM 17 XJD 1 E_index_0. html ETP_satellite_basics_02 11
Planck spacecraft at L 2 Artist conception Source: http: //www. sciencedaily. com/releases/2009/06/090605112335. htm ETP_satellite_basics_02 12
Lagrange Point Orbit Source: http: //www. tau. ac. il/~morris/03411203/chapter 4/Lagrange_Points. htm Great animation at website to http: //www. esa. int/esa. SC/SEMM 17 XJD 1 E_index_0. html ETP_satellite_basics_02 13
Why put a telescope at the Lagrange Point L 2 Lagrange points areas in space where the gravity and orbital motions of nearby bodies come into balance. There are five Lagrange points around the Earth; the Webb telescope will be located in the L 2 point, 940, 000 miles (1. 5 million km) from Earth. At L 2, the Earth’s gravity will pull Webb along, so it can “keep up” with Earth in its path around the Sun. This is important because Webb has to be kept in a very specific position that allows its sunshield to protect it from light from the Sun, Earth and Moon at the same time. At the L 2 point, the Sun and Earth will always be lined up on the other side of Webb's sunshield. ETP_satellite_basics_02 14
http: //upload. wikimedia. org/wikipedia/commons/5/ 5 f/Lagrangian_points_equipotential. jpg ETP_satellite_basics_02 15
Orbital information ETP_satellite_basics_02 16
Activity 1: Complete activity given in “Orbital worksheet_altitude-speed. doc” ETP_satellite_basics_02 17
Technology connection – TI-83/84 (Optional) ETP_satellite_basics_02 18
Satellite Ground Track ETP_satellite_basics_02 19
Basics of ground track Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 31 ETP_satellite_basics_02 20
Ground track Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 31 ETP_satellite_basics_02 21
Ground track – 2 nd pass Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 31 ETP_satellite_basics_02 22
Real time tracking data ISS Snapshot taken: July, 9, 2009 At ~9: 05 PDT Source: http: //spaceflight. nasa. gov/realdata/tracking/index. html ETP_satellite_basics_02 23
Activity 2 Use regression equation derived earlier to compare theoretical speed to actual ISS speed. ETP_satellite_basics_02 24
Real time tracking Source: http: //science. nasa. gov/Realtime/Jtrack/ spacecraft. html Snapshot taken: July, 9, 2009 At ~9: 55 PDT ETP_satellite_basics_02 25
Activity 3: For the snapshots in slides 18 and 20, what is the major noticeable difference? Explain. ETP_satellite_basics_02 26
Calculating satellite elevation angle ETP_satellite_basics_02 27
Satellite elevation angle Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 32 ETP_satellite_basics_02 28
Elevation equation Source: Gerard Maral and Michel Bousquet, Satellite Communication Systems, 4 th ed. (West Sussex, England: Wiley, 2002), 44 -45. As reported in The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 47 ETP_satellite_basics_02 29
Activity 4: 1) What is the order of operations in the equation for the maximum elevation angle? Explain. 2) Find the maximum elevation angle for an observer under the specified conditions at latitude 45° and satellite altitude of 500 km. ETP_satellite_basics_02 30
Special Web sites Topic URL Planck and Hershel launch. Java applets http: //www. esa. int/SPECIALS/Herschel/S EMK 2 AZVNUF_0. html NASA satellite ground tracks http: //science. nasa. gov/Realtime/Jtrack/sp acecraft. html NASA manned spacecraft ground tracks http: //spaceflight. nasa. gov/realdata/trackin g/index. html ETP_satellite_basics_02 31
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