1. ETP_satellite_basics_02 1 The Basic Science and Mathematics of Satellites

2. “Satellite” Word History ETP_satellite_basics_02 2 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

3. Vocabulary ETP_satellite_basics_02 3 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. 3. Earth Orbiting System - The Earth Orbiting System, or EOS, is a series of satellites that orbit Earth and collect various types of data. 4. engineers - Engineers use math and science to design new tools and devices to solve practical problems. 5. geosynchronous orbit - A geosynchronous orbit is a satellite orbit at approximately 35,800 kilometers above the Equator in which objects travel at the same speed as Earth. Objects in this orbit remain stationary in reference to Earth. (geostationary) 6. gravity - Gravity is a force between objects based on their masses and the distance between the objects. The force of gravity on the moon is less than the force of gravity on Earth because the moon has only 1/6 the mass of Earth. Earth's gravity is described as 1g. 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. 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 between 320 and 800 kilometers (200-500 miles) above the Earth’s surface. 11. orbital period - Orbital period is the time it takes a satellite to complete one orbit. 10.orbit - An orbit is the path of a celestial body or an artificial satellite as it revolves around another body. 9. medium-Earth orbit – Medium-Earth orbit (MEO) is the path in which a spacecraft or satellite moves around the Earth. This path may be between 800 and 35800 kilometers (500-22,240 miles) above the Earth’s surface. 12. apogee-the point in the orbit where the satellite is farthest from the earth. 13. perigee-the point in the orbit where the satellite is nearest the earth.

4. Do the MATH-What you should know to do Calculations in this Unit ETP_satellite_basics_02 4 y=mx + b m= y2-y1 x2-x1 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

5. ETP_satellite_basics_025 Source: http://apod.nasa.gov/apod/ap090406.html

6. ETP_satellite_basics_02 6 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.

7. ETP_satellite_basics_02 7 Orbital Information - 1 Ө Source:

8. Definitions ETP_satellite_basics_02 8 Type of OrbitCharacteristics Polarθ = 90° Equatorialθ = 0° Inclined0° < θ < 90° Geocentric – a satellite that orbits earth (e.g. moon, artificial satellites) with the following characteristics

9. ETP_satellite_basics_02 9 Definitions - 2 OrbitCharacteristic Low earth orbit (LEO) Up to 1240 miles Medium earth orbit (MEO) Between 1240 miles and just below 22,240 miles GeosynchronousAt 22,240 miles High earth orbit> 22, 240 miles

10. Orbital altitudes ETP_satellite_basics_02 10 “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).”Global Positioning SystemInternational Space Station Source: http://en.wikipedia.org/wiki/Satellite

11. Lagrange points ETP_satellite_basics_02 11 “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/esaSC/SEMM17XJD1E_index_0.html

12. Planck spacecraft at L2 ETP_satellite_basics_02 12 Source: http://www.sciencedaily.com/releases/2009/06/090605112335.htm Artist conception

13. Lagrange Point Orbit ETP_satellite_basics_02 13 Source: http://www.tau.ac.il/~morris/03411203/chapter4/Lagrange_Points.htmhttp://www.tau.ac.il/~morris/03411203/chapter4/Lagrange_Points.htm http://www.esa.int/esaSC/SEMM17XJD1E_index_0.html Great animation at website to

14. ETP_satellite_basics_02 14 Why put a telescope at the Lagrange Point L2 Lagrange points are 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 L2 point, 940,000 miles (1.5 million km) from Earth. At L2, 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 L2 point, the Sun and Earth will always be lined up on the other side of Webb's sunshield.

15. ETP_satellite_basics_02 15 http://upload.wikimedia.org/wikipedia/commons/5/ 5f/Lagrangian_points_equipotential.jpg

16. Orbital information ETP_satellite_basics_02 16

17. Activity 1 ETP_satellite_basics_02 17 Activity 1: Complete activity given in “Orbital worksheet_altitude-speed.doc”

18. Technology connection – TI-83/84 (Optional) ETP_satellite_basics_02 18

19. Satellite Ground Track ETP_satellite_basics_02 19

20. Basics of ground track ETP_satellite_basics_02 20 Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 31

21. Ground track ETP_satellite_basics_02 21 Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 31

22. Ground track – 2 nd pass ETP_satellite_basics_02 22 Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 31

23. Real time tracking data ISS ETP_satellite_basics_02 23 Source: http://spaceflight.nasa.gov/realdata/tracking/index.html Snapshot taken: July, 9, 2009 At ~9:05 PDT

24. Activity 2 ETP_satellite_basics_02 24 Activity 2 Use regression equation derived earlier to compare theoretical speed to actual ISS speed.

25. Real time tracking ETP_satellite_basics_02 25 Source: http://science.nasa.gov/Realtime/Jtrack/ spacecraft.html Snapshot taken: July, 9, 2009 At ~9:55 PDT

26. Activity 3 ETP_satellite_basics_02 26 Activity 3: For the snapshots in slides 18 and 20, what is the major noticeable difference? Explain.

27. Calculating satellite elevation angle ETP_satellite_basics_02 27

28. Satellite elevation angle ETP_satellite_basics_02 28 Source: The Physics of Satellite Security, A Reference Manual, American Academy of Arts and Sciences, Section 5, p. 32

29. Elevation equation ETP_satellite_basics_02 29 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

30. Activity 4 ETP_satellite_basics_02 30 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 500km.

31. Special Web sites ETP_satellite_basics_02 31 TopicURL Planck and Hershel launch. Java appletshttp://www.esa.int/SPECIALS/Herschel/S EMK2AZVNUF_0.html NASA satellite ground trackshttp://science.nasa.gov/Realtime/Jtrack/sp acecraft.html NASA manned spacecraft ground trackshttp://spaceflight.nasa.gov/realdata/trackin g/index.html