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Topic 2.2: Low Earth Orbit

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Topic 2.2: Low Earth Orbit TOPIC 2.2: LOW EARTH ORBIT S4P-2-6 Compare the Law of Universal Gravitation with the weight (mg) of an object at various distances from the surface of the Earth and describe the gravitational field Gm as g = Earth . r 2 S4P-2-7 Outline Newton’s thought experiment regarding how an artificial satellite can be made to orbit the earth. S4P-2-8 Use the Law of Universal Gravitation and circular motion to calculate the characteristics of the motion of a satellite. Include: orbital period, speed, altitude above a planetary surface, mass of the central body, and the location of geosynchronous satellites S4P-2-9 Define microgravity as an environment in which the apparent weight of a system is smaller than its actual weight. S4P-2-10 Describe conditions under which microgravity can be produced. Examples: jumping off a diving board, roller-coaster, free fall, parabolic flight, orbiting spacecraft S4P-2-11 Outline the factors involved in the re-entry of an object into Earth’s atmosphere. Include: friction and g-forces S4P-2-12 Describe qualitatively some of the technological challenges to exploring deep space. Examples: communication, flyby and the “slingshot” effect, Hohmann Transfer orbits (least-energy orbits) Topic 2: Fields • SENIOR 4 PHYSICS GENERAL LEARNING OUTCOME SPECIFIC LEARNING OUTCOME CONNECTION S4P-2-6: Compare the Law of Students will… Universal Gravitation with the Understand the composition of the weight (mg) of an object at various universe, the interactions within it, distances from the surface of the and the impacts of humankind’s Earth and describe the gravitational continued attempts to understand and field as explore it (GLO D6) Gm g = Earth . r 2 SUGGESTIONS FOR INSTRUCTION Entry Level Knowledge = FFgG Newton’s Law of Universal Gravitation was GMm mg = earth covered in the previous topic. The strength of r 2 Earth’s gravitational field was represented in Gm Senior 3 Physics as the force per unit mass. and g = earth r 2 Notes to the Teacher The above relation is valid not only for objects on We know that the force of gravity on an object Earth’s surface, but also for objects above the near the surface of the Earth is Fg = mg. Earth’s surface. For objects above Earth’s surface, r represents the distance from an object to the The concept of the gravitational field constants is Earth’s centre and, except for objects close to often misunderstood. In general, the strength of a Earth’s surface, g is not 9.8 N/kg. The same gravitational field is the force per unit mass equation can be used for other planets and stars by exerted by one mass on another nearby “test” mass substituting the appropriate mass M. (1 kg). Near the surface of the Earth, the force exerted on 1 kg of mass is 9.8 N. As long as we Remember: g is local, G is universal. stay near the surface of the Earth, the field is constant. Consequently, the field near the surface is Student Activity called a local constant. As we move away from Is there gravity in space? A common the surface of the Earth, the force of gravity misconception is that there is no gravity in space. decreases and the field constant changes. We can Students can calculate the gravitational constant compare the Law of Universal Gravitation with the (g) at the orbit of the shuttle (500 km above the weight (mg) of an object at various distances from Earth) and at the orbit of geosynchronous satellites the surface of the Earth to determine the value of g (1000 km above the Earth). at any point in space. 18 – Topic 2.2 Low Earth Orbit SENIOR 4 PHYSICS • Topic 2: Fields SKILLS AND ATTITUDES OUTCOMES GENERAL LEARNING OUTCOME S4P-0-2c: Formulate operational CONNECTION definitions of major variables or Students will… concepts. Describe and appreciate how the S4P-0-2d: Estimate and measure natural and constructed worlds are accurately using SI units. made up of systems and how interactions take place within and among these systems (GLO E2) SUGGESTIONS FOR INSTRUCTION SUGGESTIONS FOR ASSESSMENT Pencil-and-Paper Tasks Te a c h i n g Students solve problems to calculate the value of Notes the local g for different locations (top of a mountain, equator versus the poles, on the moon, or on another planet). Students use compare and contrast frames (SYSTH) to differentiate between the universal gravitational constant G and the local constant g. Topic 2.2 Low Earth Orbit – 19 Topic 2: Fields • SENIOR 4 PHYSICS GENERAL LEARNING OUTCOME SPECIFIC LEARNING OUTCOME CONNECTION S4P-2-7: Outline Newton’s thought Students will… experiment regarding how an Identify and appreciate contributions artificial satellite can be made to made by women and men from many orbit the Earth. societies and cultural backgrounds toward increasing our understanding of the world and in bringing about technological innovations (GLO A4) SUGGESTIONS FOR INSTRUCTION Notes to the Teacher Newton’s Thought Experiment (horizontal This topic is intended to capture the student’s projectile) imagination with a current topic in physics. Earth’s Newton imagined a tall mountain above the artificial satellites, space probes, and planetary surface of the Earth and asked himself, What if a exploration are widely reported in the media. powerful cannon, mounted on top of a mountain, Challenge students to answer the question, What is fired cannonballs parallel to the ground? Newton a satellite and how do we get one in space? knew that gravity would act on the fired cannonball, pulling it to the ground, but he Newton thought of a satellite as a projectile that considered how faster and faster cannonballs could orbit the Earth (even though he couldn’t would go further and further. Eventually, he launch one). surmised that if a cannonball were fired with Prior Knowledge Activity sufficient velocity, it would fall around the entire Earth. Students complete a KWL or rotational graffiti (SYSTH) chart for projectiles and satellites. Some questions might be: • What happens as we increase the speed of a projectile that is launched horizontally? • Can a projectile orbit the Earth? • Wouldn’t a projectile fall toward the Earth? • How fast is a satellite moving? • Will satellites eventually fall to the Earth? • How high are satellites in their orbit? • Is their gravity in space? • Does friction slow down a satellite? 20 – Topic 2.2 Low Earth Orbit SENIOR 4 PHYSICS • Topic 2: Fields SKILLS AND ATTITUDES OUTCOME GENERAL LEARNING OUTCOME S4P-0-1c: Relate the historical CONNECTION development of scientific ideas Students will… and technology to the form and Describe scientific and technological function of scientific knowledge developments, past and present, and today. appreciate their impact on individuals, societies, and the environment, both locally and globally (GLO B1) SUGGESTIONS FOR INSTRUCTION SUGGESTIONS FOR ASSESSMENT Class Discussion Pencil-and-Paper Tasks Earth satellites orbit high above the atmosphere, Students solve problems to calculate the range of a such that their motion is mostly unrestricted by projectile at various speeds. forces of air resistance. Satellites are projectiles in the sense that only the force of gravity is acting on the satellite. Without a force of gravity, a satellite would continue in a straight-line path tangent to the Earth (Law of Inertia). Indeed, a satellite does fall towards the Earth; it just never falls into the Earth. Remember that the Earth is not flat, it is round and curves about 5 metres downward every 8 kilometres. Therefore, in order for a satellite to orbit the Earth, it must travel a horizontal distance of 8000 metres before falling a vertical distance of 5 metres. How far will a horizontally launched projectile fall in its first second of motion (from Topic 1.4)? 8 kilometres SUGGESTED LEARNING RESOURCES 5 metres Many Java applets can be found on the Internet, which permit the user to control the speed of a projectile and launch it into orbit. Google “projectile java” or “satellite orbits java.” Topic 2.2 Low Earth Orbit – 21 Topic 2: Fields • SENIOR 4 PHYSICS GENERAL LEARNING OUTCOME SPECIFIC LEARNING OUTCOME CONNECTION S4P-2-7: Outline Newton’s thought Students will… experiment regarding how an Identify and appreciate contributions artificial satellite can be made to made by women and men from many orbit the Earth. societies and cultural backgrounds toward increasing our understanding of the world and in bringing about technological innovations (GLO A4) SUGGESTIONS FOR INSTRUCTION 1 ∆∆∆dvtat=+ 2 yy 2 = Since vy 0 1 ∆d = ()10() 12 2 ∆d = 5 metres Therefore, when a projectile is launched with a horizontal speed of 8000 m/s, the projectile will fall toward the Earth with a trajectory that matches the curvature of the Earth. Consequently, the projectile “falls” around the Earth, always accelerating towards the Earth under the influence of gravity, yet never colliding into the Earth since the Earth curves at the same rate. Such a projectile becomes an orbiting satellite. Demonstration See demonstration in Topic 1.6. 22 – Topic 2.2 Low Earth Orbit SENIOR 4 PHYSICS • Topic 2: Fields SKILLS AND ATTITUDES OUTCOME GENERAL LEARNING OUTCOME S4P-0-1c: Relate the historical CONNECTION development of scientific ideas Students will… and technology to the form and Describe scientific and technological function of scientific knowledge developments, past and present, and today. appreciate their impact on individuals, societies, and the environment, both locally and globally (GLO B1) SUGGESTIONS FOR INSTRUCTION SUGGESTIONS FOR ASSESSMENT Te a c h i n g Notes Topic 2.2 Low Earth Orbit – 23 Topic 2: Fields • SENIOR 4 PHYSICS GENERAL LEARNING OUTCOME SPECIFIC LEARNING OUTCOME CONNECTION S4P-2-8: Use the Law of Universal Students will… Gravitation and circular motion to Recognize that scientific knowledge calculate the characteristics of the is based on evidence, models, and motion of a satellite.
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