Gravitation & Satellites


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Gravitation & Satellites

  1. 1. Gravitation & Satellites Section 1: Topic 3 <ul><li>Brief review of scientists up to Newton </li></ul><ul><li>Newtons’ Law of gravitation </li></ul>
  2. 2. The Motion of the Planets Copernicus <ul><li>The Earth is not the centre of the universe. The planets revolve around the sun and not the earth. </li></ul>
  3. 3. Tycho Brahe <ul><li>Took very careful measurements of the motion of the planets. </li></ul>
  4. 4. Johannes Kepler <ul><li>Used Tycho’s data </li></ul><ul><li>The Music of the Spheres </li></ul>
  5. 5. Johannes Kepler The 3 Laws of Planetary Motion <ul><li>Planets move in elliptical orbits with the sun at one of the foci. </li></ul><ul><li>The line joining the sun and the planet sweeps out equal areas in equal times. </li></ul><ul><li>The cube of the distance of the planet from the sun is proportional to the square of the period. r 3  T 2 </li></ul>
  6. 6. Galileo <ul><li>The first real experimenter, turned the telescope to the sky. He found that there were moons orbiting Jupiter – evidence that the Earth was not the centre of all. </li></ul><ul><li>Persecuted for his beliefs and only very recently has been given a pardon from the pope! </li></ul>
  7. 7. Isaac Newton
  8. 8. Newton’s Law of Gravitation <ul><li>Gravitation is the force of attraction that acts between all objects because they have mass. </li></ul><ul><ul><li>This force holds the universe together. </li></ul></ul><ul><li>Aristotle (384 - 322 BC) said that a heavier object should fall faster than a lighter one. </li></ul><ul><li>Newton was able to describe the gravitational forces between the earth and the moon. </li></ul>
  9. 9. Newton’s Law of Gravitation <ul><li>He determined that a  1/d 2 . </li></ul><ul><ul><li>d = distance from the centres of the objects and not the surfaces. </li></ul></ul><ul><ul><li>This is true for spherical objects. </li></ul></ul><ul><li>Newton’s 2 nd law also states that F  a . </li></ul><ul><ul><li>This means that F  1/d 2 . </li></ul></ul>
  10. 10. Newton’s Law of Gravitation <ul><li>His second law also says F  m. </li></ul><ul><li>As two masses are involved, Newton suggested that the force should be proportional to both masses. </li></ul><ul><ul><li>This is also consistent with his third law. If one mass applies force on a second object, the second mass should also apply an equal but opposite force on the first. </li></ul></ul>
  11. 11. Newton’s Law of Gravitation <ul><li>Combining these properties, we arrive at Newton’s law of universal gravitation. </li></ul><ul><li>Turning this into an equality: </li></ul>
  12. 12. Newton’s Law of Gravitation <ul><li>Definition: </li></ul><ul><li>Between any two objects there is a gravitational attraction F that is proportional to the mass m of each object and inversely proportional to the square of the distance d between their centres. </li></ul>
  13. 13. Newton’s Law of Gravitation <ul><li>Near the Earth’s surface </li></ul><ul><li>B etween mass m and m e </li></ul><ul><li>m e = mass of earth </li></ul><ul><li>A t r e </li></ul><ul><ul><li>r e = radius of earth </li></ul></ul><ul><ul><li>r e = 6380 km </li></ul></ul>
  14. 14. Gravitational Field Strength g <ul><li>The gravitational field strength g is the gravitational force acting per unit mass – ie the weight of 1 kg. </li></ul><ul><li>This varies depending on the location. </li></ul><ul><li>It is also numerically equal to the acceleration due to gravity at that point. </li></ul>
  15. 15. Newton’s Law of Gravitation <ul><li>We can find the value of g at any height above the earth’s surface. </li></ul>
  16. 16. Newton’s Law of Gravitation <ul><li>The acceleration due to gravity, g : </li></ul><ul><ul><li>A t sea level. </li></ul></ul><ul><ul><ul><li>g = 9.8 m s -2. </li></ul></ul></ul><ul><li>O n the top of Mt Everest. </li></ul><ul><ul><li>A t 8848 m. </li></ul></ul><ul><ul><ul><li>g = 9.77 m s -2 . </li></ul></ul></ul><ul><li>Note: You must change r e to r e + r above the surface of the Earth. </li></ul>
  17. 17. Satellites in Circular Orbits <ul><li>Objects will continue to move at a constant velocity unless acted upon by an unbalanced force. </li></ul><ul><ul><li>Newton’s first law. </li></ul></ul><ul><li>As satellites move in a circular path, their direction (and hence velocity) is continually changing. </li></ul>
  18. 18. Satellites in Circular Orbits <ul><li>This gives rise to centripetal acceleration. </li></ul><ul><li>The cause of this centripetal acceleration is gravity. </li></ul>
  19. 19. Satellites in Circular Orbits <ul><li>The acceleration due to gravity at the surface of the Earth is approximately 10 ms -2 . This means that in one second an object falls approximately 5.0 m. </li></ul><ul><li>The curvature of the surface of the Earth is such that the Earth curves down 5 m in 8 km. </li></ul><ul><li>Thus, if an object moves at 8 kms -1 , then it will remain at the same height above the surface of the Earth. </li></ul>
  20. 20. Centripetal Acceleration and Friction <ul><li>If there was no gravitational force: </li></ul><ul><ul><li>The satellite was fly off in the direction of the applied force. </li></ul></ul>
  21. 21. Satellites in Circular Orbits <ul><li>If v on launch is too high : </li></ul><ul><ul><li>satellite will escape from Earth’s gravitational attraction. </li></ul></ul>
  22. 22. Satellites in Circular Orbits <ul><li>If v is too low : </li></ul><ul><ul><li>satellite will fall back to Earth. </li></ul></ul><ul><ul><li>The launch speed is less than 8.0 x 10 3 m s -1 </li></ul></ul>
  23. 23. Satellites in Circular Orbits <ul><li>If the launch speed is exactly: </li></ul><ul><ul><li>8.0 x 10 3 m s -1 the orbit is, </li></ul></ul><ul><ul><li>Circular. </li></ul></ul>
  24. 24. Satellites in Circular Orbits <ul><li>If the launch speed is greater than: </li></ul><ul><ul><li>8.0 x 10 3 ms -1 the orbit is, </li></ul></ul><ul><ul><li>Elliptical. </li></ul></ul>
  25. 25. Satellites in Circular Orbits <ul><li>Galileo's Thought Experiment </li></ul><ul><li>Can you fire a cannon and shoot yourself in the back of the head? </li></ul><ul><li>Shooting for Mars </li></ul>
  26. 26. Satellites in Circular Orbits <ul><li>It is important to keep v at the correct value to keep the satellite in orbit at a particular value of r. </li></ul><ul><li>How is this determined? </li></ul>
  27. 27. Satellites in Circular Orbits <ul><li>A s it is a circular orbit, </li></ul>
  28. 28. Satellites in Circular Orbits <ul><li>This will give the orbital velocity for a satellite to remain in an orbit of r from the centre of the Earth (ie r e + r) irrespective of the mass of the satellite. </li></ul><ul><li>You are expected to be able to derive this equation. </li></ul>
  29. 29. Satellites in Circular Orbits <ul><li>Speed is also given by the equation: </li></ul><ul><li>In one revolution, </li></ul><ul><li>Orbiting satellite moves a distance equivalent to the circumference of the circular path it is following . </li></ul><ul><ul><li>2  r </li></ul></ul><ul><li>The time it takes for this revolution : </li></ul><ul><ul><li>Period ( T ). </li></ul></ul><ul><li>Hence; </li></ul>
  30. 30. Weightlessness <ul><li>People in satellites experience weightlessness. </li></ul><ul><li>F g acts towards Earth . </li></ul><ul><li>The satellite ‘falls’ towards Earth with the only force acting being gravity. </li></ul>
  31. 31. Weightlessness <ul><li>The satellite must be ‘falling’ at F g . </li></ul><ul><ul><li>resultant force = 0. </li></ul></ul><ul><ul><li>weightlessness. </li></ul></ul><ul><li>This also occurs when in an elevator or a diving plane. </li></ul>
  32. 32. Weightlessness <ul><li>True weightlessness occurs when r is very large. </li></ul><ul><ul><li>I n deep space. </li></ul></ul> F is very small.
  33. 33. Artificial Earth Satellites <ul><li>Once a satellite has been launched, no further propulsion is necessary. </li></ul><ul><li>If the orbit is circular : </li></ul><ul><ul><li>Force caus ing the centripetal acceleration must be towards the centre of the circle. </li></ul></ul><ul><ul><li>The force is gravity. </li></ul></ul>
  34. 34. Artificial Earth Satellites <ul><li>Gravity acts toward the centre of the earth . </li></ul><ul><li>The centre of the orbit must coincide with the centre of the Earth. </li></ul>
  35. 35. Artificial Earth Satellites <ul><li>As long as this requirement is fulfilled. </li></ul><ul><li>Satellites s can have any radius and orientation. </li></ul><ul><li>Radius is determined only by the velocity of the satellite. </li></ul>
  36. 36. Artificial Earth Satellites <ul><li>Some orbits that are preferred over others . </li></ul><ul><li>Meteorological and communication purposes. </li></ul><ul><li>Polar orbit is useful as well. </li></ul>
  37. 37. Satellites
  38. 38. Geostationary Orbits <ul><li>U sed in communication and monitoring weather patterns of a specific region. </li></ul><ul><li>Requires a satellite to orbit the Earth : </li></ul><ul><ul><li>I n the same direction as the earth is rotating. </li></ul></ul><ul><ul><li>Speed such that it remains fixed over one point on the Earth’s surface. </li></ul></ul><ul><li>They are often called GEO (geostationary earth orbit) satellites. </li></ul>
  39. 40. Geostationary Orbits <ul><li>They must satisfy the following conditions: </li></ul><ul><li> They must be equatorial. </li></ul><ul><ul><li>Only orbit in which the satellite move s in plane perpendicular to earth’s axis of rotation. </li></ul></ul><ul><li> The orbit must be circular. </li></ul><ul><ul><li>Must have a constant speed to match the earth’s rotation. </li></ul></ul>
  40. 41. Geostationary Orbits <ul><li> The radius must match a period of 23 hrs 56 min. </li></ul><ul><ul><li>The radius, speed and centripetal acceleration can be calculated from the period. </li></ul></ul><ul><li> The direction of orbit must be the same as the earth’s rotation . </li></ul><ul><ul><li>west to east. </li></ul></ul>
  41. 42. Geostationary Orbits <ul><li>Australia is covered by a Japanese weather satellite GMS at 140 o E. </li></ul><ul><ul><li>This is north of New Guinea. </li></ul></ul><ul><li>There are presently only 5 orbiting the Earth. </li></ul>
  42. 43. Geostationary Orbits
  43. 44. Low Altitude Satellites <ul><li>200 - 3000 km above earth’s surface. </li></ul><ul><li>U sed for meteorology and surveillance. </li></ul><ul><li>S maller radius means smaller period. </li></ul>
  44. 45. Low Altitude Satellites Calculate the period and speed of a satellite orbiting at 200 km and another satellite at 3000 km.
  45. 46. Low Altitude Satellites <ul><li>E specially useful when it passes over, or nearly over the poles. </li></ul><ul><li>C alled : </li></ul><ul><ul><li>Sun Synchronous or. </li></ul></ul><ul><ul><li>Heliosynchronous . </li></ul></ul>
  46. 47. Low Altitude Satellites <ul><li>The orbit is chosen so that : </li></ul><ul><ul><li>I t passes over the same location twice each day at 12 hour intervals. </li></ul></ul><ul><ul><ul><li>6am and 6pm. </li></ul></ul></ul><ul><ul><li>O nce in each direction. </li></ul></ul><ul><ul><ul><li>A s seen from the ground. </li></ul></ul></ul><ul><li>Geostationary & Polar Orbits </li></ul>
  47. 48. Low Altitude Satellites <ul><li>Normal orbit has a period of 100 minutes. </li></ul><ul><li>A s the earth rotates below, it moves a distance equal to its field of view. </li></ul><ul><li>Observes the whole earth a piece at a time twice a day. </li></ul>
  48. 49. Low Altitude Satellites <ul><li>Satellites that are used for the transfer of information : </li></ul><ul><ul><li>Found in orbits ranging from 100 - 3000 kms. </li></ul></ul><ul><li>Below 100 km, the air friction is too great. </li></ul><ul><li>Above 3000km they are referred to as MEO (medium earth orbits) </li></ul>
  49. 50. International Space Station <ul><li>Orbits at 345km </li></ul><ul><li>Is beneath the first of the Van Allen Belts because it has humans on board. </li></ul>