Gravitation & Satellites

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