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# 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.