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Escape Speed
Earth Satellites
Geostationary And Polar Satellites
Weightlessness
ESCAPE SPEED
 Escape speed on earth (or any other planet) is defined as the
  minimum speed with which the body has to be projected
  vertically upwards from the surface of the earth(or any other
  planet) so that it just crosses the gravitational field of
  earth(or of that planet) and never returns on its own.
 For a spherically-symmetric body, escape velocity is
  calculated by the formula :



 Where G is the universal gravitational constant
 G=6.67×10−11 m3 kg−1 s−2 . M the mass of the planet, star or
 other body, and r the distance from the center of gravity
Important points :
         The value of escape speed does not
          depend on the mass (m) of the body
          and its angle of projection from the
          surface of earth or a planet.
         It depends on the radius of the planet
          from the surface of which the body is
          projected.
         If a body is projected from a planet
          with a speed v which is smaller than
          the escape speed ve (i.e., v < ve), the
          body will reach a certain height and
          may either move in an orbit around
          the planet or may fall back to the
          planet .
         The escape velocity from the surface
          of the Earth is about 11.2 km/s or
          25,055 miles per hour.
Problems With Equation Near Earth
 The calculated escape velocity from gravity near the Earth's surface of
  11.2 km/s or 26,000 miles per hour is too high to be practical. Also, the
  effect of the Sun is not taken into account.
Assumes extremely high acceleration :
 A major problem with the escape velocity from gravity value is that the
  velocity is calculated at or near the Earth's surface. An infinite
  acceleration would be required to project an object at 11.2 km/s from the
  Earth's surface. Also, it would be very difficult—if not impossible—for a
  rocket to attain a velocity of 11.2 km/s relatively close to the Earth's
  surface. The Saturn rocket that was used to go to the Moon did not reach
  that speed until it was over 193 km (180 miles) from the Earth's surface.
Rocket would burn up
 Also, in order to reach the escape velocity at lower altitudes, the rocket
  would be traveling at hypersonic speed, which would be so far above the
  speed of sound that it could cause the burn-up of a rocket exterior
  before it left the Earth's atmosphere. Realistically, a rocket would have to
  build up its speed until it reached the extreme upper atmosphere, where
  air resistance is negligible at high speeds.
Earth Satellites
 Earth satellites are the objects which revolve around the earth.
 Their orbits around the earth are circular or elliptic.
 Moon is the only natural satellite of the earth with a near
  circular orbit with a time period of approximately 27.3 days
  which is roughly equal to the rotational period of the moon
  about its own axis.
 With the advancements of science and technology, since 1957,
  many man made satellites have been put in different orbits
  around the earth.
 Russians were the first to launch the artificial satellite Sputnik
  I, on Oct 4, 1957. India launched its first artificial
  satellite,Aryabhatta in 1957. Since the Indi has put many
  satellites in various orbits around the earth e.g., Bhaskara,
  Rohini, Apple, IA, IB, Insat, IRS etc.
Orbital Speed :
 Orbital speed of a satellite is the minimum speed required
  to put the satellite into a given orbit around earth.
 Expression - v = sqrt(Re.g) Where, g=9.8 m/s & Re = radius
                  o

  of earth. The value for orbital velocity was found to be 7.9
  km/s.


 It is independent   of mass of the satellite.
 Decrease with an increase in the radius in the radius in the
  height of satellite.
 Depends upon the mass and radius of the earth/planet around
  which the revolution of satellite is talking place.
 The direction of orbital speed of a satellite at an instant is
  along the tangent to the orbital path of satellite at that instant.
Time Period And Height Of A Satellite
 Time period of a satellite is the time taken by satellite to
  complete one revolution around the earth and is denoted by
  T.

 By substituting the values we get, T = 84.6 minutes.
 It means that a satellite orbiting close to the surface of the
  earth has a time period of revolution about 84.6 minutes.
 The height of a satellite is given by the exp.



 By substituting the values, h=36000m
Geostationary And Polar Satellites:
                A satellite whose period of
                   revolution is 24 hours, is a
                   geostationary satellite.
                  It always appears to be at a fixed
                   point in space, because the period of
                   rotation of the Earth about its own
                   axis is also equal to 24 hours.
                  Knowing T = 24 hours, g = 9.8 ms-1,
                   the height of a geostationary satellite
                   is calculated to be 36000km.Its
                   orbital velocity is 3.1 km/s.
                  Its plane of orbit is the equatorial
                   plane.
                  It revolves from west to east which is
                   similar to the Earth's movement.
                  It is very useful in
                   telecommunication.
 Polar orbiting weather satellites
  circle the Earth at a typical altitude
  of 850 km (530 miles) in a north to
  south (or vice versa) path, passing
  over the poles in their continuous
  flight. Polar satellites are in sun-
  synchronous orbits, which means
  they are able to observe any place on
  Earth and will view every location
  twice each day with the same general
  lighting conditions due to the near-
  constant local solar time. Polar
  orbiting weather satellites offer a
  much better resolution than their
  geostationary counterparts due their
  closeness to the Earth. Satellites in
  polar orbits are used for
  environmental and earth resources'
  survey
Different types of satellites :
Astronomy satellites - Hubble Space Telescope
Atmospheric Studies satellites - Polar
Communications satellites - Anik E
Navigation satellites - Navstar
Reconaissance satellites - Kennan, Big Bird,
Lacrosse
Remote Sensing satellites - Radarsat
Search and Rescue satellites - Cospas-Sarsat
Space Exploration satellites - Galileo
Weather satellites - Meteosat
Weightlessness
 When the astronaut in the spaceship is orbiting the
 Earth, then both, the astronaut and the spaceship are
 in a state of free fall towards the Earth. During a free
 fall, both travel downwards with the same
 acceleration, equal to the acceleration due to gravity.
 As a result, the astronaut does not exert any force on
 the sides or floor of the spaceship, and the sides and
 floor of the spaceship do not push the astronaut up.
 The astronaut therefore experiences weightlessness
 while orbiting around the Earth in a spaceship.
Gravitation
Gravitation

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Gravitation

  • 1.
  • 2. Escape Speed Earth Satellites Geostationary And Polar Satellites Weightlessness
  • 3. ESCAPE SPEED  Escape speed on earth (or any other planet) is defined as the minimum speed with which the body has to be projected vertically upwards from the surface of the earth(or any other planet) so that it just crosses the gravitational field of earth(or of that planet) and never returns on its own.  For a spherically-symmetric body, escape velocity is calculated by the formula :  Where G is the universal gravitational constant G=6.67×10−11 m3 kg−1 s−2 . M the mass of the planet, star or other body, and r the distance from the center of gravity
  • 4. Important points :  The value of escape speed does not depend on the mass (m) of the body and its angle of projection from the surface of earth or a planet.  It depends on the radius of the planet from the surface of which the body is projected.  If a body is projected from a planet with a speed v which is smaller than the escape speed ve (i.e., v < ve), the body will reach a certain height and may either move in an orbit around the planet or may fall back to the planet .  The escape velocity from the surface of the Earth is about 11.2 km/s or 25,055 miles per hour.
  • 5. Problems With Equation Near Earth  The calculated escape velocity from gravity near the Earth's surface of 11.2 km/s or 26,000 miles per hour is too high to be practical. Also, the effect of the Sun is not taken into account. Assumes extremely high acceleration :  A major problem with the escape velocity from gravity value is that the velocity is calculated at or near the Earth's surface. An infinite acceleration would be required to project an object at 11.2 km/s from the Earth's surface. Also, it would be very difficult—if not impossible—for a rocket to attain a velocity of 11.2 km/s relatively close to the Earth's surface. The Saturn rocket that was used to go to the Moon did not reach that speed until it was over 193 km (180 miles) from the Earth's surface. Rocket would burn up  Also, in order to reach the escape velocity at lower altitudes, the rocket would be traveling at hypersonic speed, which would be so far above the speed of sound that it could cause the burn-up of a rocket exterior before it left the Earth's atmosphere. Realistically, a rocket would have to build up its speed until it reached the extreme upper atmosphere, where air resistance is negligible at high speeds.
  • 6. Earth Satellites  Earth satellites are the objects which revolve around the earth.  Their orbits around the earth are circular or elliptic.  Moon is the only natural satellite of the earth with a near circular orbit with a time period of approximately 27.3 days which is roughly equal to the rotational period of the moon about its own axis.  With the advancements of science and technology, since 1957, many man made satellites have been put in different orbits around the earth.  Russians were the first to launch the artificial satellite Sputnik I, on Oct 4, 1957. India launched its first artificial satellite,Aryabhatta in 1957. Since the Indi has put many satellites in various orbits around the earth e.g., Bhaskara, Rohini, Apple, IA, IB, Insat, IRS etc.
  • 7.
  • 8. Orbital Speed :  Orbital speed of a satellite is the minimum speed required to put the satellite into a given orbit around earth.  Expression - v = sqrt(Re.g) Where, g=9.8 m/s & Re = radius o of earth. The value for orbital velocity was found to be 7.9 km/s.  It is independent of mass of the satellite.  Decrease with an increase in the radius in the radius in the height of satellite.  Depends upon the mass and radius of the earth/planet around which the revolution of satellite is talking place.  The direction of orbital speed of a satellite at an instant is along the tangent to the orbital path of satellite at that instant.
  • 9.
  • 10. Time Period And Height Of A Satellite  Time period of a satellite is the time taken by satellite to complete one revolution around the earth and is denoted by T.  By substituting the values we get, T = 84.6 minutes.  It means that a satellite orbiting close to the surface of the earth has a time period of revolution about 84.6 minutes.  The height of a satellite is given by the exp.  By substituting the values, h=36000m
  • 11. Geostationary And Polar Satellites:  A satellite whose period of revolution is 24 hours, is a geostationary satellite.  It always appears to be at a fixed point in space, because the period of rotation of the Earth about its own axis is also equal to 24 hours.  Knowing T = 24 hours, g = 9.8 ms-1, the height of a geostationary satellite is calculated to be 36000km.Its orbital velocity is 3.1 km/s.  Its plane of orbit is the equatorial plane.  It revolves from west to east which is similar to the Earth's movement.  It is very useful in telecommunication.
  • 12.  Polar orbiting weather satellites circle the Earth at a typical altitude of 850 km (530 miles) in a north to south (or vice versa) path, passing over the poles in their continuous flight. Polar satellites are in sun- synchronous orbits, which means they are able to observe any place on Earth and will view every location twice each day with the same general lighting conditions due to the near- constant local solar time. Polar orbiting weather satellites offer a much better resolution than their geostationary counterparts due their closeness to the Earth. Satellites in polar orbits are used for environmental and earth resources' survey
  • 13. Different types of satellites : Astronomy satellites - Hubble Space Telescope Atmospheric Studies satellites - Polar Communications satellites - Anik E Navigation satellites - Navstar Reconaissance satellites - Kennan, Big Bird, Lacrosse Remote Sensing satellites - Radarsat Search and Rescue satellites - Cospas-Sarsat Space Exploration satellites - Galileo Weather satellites - Meteosat
  • 14. Weightlessness  When the astronaut in the spaceship is orbiting the Earth, then both, the astronaut and the spaceship are in a state of free fall towards the Earth. During a free fall, both travel downwards with the same acceleration, equal to the acceleration due to gravity. As a result, the astronaut does not exert any force on the sides or floor of the spaceship, and the sides and floor of the spaceship do not push the astronaut up. The astronaut therefore experiences weightlessness while orbiting around the Earth in a spaceship.