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Who could say what
 the Earth’s like?
Feb-12   Alejandro Menéndez , MA. 2011   2
•ICAO STANDARD – WGS84 (World Geodetic
      System 1984)
                                        POLAR RADIUS: 3432nm
 •2 Different Radius
                                        EQUATORIAL RADIUS:
                                        3443nm

 •COMPRESSION RATIO : 1/297 (a-b/a)




Feb-12        Alejandro Menéndez , MA. 2011                  3
•EAST: Direction in which the Earth
    rotates. Anticlockwise to a person
    looking down on the N.Pole
 •WEST: Opposite to East



Feb-12      Alejandro Menéndez , MA. 2011   4
DEFINITION: Circle drawn on the surface of the
     Earth that divides the world into 2 equal
     hemispheres. Its center is the same that
     the one from the Earth it self. (Great
     Circle & Rhumb line)

         Sets a reference for North and South latitudes




Feb-12           Alejandro Menéndez , MA. 2011            5
Feb-12   Alejandro Menéndez , MA. 2011   6
DEFINITION: Circles drawn on the surface of
      the Earth parallel to the Equator that extend
      up to the Poles. Named by the angle between
      the plane of the Equator and the line joining
      the center of the Earth and any point on
      parallel (Small circles)

     Extention: From 0º (Equator) to 090º N/S (North/South Poles)




Feb-12               Alejandro Menéndez , MA. 2011                  7
Feb-12   Alejandro Menéndez , MA. 2011   8
DEFINITION: Semi circles drawn on the surface
     of the earth that joint the 2 Poles and
     cross the Equator and all the parallels at
     right angles.
         PROPERTIES:
         • The special one: PRIME MERIDIAN (Sets
                 reference for East and West)
         • Each meridian has an ANTI-MERIDIAN
         • Forms a complete GC with its anti-meridian
Feb-12        Alejandro Menéndez , MA. 2011             9
Feb-12   Alejandro Menéndez , MA. 2011   10
Feb-12   Alejandro Menéndez , MA. 2011   11
DEFINITION: Circle drawn on the surface of a
     sphere with its center on the center of the
     sphere. E.g.: Equator and Meridians

                PROPERTIES

         • Connects any 2 points on Earths surface
         • Only 1 GC over 2 points (Exceptions)
         • Is the path RADIO SIGNALS follow
                ORTHOMORPHIC PATH
         • Short path: Shortest possible
Feb-12        Alejandro Menéndez , MA. 2011          12
VERTEX OF A GREAT CIRCLE: Most northerly
     and southerly points of a GC.

              PROPERTIES

         • Northern and southern are ANTIPODAL
                 (Diametrically opposed)
         • 10,800 nm distant
         • At the vertex the direction of the GC is 090º –
                 270º
         • Are placed at 90º longitude from the point where
Feb-12
                 the GCMenéndez ,the2011
                   Alejandro
                             cuts MA. Equator                 13
Feb-12   Alejandro Menéndez , MA. 2011   14
DEFINITION: Circle drawn on the surface of a sphere
      that doesn’t have its center co-located with the
      one of the sphere. E.g.: Parallels of latitude




Feb-12          Alejandro Menéndez , MA. 2011            15
DEFINITION: Regularly curved line on the
     surface of the Earth that cuts all meridians
     at same angle. LOXODROMIC path.
             PROPERTIES

         • Only 1 RL through 2 points on Earths surface
         • Not GC (Exceptions: Meridians & Equator)
         • Mathematically will never reach the Pole (Spiral)
         • Distance with GC
                                                 Greater over long distances.

                                                 Increases with latitude
Feb-12           Alejandro Menéndez , MA. 2011                                  16
Feb-12   Alejandro Menéndez , MA. 2011   17
• Normally , flights of less than 1,000 nm are flown
         along a rhumb line.

 • Long trips can be divided into short legs of rhumb
         lines.

 • The easiest to follow because you only have to set a
         heading. Constant direction track



Feb-12            Alejandro Menéndez , MA. 2011           18
Feb-12   Alejandro Menéndez , MA. 2011   19
1. How can we know one vertex knowing the other?
 2. How can we know the cutting angle between GC and
    Equator knowing one vertex position?
 3. How can we know the vertex longitudes by knowing the
    long of the cutting point between Eq and GC?
 4. How can we get one of the Earth’s radius knowing the
    other and the compression ratio?



Feb-12          Alejandro Menéndez , MA. 2011              20

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1.the form of the earth

  • 1. Who could say what the Earth’s like?
  • 2. Feb-12 Alejandro Menéndez , MA. 2011 2
  • 3. •ICAO STANDARD – WGS84 (World Geodetic System 1984) POLAR RADIUS: 3432nm •2 Different Radius EQUATORIAL RADIUS: 3443nm •COMPRESSION RATIO : 1/297 (a-b/a) Feb-12 Alejandro Menéndez , MA. 2011 3
  • 4. •EAST: Direction in which the Earth rotates. Anticlockwise to a person looking down on the N.Pole •WEST: Opposite to East Feb-12 Alejandro Menéndez , MA. 2011 4
  • 5. DEFINITION: Circle drawn on the surface of the Earth that divides the world into 2 equal hemispheres. Its center is the same that the one from the Earth it self. (Great Circle & Rhumb line) Sets a reference for North and South latitudes Feb-12 Alejandro Menéndez , MA. 2011 5
  • 6. Feb-12 Alejandro Menéndez , MA. 2011 6
  • 7. DEFINITION: Circles drawn on the surface of the Earth parallel to the Equator that extend up to the Poles. Named by the angle between the plane of the Equator and the line joining the center of the Earth and any point on parallel (Small circles) Extention: From 0º (Equator) to 090º N/S (North/South Poles) Feb-12 Alejandro Menéndez , MA. 2011 7
  • 8. Feb-12 Alejandro Menéndez , MA. 2011 8
  • 9. DEFINITION: Semi circles drawn on the surface of the earth that joint the 2 Poles and cross the Equator and all the parallels at right angles. PROPERTIES: • The special one: PRIME MERIDIAN (Sets reference for East and West) • Each meridian has an ANTI-MERIDIAN • Forms a complete GC with its anti-meridian Feb-12 Alejandro Menéndez , MA. 2011 9
  • 10. Feb-12 Alejandro Menéndez , MA. 2011 10
  • 11. Feb-12 Alejandro Menéndez , MA. 2011 11
  • 12. DEFINITION: Circle drawn on the surface of a sphere with its center on the center of the sphere. E.g.: Equator and Meridians PROPERTIES • Connects any 2 points on Earths surface • Only 1 GC over 2 points (Exceptions) • Is the path RADIO SIGNALS follow ORTHOMORPHIC PATH • Short path: Shortest possible Feb-12 Alejandro Menéndez , MA. 2011 12
  • 13. VERTEX OF A GREAT CIRCLE: Most northerly and southerly points of a GC. PROPERTIES • Northern and southern are ANTIPODAL (Diametrically opposed) • 10,800 nm distant • At the vertex the direction of the GC is 090º – 270º • Are placed at 90º longitude from the point where Feb-12 the GCMenéndez ,the2011 Alejandro cuts MA. Equator 13
  • 14. Feb-12 Alejandro Menéndez , MA. 2011 14
  • 15. DEFINITION: Circle drawn on the surface of a sphere that doesn’t have its center co-located with the one of the sphere. E.g.: Parallels of latitude Feb-12 Alejandro Menéndez , MA. 2011 15
  • 16. DEFINITION: Regularly curved line on the surface of the Earth that cuts all meridians at same angle. LOXODROMIC path. PROPERTIES • Only 1 RL through 2 points on Earths surface • Not GC (Exceptions: Meridians & Equator) • Mathematically will never reach the Pole (Spiral) • Distance with GC Greater over long distances. Increases with latitude Feb-12 Alejandro Menéndez , MA. 2011 16
  • 17. Feb-12 Alejandro Menéndez , MA. 2011 17
  • 18. • Normally , flights of less than 1,000 nm are flown along a rhumb line. • Long trips can be divided into short legs of rhumb lines. • The easiest to follow because you only have to set a heading. Constant direction track Feb-12 Alejandro Menéndez , MA. 2011 18
  • 19. Feb-12 Alejandro Menéndez , MA. 2011 19
  • 20. 1. How can we know one vertex knowing the other? 2. How can we know the cutting angle between GC and Equator knowing one vertex position? 3. How can we know the vertex longitudes by knowing the long of the cutting point between Eq and GC? 4. How can we get one of the Earth’s radius knowing the other and the compression ratio? Feb-12 Alejandro Menéndez , MA. 2011 20