Earth and Moon

 

 

       Lunar motions

 

  The Moon rotates around the Earth in a period of time equal to that of its rotation around itself. Also, it rotates with the Earth around the Sun.

  The simulation shows the motion of revolution around the Earth and around the Sun.

 

  With button  it is possible to have a point of view perpendicular to the plane of revolution of the Earth around the Sun or an axonometric view.

  Button  shows the orbits.

  Start by clicking the button .

  By clicking the button  it is possible to start a new simulation.

 

 

 

 

 

      Lunar phases

 

  During the period of revolution around the earth, the Moon shows the side illuminated by the Sun or the non- illuminated side. This happens over a period of twenty-nine days.

  Particular situations are those in which the Moon shows its dark side (new moon), totally illuminated side (full moon) and its half illuminated side.

  The simulation shows all the situations.

 

  Button  shows the trajectories of the Earth and of the Moon.

  By clicking the button the simulation is put in stand by and it is possible to see the zones of the Earth and of the Moon reciprocally visible are shown.

  At the end of the simulation with button   it is possible to see the particular situations described above.

  Start by clicking the button .

  By clicking the button  it is possible to start a new simulation.

 

 

 

 

 

      Tides

 

  Because of the gravitational attraction of the Moon and a lesser degree of the Sun, the oceans and the seas oscillate with a risings (flood tide) and lowering (ebb tide) of their level.

  The simulation shows an Earth uniformly covered with water, the level of which is linked to the relative Earth - Moon and Earth - Sun positions.

  The centrifugal force due to the rotation of the system Earth - Moon around their centre of mass acts on the ocean level. This force acts on the opposite side in respect to the force of attraction. In the simulation the forces are represented by vectors.

   The maximum variation of the level happens when the Moon and the Sun are on the same line (spring tides), while the minimum variation happens when the Moon and the Sun are disposed at a right angle with respect to the Earth (neap tide).

 

  Button  shows the vectors that represent the force of attraction between Earth and Moon.

  Button  shows the vectors that represent the centrifugal forces.

  Button  shows the resultants.

 

 

 

 

 

    Axonometry

 

  It is a graphic representation of spatial figures.

 

 

 

 

 

    Trajectory 

 

  The trajectory is the line followed by a moving body.

 

 

 

 

 

    Force of attraction

 

  This is the force which two masses M and m attract one another. It is proportional to the mass, and inversely proportional to the square of the distance between two centres.

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  where G is the universal gravitational constant.

 

 

 

 

 

    Centre of mass

 

  Lets consider a system of bodies of mass along a line, at different distances from a point O.

  The centre of mass is the point:

  It is possible to broaden the definition to the space by considering also coordinate y and z.

 

 

 

 

 

    Vector

 

  A vector is a quantity characterized by the fact that has a direction and a magnitude.

  It is represented by an oriented segment in which:

  • The direction is given by the line the segment is part and by the parallels.
  • The magnitude is given by the length of the arrow once a scale has been introduced.

 

 

 

 

 

    Resultant

 

  The resultant or sum between two vectors applied to the same point is obtained with the rule of the parallelogram.

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    Proportionality

 

  • Between two quantities a and b there is a direct proportionality when the ratio a/b = k is constant.
  • Between two quantities a and b there is an inverse proportionality when the product a * b = k is constant.
  • Between two quantities a and b there is square proportionality when the ratio between one of them and the square of the other a /bČ = k is constant.
  • Between two quantity a and b there is an inverse square proportionality when the product between one of them and the square of the other a * bČ = k is constant.