Gravitational Fields Mind Map

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  • Gravitational Fields--DM
    • A Gravitational field is the region around a mass where another mass experiences a force.
      • Radial Field
        • a symmetrical field that diminishes with (distance)^2 from its centre
    • Newtons Law of Gravitation
      • Any two point masses attract each other with a force that is directly proportional to the product of their masses & inversely proportional to the square of their separation.
      • F=GMm/r^2
      • Universal Gravitational Constant(G)=6.673×10-11 N m2 kg-2
      • The gravitational force between two masses is independent of the medium separating the mass and is always an attractive force 
    • Gravitational Field Strength
      • The gravitational force exerted per unit mass on a small object placed at that point.
      • g=GM/r^2
        • Units: N/kg
    • Gravitational Potential
      • The gravitational potential at a point is work done per unit mass in bringing a mass from infinity to the point 
      • P=-(GM)/r
        • The negative sign is because:       -Gravitational force is always attractive        -Gravitational potential reduces to zero at infinity -Gravitational potential decreases in direction of field 
          • Ep=-(GMm)/r
      • The gravitational potential energy difference between two points is the work done in moving a mass from one point to another.
        • Gravitational Potential Energy
          • Gravitational potential energy of a mass m at a point in the gravitational field of another mass m, is the work done in bringing that mass m from infinity to that point 
          • Ep=-(GMm)/r
    • Gravitational Potential Energy
      • Gravitational potential energy of a mass m at a point in the gravitational field of another mass m, is the work done in bringing that mass m from infinity to that point 
    • Critical Velocity
      • The minimum velocity that should be given to a satellite from a point above the earth's surface so that it moves in a circular orbit around the earth.
      • V=?(GM/r)
        • The orbital velocity does not depend on the mass of the satellite.
          • Orbital Velocity is the velocity that should be given to a satellite so that it moves in a circular orbit around a planet.
    • Orbital Period
      • T² = (4?^2r^3)/GM
        • Keplar's Law of Planetary Motion
          • T² ? r³
        • T² ? r³
      • Keplar's Law of Planetary Motion
        • The time taken for one complete revolution
          • T² = (4?^2r^3)/GM
        • Escape Velocity of a Satellite
          • The minimum velocity with which an object must be projected from the earth's surface so that it escapes from the gravitational field.
          • Ve=?(2GM/r)

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