Gravitational fields

• Gravitational field


  A region of space which any object with mass experiences a gravitational force
• Gravitation field lines are directed towards the centre of mass of a body
• Newtons law of universal gravitation


  The gravitational force Fg between two masses m1 and m2 is proportional to the product of their masses and inversely proportional to the square of their separation , r
• In a radial field G.P.E is defined as


  the energy an object possesses due to its position in a gravitational field
• Gravitational potential at a point is the gravitational potential energy per unit mass at that point
• Gravity is always attractive so work must be done on a mass to move it away to a point infinitely far away from every other mass
• Gravitational potential energy


  The work done per unit mass in bringing a test mass from infinity to a defined point
• What type of force acts on bodies in orbit?

  Resultant force
• What is the source of the gravitational force acting on bodies in orbit?


  The mass M being orbited
• Why is the gravitational force considered a centripetal force?


  Because it acts towards the center of mass M
• How does the direction of the centripetal force relate to the velocity of the planet or satellite?


  The centripetal force acts perpendicular to the velocity
• Newtons law of gravitation equation

  F = -GMm / r^2
• Gravitational constant value

  6.67 x 10^-11 Nm^2kg^-2
• Equations for gravitational field strength


  g = GM / r^2 g = F / m
• Gravitational potential at a point


  Energy transferred per unit mass when moving an object from infinity to that point
• Gravitational potential equation


  V = -GM / r
• Gravitational potential energy equation


  E = -GMm / r
• What is equipotential


  A plane in which all points have the same potential
• Whats true when a mass moves along an equipotential?


  No work is done when moving along an equipotential
• What is the area under a force-seperation graph


  Energy
• How do you calculate the work done by a moving mass in a field?


  Work done = mass x change in gravitational potential
• What is gravitational potential difference


  It's the difference in the gravitational potentials of two points in a field
• How are the orbital period and the radius of a circular orbit related


  T^2 is directly proportional to R^3
• What is a point mass


  A point mass is a theoretical object that has a mass but no dimensions so all mass acts at a single point
• Whats the relationship between field strength and the field lines that represent it


  The closer the lines are together the stronger the gravitational field strength, and the further apart the lines are the weaker the field strength
• What are the two types of fields

  • Uniform
  • Radial
• Uniform field

  It exerts the same gravitational force on a mass everywhere in the field
• Radial field

  In a radial field the force exerted depends in the position of the object in the field
• What are the similarities between electric and gravitational fields?

  • Forces both follow an inverse square law
  • Both use field lines to be represented and can be both radial or uniform
  • Both use equations of a similar form to find the force exerted and field strength
• What are the differences between electric and gravitational fields?

  • In a gravitational field the force exerted is always attractive but in an electric field the force can either be repulsive or attractive
  • Electric fields act on charge while gravitational fields act on mass
• Keplers third law

  Keplers third law states that the square of the orbital period is directly proportional to the cube of the radius