Gravitational Fields

• Gravitational field: The region of space surrounding a body in which another body experiences a force of gravitational attraction.
• Field line density: Number of field lines per unit area indicating the field strength
• Gravitational field strength (uniform)

  g=F/m
• Gravitational field strength (radial)

  g= GM/r^2
• Newton's Law of Gravitation: The force between two point masses is directly proportional to the product of the masses and inversely proportional to the square of the separation between them
• What type of law is Newton's law of gravitation: Inverse square law
• Which mass is M1: The larger mass / one creating the field
• Which mass is M2: The object in the field / the smaller mass
• What type of force is gravity

  Non-contact, attractive face
• What is the value of G

  6.67 x 10^-11
• Units of gravitational force

  Newtons (N)
• Units of gravitational field strength

  Newtons per kilogram (N/kg)
• Gravitational Field strength: The force per unit mass experienced by a small test mass placed in the field
• What type of objects experience a gravitational force? Objects with mass
• Gravitational potential: Work done per unit mass in bringing a test mass from infinity to that point in the field.
• gravitational potential energy: Energy stored by objects due to their position above Earth's surface.
• Gravitational potential (radial)


  V=- GM/r
• Graph of gravitational potential against distance gradient: Gravitational field strength (g= - ∆V/∆r)
• Gravitational potential difference: The energy needed to move a unit mass between two points in a gravitational field
• Where is gravitational potential zero?

  At infinity
• Gravitational potential difference (equation)

  ∆W=m∆V
• Gravitational potential energy (radial)

  Ep=-GMm/r
• Equipotential's: Positions within a field with zero potential difference between them
• When moving along an equipotential, how much work is done? Zero
• Work done units


  Joules (J)
• Gravitational potential units


  Jkg^-1
• synchronous orbit: An orbit in which the period of the orbit is equal to the rotational period of the object that it is orbiting.
• Geostationary orbit: An orbit in which a satellite orbits Earth at the same rate as Earth rotates and thus stays over the equator all the time.
• Low orbiting satellites: Satellites that orbit close to the earth (180 - 2000km above the surface)
• Escape velocity: the minimum velocity needed to escape a gravitational field
• Total energy of a satellite: kinetic energy + potential energy
• Elliptical orbit: The satellite will speed up as its orbital radius decreases and slows down when the orbital radius increases
• Low orbit satellites are used for: Imaging and monitoring the weather
• Orbital period of a geostationary orbit

  24hrs
• Orbital period of a synchronous orbit of earth

  24hrs
• Orbital speed formula


  v = 2πr/T
• Escape velocity formula


  v= √(2GM/r)
• Kepler's Law: The square of the time period of an orbit is directly proportional to the cube of the orbital radius
• State two features of a two-synchronous orbit: - Time period of 24hrs