gravitational fields

• What topic is being discussed in this lesson?

  Gravitational fields
• What causes gravitational fields?

  Objects having mass
• How do two objects with mass interact in a gravitational field?

  They experience an attractive force
• How are spheres modeled in gravitational fields?

  As having all mass concentrated at the center
• What do gravitational field lines represent?

  The direction of force on a test mass
• What happens if there are twice as many gravitational field lines?

  The gravitational field is twice as strong
• How is gravitational field strength represented mathematically?

  g = gravitational force / mass
• What are the units for gravitational field strength?

  Newtons per kilogram (N/kg)
• What does Newton's law of universal gravitation state?

  Attractive force acts between two masses
• What is the equation for gravitational force?

  F = -g(m1*m2)/r^2
• What does the negative sign in the gravitational force equation indicate?

  The force is attractive
• How does gravitational acceleration relate to gravitational force?

  It is derived from the gravitational force equation
• What is the formula for gravitational acceleration?

  g = -GM/r^2
• How is gravitational acceleration measured?

  As gravitational field strength
• What does it mean if the gravitational field is uniform?

  Field lines are parallel and equidistant
• What is Kepler's first law of planetary motion?

  Orbits are ellipses with the sun at a focus
• What does Kepler's second law state?

  Equal areas are swept out in equal times
• What is the implication of Kepler's second law for a planet's speed?

  It speeds up when closer to the sun
• What is Kepler's third law of planetary motion?

  The square of the period is proportional to the cube of distance
• How can Kepler's third law be expressed mathematically?

  t^2 is proportional to r^3
• How do we derive Kepler's third law?

  By equating gravitational and centripetal forces
• What is the formula for centripetal force?

  Fc = mv^2/r
• What is the relationship between speed and orbital period?

  Speed is circumference divided by period
• What is the formula for escape velocity?

  v = sqrt(2GM/r)
• How do you calculate the escape velocity for Earth?

  Use v = sqrt(2GM/r)
• What is the escape velocity of Earth?

  Approximately 11 km/s
• What happens to gravitational potential energy at infinite distances?

  It approaches zero
• What is gravitational potential energy expressed as?

  U = -GMm/r
• What is gravitational potential expressed as?

  V = -GM/r
• What does gravitational potential represent?

  Energy per unit mass
• How is work done calculated in a force-distance graph?

  As the area under the curve
• What is the formula for work done?

  Work done = force × distance
• What is the significance of escape velocity?

  It allows an object to leave gravitational field
• What is the relationship between gravitational potential energy and kinetic energy at escape velocity?

  They are equal at escape velocity
• What is the mass of the Earth?

  Approximately 6.0 × 10^24 kg
• What is the radius of the Earth?

  Approximately 6400 km
• What is the significance of gravitational potential and gravitational potential energy being negative?

  They increase towards zero at infinity
• What does the gravitational potential represent in terms of work done?

  Work done to bring unit mass from infinity
• What are the three main equations in gravitational fields?

  1. Gravitational force: F = -G(m1*m2)/r^2
  2. Gravitational potential energy: U = -GMm/r
  3. Gravitational potential: V = -GM/r
• What are Kepler's three laws of planetary motion?

  1. Orbits are ellipses with the sun at a focus.
  2. Equal areas are swept out in equal times.
  3. The square of the period is proportional to the cube of distance.