Circular Orbits in Gravitational Fields

• What type of orbit do most planets and satellites have?

  Near circular orbit
• What provides the centripetal force for a planet in orbit?

  The gravitational force between the Sun and planet

  
• How is the gravitational force related to the direction of travel of a planet?

  It is perpendicular to the direction of travel
• What is the formula for gravitational force in relation to centripetal force?

  F = F

  
• What happens to the mass of the satellite when equating gravitational and centripetal forces?

  The mass cancels out on both sides

  
• What does the variable v represent in orbital motion?

  Linear speed of the mass in orbit
• What does G represent in the context of gravitational fields?

  Newton's Gravitational Constant
• What does the orbital radius r refer to?

  Distance from the center of the orbiting body
• What is true about the speed of all satellites in a particular orbit radius?

  They travel at the same speed v
• What type of acceleration does a planet in circular motion experience?

  Centripetal acceleration
• What is the relationship between the time period T and the circumference of the orbit?

  T is the time to travel the circumference

  
• How is linear speed v calculated in circular motion?

  Speed = distance / time
• What happens when you substitute the value of linear speed v into the time period equation?

  You derive the equation relating T and r
• What does the equation relating time period T and orbital radius r show?

  T is related to r of the orbit

  
• What is Kepler’s third law about circular orbits?

  The square of T is proportional to the cube of r

  
• How can the relationship between T and r be graphically represented?

  • Logarithmic plot of log(T) vs. log(r)
  • Results in a straight line graph
  • Does not pass through the origin
  • Has a negative y-intercept
• What does the symbol ∝ mean in mathematical terms?

  Proportional to
• In a binary star system, what is the relationship between the two stars' masses and their orbits?

  Both stars orbit about a fixed point
• What is essential to remember for calculations in gravitation questions?

  Equations for circular motion

  
• Why is it important to understand the derivation for T ∝ r relation?

  It will be expected in exams
• What is the significance of the negative y-intercept in the logarithmic plot of T vs. r?

  Indicates a non-zero starting point for T
• What specific values of G are important in gravitational calculations?

  6.674 × 10^-11 N(m/kg)^2
• Why is it important to understand the derivation steps for the relationship between T and r?

  To apply them correctly in exams
• How do Kepler's laws apply to practical scenarios in astronomy?

  They help predict planetary motion