Graphical Representation of Gravitational Potential

• What are the two quantities that can be graphically represented against distance from the center of a planet?

  Gravitational field strength and gravitational potential

  
• How are gravitational field strength, g, and gravitational potential, V, related mathematically?

  g = $\frac{\Delta V}{\Delta r}$
• What does ΔV represent in the equation for gravitational field strength?

  Change in gravitational potential
• What does Δr represent in the equation for gravitational field strength?

  Distance from the center of a point mass
• What type of relation does the graph of gravitational potential V against distance r follow?

  -1/r relation

  
• What are the key features of the gravitational potential graph?

  Values for V are all negative
• What happens to V as r increases?

  V follows a -1/r relation
• What does the gradient of the V against r graph represent?

  The value of g at that point
• How can g be calculated from the graph of V against r?

  By drawing a tangent and calculating the gradient
• What is the relationship of the graph of g against r for a planet?

  It follows a 1/r² relation

  
• What are the key features of the g against r graph?

  Values for g are all positive
• What happens to g as r increases?

  g follows a 1/r² relation

  
• What does the area under the g against r graph represent?

  Change in gravitational potential ΔV

  
• How can the area under the g against r graph be estimated?

  By counting squares or using trapeziums
• What does the inverse square law relation imply about g when r doubles?

  g decreases by a factor of 4
• How does the gravitational potential vary with distance from planet A compared to planet B?

  • Graph starts from a large negative value for V at planet A's surface
  • V approaches zero near planet B's surface
  • Graph falls near the surface of planet B

  
• What are the key differences in the graphs of g against r and V against r?

  • g against r:
  • Follows a 1/r² relation
  • Values are positive
  • Steep decline as r increases
  • V against r:
  • Follows a -1/r relation
  • Values are negative
  • Shallow increase as r increases
• What is a common exam question related to these graphs?

  Drawing, interpreting, or calculating from the graphs
• How should the graph of g against r be distinguished from that of V against r?

  It should start off steeper and decrease rapidly