Lesson 5.1 – Newton’s Law of Gravitation (35 Prompts)

Foundation (1–10)

1. State Newton’s universal law of gravitation.

2. Define gravitational force.

3. Identify what G represents.

4. Write the formula F = Gm₁m₂/r².

5. State whether gravity is attractive or repulsive.

6. Give an example of gravitational force in nature.

7. Define inverse-square law.

8. Identify two factors affecting gravitational force.

9. State what happens to force when masses increase.

10. Draw simple diagram of gravitational attraction.

Intermediate (11–23)

11. Calculate gravitational force between two masses.

12. Explain effect of doubling distance.

13. Compare gravity and magnetic force qualitatively.

14. Describe gravitational field around Earth.

15. Solve multi-mass gravitational scenario.

16. Explain why gravitational force decreases with altitude.

17. Derive proportionality relation F ∝ 1/r².

18. Analyze gravitational interaction between celestial bodies.

19. Solve gravitational problem with units.

20. Explain significance of gravitational constant.

21. Sketch force vs distance graph.

22. Determine force ratio when both masses change.

23. Discuss experimental challenges measuring G.

Advanced (24–35)

24. Derive Newton’s formula using inverse-square assumption.

25. Compare gravitational and electrostatic force mathematically.

26. Solve gravitational field vectors from multiple bodies.

27. Analyze gravitational stability in planet–moon systems.

28. Explain shell theorem qualitatively.

29. Solve gravitational force inside a hollow sphere.

30. Discuss modern methods of measuring G.

31. Derive escape conditions using Newton’s law.

32. Evaluate gravity variation on non-spherical bodies.

33. Model gravitational interaction using calculus.

34. Compare Newtonian gravity vs general relativity qualitatively.

35. Solve multi-step gravitational system problem.

Lesson 5.2 – Gravitational Field & Field Intensity (35 Prompts)

Foundation (1–10)

1. Define gravitational field.

2. State formula g = GM/r².

3. Define gravitational field intensity.

4. Give unit of g.

5. Identify direction of gravitational field.

6. Draw field lines for a point mass.

7. Distinguish between gravitational force and field.

8. Define radial field.

9. State typical value of g on Earth.

10. Explain why g is nearly constant near Earth’s surface.

Intermediate (11–23)

11. Calculate gravitational field at given distance.

12. Explain why g decreases with altitude.

13. Sketch field lines of Earth.

14. Compare g on Earth and Moon.

15. Solve g at 2R from Earth's center.

16. Describe variation of g inside Earth.

17. Discuss how Earth’s rotation affects g.

18. Differentiate uniform and radial fields.

19. Analyze field strength at planetary surfaces.

20. Solve multi-body gravitational field problem.

21. Graph g vs r for Earth.

22. Explain relationship between field intensity and mass distribution.

23. Evaluate g near massive objects.

Advanced (24–35)

24. Derive g = −dV/dr.

25. Solve gravitational field from spherical shells.

26. Analyze g variation inside a non-uniform planet.

27. Derive gravitational field for ring mass qualitatively.

28. Solve vector superposition of fields.

29. Discuss gravitational shielding (why impossible).

30. Model gravitational well using potential energy graphs.

31. Derive orbital speed from g.

32. Analyze difference between local g and standard g.

33. Evaluate field intensity using calculus methods.

34. Compare Newtonian vs relativistic field interpretation.

35. Solve advanced gravitational gradient problem.

Lesson 5.3 – Gravitational Potential & Potential Energy (35 Prompts)

Foundation (1–10)

1. Define gravitational potential.

2. State formula V = −GM/r.

3. Define gravitational potential energy.

4. Write U = mV.

5. State potential at infinity.

6. Explain why gravitational potential is negative.

7. Draw V–r graph.

8. Identify difference between potential and field.

9. Define potential difference.

10. Give example of gravitational potential in daily life.

Intermediate (11–23)

11. Calculate potential at given distance.

12. Solve potential energy problem for two masses.

13. Compare potential and potential energy.

14. Sketch potential inside a planet.

15. Explain significance of zero potential at infinity.

16. Determine work needed to move mass between points.

17. Solve gravitational energy change for satellite.

18. Analyze potential gradient.

19. Explain escape condition using potential.

20. Derive relation between V and orbital radius.

21. Calculate potential difference between orbits.

22. Discuss potential energy’s negative sign physically.

23. Analyze potential well depth.

Advanced (24–35)

24. Derive V = −GM/r from work-energy concept.

25. Model gravitational potential inside uniform sphere.

26. Solve multi-layer planetary potential.

27. Derive potential for ring distribution.

28. Solve potential in multi-body system.

29. Evaluate escape velocity from potential diagrams.

30. Model gravitational binding energy.

31. Solve calculus-based potential problems.

32. Evaluate total energy of orbiting bodies.

33. Compare gravitational potential wells of planets.

34. Analyze potential curvature near black holes qualitatively.

35. Apply gravitational potential to astrophysical systems.

Lesson 5.4 – Orbital Motion & Satellites (35 Prompts)

Foundation (1–10)

1. Define orbit.

2. Identify centripetal force for satellites.

3. Write orbital speed formula v = √(GM/r).

4. Define orbital period.

5. Define geostationary orbit.

6. Distinguish circular and elliptical orbits.

7. Give example of satellite use.

8. State why satellites remain in orbit.

9. Identify direction of satellite velocity.

10. Sketch circular orbit.

Intermediate (11–23)

11. Calculate orbital speed.

12. Solve time period using T = 2π√(r³/GM).

13. Compare LEO and GEO orbits.

14. Explain weightlessness.

15. Sketch velocity and acceleration vectors.

16. Determine orbit radius for 24 hr period.

17. Analyze energy of satellite.

18. Compare kinetic and potential energy in orbit.

19. Solve multi-step orbital parameter problem.

20. Explain synchronous orbit.

21. Describe uses of GPS satellites.

22. Discuss orbital decay.

23. Predict effect of increasing orbit radius.

Advanced (24–35)

24. Derive orbital speed equation.

25. Solve elliptical orbit problem.

26. Analyze Hohmann transfer orbits conceptually.

27. Calculate total orbital energy E = −GMm/2r.

28. Evaluate escape vs orbital velocity.

29. Solve complex satellite energy problem.

30. Compare gravitational time dilation qualitatively.

31. Model orbital insertion conditions.

32. Analyze perturbations from other celestial bodies.

33. Apply Kepler’s third law to planetary systems.

34. Predict orbit changes due to atmospheric drag.

35. Evaluate limitations of Newtonian orbital mechanics.

Lesson 5.5 – Escape Velocity & Energy of Orbits (35 Prompts)

Foundation (1–10)

1. Define escape velocity.

2. Write vₑ = √(2GM/R).

3. Define binding energy.

4. Distinguish escape and orbital velocity.

5. Identify whether escape velocity depends on mass.

6. Explain concept of zero total energy.

7. State meaning of unbound orbit.

8. Draw energy vs radius graph.

9. Identify conditions for escape.

10. Give example of object achieving escape velocity.

Intermediate (11–23)

11. Calculate escape velocity for planet.

12. Compare escape velocity of Moon and Earth.

13. Solve total energy at escape.

14. Analyze escape using potential energy.

15. Discuss role of atmosphere in escape.

16. Determine energy needed to escape from orbit.

17. Solve multi-level escape problem.

18. Compare parabolic and hyperbolic trajectories.

19. Sketch energy curves for bounded/unbounded states.

20. Explain effect of planetary mass on escape.

21. Predict escape conditions for spacecraft.

22. Compare rocket equation and escape velocity qualitatively.

23. Analyze energy transfer during launch.

Advanced (24–35)

24. Derive escape velocity using work-energy principle.

25. Solve escape from rotating planet.

26. Model multi-body escape scenario.

27. Determine escape energy including atmospheric drag.

28. Evaluate escape from binary systems.

29. Analyze escape trajectories using calculus.

30. Compare escape velocity in Newtonian vs relativistic frameworks.

31. Solve gravitational slingshot energy gain.

32. Evaluate binding energy of celestial bodies.

33. Calculate total energy of spacecraft during escape.

34. Model escape from non-spherical bodies.

35. Discuss limitations of escape velocity formula.