3. IB Assessment Statements Topic 9.2, Gravitational Field, Potential and Energy 9.2.1.Define gravitational potential and gravitational potential energy. 9.2.2.State and apply the expression for gravitational potential due to a point mass. 9.2.3.State and apply the formula relating gravitational field strength to gravitational potential gradient.

4. IB Assessment Statements Topic 9.2, Gravitational Field, Potential and Energy 9.2.4.Determine the potential due to one or more point masses. 9.2.5.Describe and sketch the pattern of equipotential surfaces due to one and two point masses. 9.2.6.State the relation between equipotential surfaces and gravitational field lines.

5. Objectives  Appreciate that there is an attractive force between any two point masses that is directed along the line joining the two masses,  State the definition of gravitational field strength,

6. Introductory Video The Force of Gravity The Force of Gravity

7. Newton’s 2 nd Law  Newton’s second law (F=ma) implies that if a mass is accelerating, there must be a force acting on it  An object falls because of gravity  What holds planets in their orbits?

8. Newton’s 2 nd Law  Newton’s second law (F=ma) implies that if a mass is accelerating, there must be a force acting on it  An object falls because of gravity  What holds planets in their orbits?  Gravitational Force

9. Newton’s Law of Gravitation  The attractive force between two point masses is,  Where,  M1 and M2 are the masses of the attracting bodies  r is the distance between them  G is Newton’s constant of universal gravitation and has a value of 6.667 x 10 -11 N m 2 kg -2

10. Newton’s Law of Gravitation  The direction of the force is along the line joining the two masses,

11. Newton’s Law of Gravitation  The formula applies to point masses, which means the masses are small in relation to the separation between them

12. Newton’s Law of Gravitation  What is the gravitational force between the earth and the sun?

13. Newton’s Law of Gravitation  What is the gravitational force between the earth and the sun?

14. Newton’s Law of Gravitation  How does this compare to the gravitational force between the earth and you?

15. Newton’s Law of Gravitation  How does this compare to the gravitational force between the earth and you?

16. Newton’s Law of Gravitation  Since F=ma, what value of a does this yield?

17. Newton’s Law of Gravitation  Since F=ma, what value of a does this yield?  Sound Familiar?

18. Gravitational Field Strength  The gravitational field strength at a certain point is the force per unit mass experienced by a small point mass, m, at that point.

19. Gravitational Field Strength  The units of gravitational field strength are N  kg -1  1N = 1 kg  m  s -2  So units become m  s -2

20. Gravitational Field Strength  Gravitational field strength is a vector quantity whose direction is given by the direction of the force a point mass would experience if placed at the point of interest.

21. Gravitational Field Strength  The gravitational field strength around a single point mass is radial which means it is the same for all points equidistant from the center of mass and directed toward the center.

22. Gravitational Field Strength  On a micro- versus macro- level (like the projectile motion of a football), the field strength can be considered to be uniform with a constant value.

23. Summary Video: The Law of Gravitation and Planetary Motion The Law of Gravitation and Planetary Motion

24. Objectives  Appreciate that there is an attractive force between any two point masses that is directed along the line joining the two masses,  State the definition of gravitational field strength,

25. IB Assessment Statements Topic 9.2, Gravitational Field, Potential and Energy 9.2.1.Define gravitational potential and gravitational potential energy. 9.2.2.State and apply the expression for gravitational potential due to a point mass. 9.2.3.State and apply the formula relating gravitational field strength to gravitational potential gradient.

26. IB Assessment Statements Topic 9.2, Gravitational Field, Potential and Energy 9.2.4.Determine the potential due to one or more point masses. 9.2.5.Describe and sketch the pattern of equipotential surfaces due to one and two point masses. 9.2.6.State the relation between equipotential surfaces and gravitational field lines.

28. Homework #1-8