1. Gravitation In galaxy M31, one very similar to our own, there is almost certainly a super massive black hole at the center. This very massive object supplies an enormous amount of gravitational pull.

2. Direction of Gravitation Isaac Newton described this attractive force that acts between all pieces of matter in the universe. Gravity is always attractive. There is no “repulsive” gravity. So far, antigravity is just science fiction...

3. Law of Universal Gravitation What factors do you think the gravitational attraction of two bodies would depend on? mass of objects, and distance between objects

4. Universal Gravitational Constant The previous relationship only describes the factors that influence gravity. To get a numerically correct answer, with units, you need a constant added to the equation. This constant is called the universal gravitational constant: G = 6.67 x 10 -11 N m 2 /kg 2

5. Universal Law of Gravitation Force from gravity, N Universal Gravitational constant Two masses, kg Distance between objects, m Because there is a quantity squared in the denominator of the fraction, this formula may be referred to as an inverse square law.

6. Gravitation Calculation Example Calculate the gravitation force between the planet Mars, 6.4 x 10 23 kg, and the sun, 2 x 10 30 kg. Assume a distance of 2.0 x 10 11 m. FgFg

7. Gravitation Example Solution Substitute values, do math carefully! F g = 2.13 x 10 21 N Notice how the units cancel leaving the correct force unit of Newtons.

8. Gravitational Fields Field lines show which way an object will move when exposed to some force. Thus, gravitational field lines on earth always point to the center of the earth.

9. Many Gravitational Forces Any object may have gravitational forces from different objects acting upon it. The net gravitational force on any object is the sum of all the forces acting upon it. For however many objects you are considering, simply sum their influences to get the total gravitational force on an object.

10. Combining Forces An astronaut is near two massive asteroids as shown. Describe the net gravitational force acting on him. The exact magnitudes of the forces could be found if the masses and distances were known. The net force is simply the sum of all gravitational influences acting on him. F1F1 F1F1 F net

11. Thought Question Imagine you are deep inside the earth in a cave. Would you weigh more, less, or the same as on the surface of the earth?

12. Thought Question Answer When on the surface of the earth, all of the mass of the earth is pulling you down. When underground, the mass above you actually pulls you up, countering some of pull from the bulk of the planet. You weigh less!

13. Extension of Thought Question What would happen if you were at a cave at the center of the earth? Because the gravitational pull from the matter equally all around you would cancel out, you would be weightless! F net would be 0.

14. Newton’s Shell Theorem The previous two thought questions can be described with the shell theorem: A uniform spherical shell of matter attracts an outside particle as if all the shell’s mass were concentrated at its center. Here we consider the earth to be many shells nested inside each other. The entire mass of the earth seems to be concentrated at its center.

15. More Shell Theorem If you are inside the shell, that helps describe our cave questions: A uniform spherical shell of matter exerts no net gravitational force on a particle located inside it. No net influence from gravity inside the cave/shell.

16. Gravitational Field Inside a Planet Notice how outside the planet the graph shows an inverse square law. Inside, it is linear. A maximum at the surface…

17. Planet Discovery Gravity can have much more subtle effects. The existence of Pluto and Neptune was predicted before they were ever observed. Their slight gravitational effects wobble the orbits of the other planets, betraying their presence before they were ever seen visually.

18. Gravitational Potential Energy In a previous class, we had a formula for the gravitational potential energy of an object here on earth: Now that we have learned more about the universal nature of gravity, we will explore a more generic formula for gravitational potential energy. This formula would apply to any two or more objects that gravitationally attract each other.

19. New Potential Energy Formula Universal Gravitational constant Two masses, kg Distance between objects, m You may notice some obvious similarities between this formula and the gravitational force formula. Minus sign because the force and displacement are in opposite directions

20. 20 Ex: Imagine a mattress with a heavy bowling ball thrown in the middle. It forces the surface to conform around it. Thus, Einstein would say that space is not a flat 2D grid like we often imagine. Einstein’s Theory of Gravitation The very existence of any massive body warps or bends space around it.

21. Gravity: Force or Curved Space We typically think of gravity as a force. However, we could consider it a result of the curve that massive bodies create. Objects move as they roll along these curved created by massive objects. A black hole is the ultimate in massive bodies curving space: A black hole is often imagined like a funnel since it engulfs matter and crams it into an infinitely small spot called a singularity.

22. Questions? Assignment: p 351 P # 1,18,24,29 See inside text cover for some useful data