1. Gravity Physics 6A Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB GRAVITY Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity. There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you!

3. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB GRAVITY Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity. There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you! Newton’s law of gravitation gives us a formula to calculate the attractive force between 2 objects: m 1 and m 2 are the masses, and r is the center-to-center distance between them G is the gravitational constant – it’s tiny: G≈6.674*10 -11 Nm 2 /kg 2 m1 m2 r F 1 on 2 F 2 on 1 Use this formula to find the magnitude of the gravity force. Use a diagram or common sense to find the direction. The force will always be toward the other mass.

4. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m

5. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m We should start by defining our coordinate system. Let’s put the origin at planet H and say positive is to the right.

6. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m We can also draw the forces on planet H in our diagram. F DP on H F Apes on H

7. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m F DP on H F Apes on H Our formula will find the forces (we supply the direction from looking at the diagram):

8. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m F DP on H F Apes on H Our formula will find the forces (we supply the direction from looking at the diagram):

9. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m Our formula will find the forces (we supply the direction from looking at the diagram): F DP on H F Apes on H This is negative because the force points to the left

10. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m Our formula will find the forces (we supply the direction from looking at the diagram): F DP on H F Apes on H This is negative because the force points to the left This is positive because the force points to the right

11. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). Planet Hollywood: mass=6 x 10 20 kg Planet of the Apes: mass=6 x 10 24 kg Daily Planet: mass=3 x 10 25 kg 10 12 m3 x 10 12 m Our formula will find the forces (we supply the direction from looking at the diagram): F DP on H F Apes on H This is negative because the force points to the left This is positive because the force points to the right Add the forces to get the net force on H: Net force is to the left

12. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB R planet m GRAVITY One more useful detail about gravity: The acceleration due to gravity on the surface of a planet is right there in the formula. Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet.

13. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB R planet m We already know that F grav is the weight of the object, and that should just be mg (if the planet is the Earth) GRAVITY One more useful detail about gravity: The acceleration due to gravity on the surface of a planet is right there in the formula. Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet.

14. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB GRAVITY One more useful detail about gravity: The acceleration due to gravity on the surface of a planet is right there in the formula. Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet. R planet m We already know that F grav is the weight of the object, and that should just be mg (if the planet is the Earth) This part is g

15. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Kepler’s Laws 1 st Law: The orbits of the planets are elliptical, with the sun at one focus of the ellipse. a=Semi-major axis

16. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Kepler’s Laws 2nd Law: A line from the sun to a given planet sweeps out equal areas in equal times.

17. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Kepler’s Laws 3rd Law: The periods of the planets are proportional to the 3/2 power of the major axis length. Here is a formula: Radius of orbit (assuming circular instead of elliptical) Mass of central object – orbiting mass does not matter