Gravity

1. Gravity

2. Review Question What are Kepler’s laws of planetary motion?

3. Kepler’s Laws Planets orbit Sun in elliptical orbits Line drawn from planet to Sun sweeps out equal areas in equal times The cube of the semimajor axis is equal to the square of the sidereal period

4. Review Question What time of year does the Earth move the fastest in its orbit around the Sun?

5. Review Question Although the Moon is in synchronous rotation, we can actually see 59% of its surface from the Earth. Explain why this is the case using Kepler’s laws.

7. Kepler’s Laws can correctly predict the future positions of the planets Everyone used Kepler’s laws to predict the positions of the planets, even those that continued to believe the Sun orbited the Earth. Kepler offered no explanation as to why the planets followed these laws.

8. Newton

9. Speed Example: a car moving at 60 miles/hour

10. Velocity Velocity is speed and direction Example: a car moving 60 miles/hour due west.

11. Speed vs. Velocity A race car may move at a constant speed around a race track but its velocity is changing because the direction of motion is changing.

12. Newton’s first law of motion The Law of inertia An object at rest or in motion will stay at rest or in motion with a constant velocity unless acted on by an outside force.

13. Discussion Using Newton’s first law of motion why is it a good idea to be wearing a seatbelt in case of a car accident?

14. Acceleration Acceleration is the rate of change in the velocity of an object. An acceleration can mean a speeding up, a slowing down, or simply a change in the direction of motion with no change in speed.

15. Units of acceleration

16. Example A car accelerates from a stop light at 10 m/sec2 following a straight path. So, at time t = 0 the car’s speed is 0 m/sec. After one second of acceleration, the car’s speed is 10 m/sec (velocity 10 m/sec south). After two seconds, the car’s speed is 20 m/sec.

18. Discussion After one minute of accelerating at 10 m/sec2 at what speed is the car moving?

19. Newton’s second law of motion Force = mass  acceleration If the same force is applied to an object with half the mass, the acceleration of that object will be twice as much.

20. Discussion Using Newton’s 2nd law of motion, explain why you can throw a baseball farther than a shot-put.

21. Discussion If I pull on either side of the a pen as hard as I can, what is the net force I exert on the pen?

22. Discussion Which will do more damage to your car. Hitting a brick wall at 60 miles per hour which does little damage to the brick wall. A head on collision with another car traveling at 60 miles per hour in the opposite direction with the same mass such that both cars immediately come to rest.

23. Newton’s third law of motion For any force there is always an equal and opposite reaction force

24. Example: Walking In order to walk, you have to push, with your foot, back on the ground. The ground pushes back on your foot with an equal and opposite force.

25. Discussion If I put my car in neutral and try to push it with a force F, according to Newton’s third law my car pushes back with the same force. Therefore, the car should never move. Is Newton wrong? Why or why not?

26. Discussion You’re an astronaut working on the Hubble Space Telescope (HST) with a number of tools. You lose your grip and start floating away from the space shuttle. How do you get back to safety?

27. Rocket Power A rocket engine works by accelerating rocket fuel out the back of the rocket. A force is required to accelerate the exhaust, which applies an equal force in the opposite direction on the rocket.

28. Discussion Consider an object in uniform circular motion. That is, an object traveling in a circle with a constant speed. Is there a force acting on this object? Why or why not?

29. Discussion Consider an object in uniform circular motion: that is, an object traveling in a circle with a constant speed. How is the velocity of the object changing and how must the force on the object be directed to change its velocity in this way?

31. Discussion Is there a force acting on the Moon? How can you tell?

32. The Moon is falling The nearly circular orbit of the Moon is constantly accelerating toward the Earth. The Moon is constantly falling toward the Earth.

33. What was Newton thinking? Consider tossing a baseball. It travels a certain distance before it hits the ground. Now image throwing it as hard as you can. It travels further before it hits the ground. Now imagine throwing it even harder.

35. Discussion If I swing a ball in a circle over my head with a short string and a long string with the same speed, which ball has the greater force acting on it? Explain why.

39. Force on the planets depends on distance The higher the speed an object moves in a circle the greater acceleration and the force needed to hold it in that circle. The force on the planets closest to the Sun has to be greater than that on the planets further away.

40. Newton’s Universal Law of Gravity • Every mass attracts every other mass through a force called gravity • The force is directly proportional to the product of their masses • The force is inversely proportional to the square of the distance between them

42. Discussion Consider the gravitational force between two objects with mass M1 and M2 separated by a distance d. How would the gravitational force change if the distance between them increases to 3  d. How will it change in the distance in decreased to 0.1  d?

43. Why the square of the distance? An inverse square central force law is required to get orbits that are conic sections, i.e. orbits that are elliptical.

45. Why is the force of gravity proportional to the mass? All objects, regardless of their mass, fall with the same acceleration. Because F = ma, To keep the acceleration constant, the force must vary proportional to the mass.

46. Discussion Newton’s third law tells us that the force of the Sun on the Earth is the same as the force of the Earth on the Sun. Why then does the Earth orbit the Sun instead of the other way around?

47. Gravitational forces between spherical masses d The distance to use is the distance between the two spheres centers.

48. Discussion Suppose a new planet is discovered out in the Kuiper belt. This planet has twice the mass of the Earth but is also twice the radius. Is the surface gravity of this new planet greater than, less than or the same as the surface gravity of the Earth?

49. Discussion You dig a very deep mine shaft. As you get closer to the center of the Earth, does your weight increase or decrease? Why? (Hint: consider what the force of gravity will be at the very center of the Earth.)

50. Escape Velocity If an object is thrown up with a high enough velocity it will leave Earth forever. For Earth this velocity is about 11 km/sec.