1. Astronomy 100 Tuesday, Thursday 2:30 - 3:45 pm Tom Burbine tburbine@mtholyoke.edu www.xanga.com/astronomy100

2. Help Desk There is an Astronomy Help Desk in HAS 205. It will be open from Monday through Thursday from 7-9 pm.

3. Another Homework Assignment (Due Thursday March 3 rd ) Make up a test question Multiple Choice A-E possible answers 1 point for handing it in 1 point for me using it on test

4. Homework assignments due today (or it is late) Two due today One is from this sheet that I handed out Two calculations Worth 1 HW point I will discuss them next class

5. 2 nd HW assignment due today (or it is late) I want you to pick an element Write its symbol Is it a solid, metal, or gas? Atomic Number Atomic Mass Its isotopes What this element is used for? http://www.webelements.com/ Worth 1 HW point

6. Next assignment Handed out today More calculations Due Feb. 24 (Thursday) by 3:45 pm You need to show work to get credit

7. PRS You need to make sure that you have a clicker registered And your name appears on screen If your name does not appear onscreen, I don’t know you are when you use the clicker

8. Monkey Drop Experiment A hunter shoots at a monkey in the tree The monkey drops the second that the hunter pulls the trigger What happens?

9. Show video http://www.ap.stmarys.ca/demos/content/mechanics/monkey_and_hunter/monkey_and_hunter.html

10. So what is happening The monkey and the bullet are accelerating at the same speed downwards g = 9.8 m/s 2 = acceleration due to gravity Objects fall faster by 9.8 m/s with every second Even though the bullet has a velocity in the horizontal direction, it is also moving downwards in the vertical direction

11. Acceleration Acceleration is when your velocity is changing Velocity not changing, no acceleration

12. Difference between mass and weight Mass is the amount of matter in your body Weight is the amount of force acting on your body So on the Moon, you would have the same mass as on Earth but weigh less on the Moon since the Moon is less massive than Earth

13. Who came up with the first understanding of how gravity and forces really work?

14. Isaac Newton (1642-1727)

16. Supposedly saw an apple fall to the ground He then understood that gravity was universal, meaning it affected both the planets and us on Earth Came up with 3 Laws of Motion Isaac Newton (1642-1727)

17. 1 st Law In the absence of a net (overall) force acting upon it, an object moves with a constant velocity An object at rest remains at rest An object in motion tends to remain in motion unless a force is acting upon it

18. 2 nd Law Force = mass x acceleration Units of Force kg  m/s 2 = newton So much do you weigh Say your mass is 100 kg F = 100 kg x 9.8 m/s 2 F = 980 Newtons

19. Show video

20. 3 rd Law For any force, there is an equal and opposite reaction force Gravity is holding you on the ground The ground is also pushing back up on you with the same amount of force

22. Conservation of Momentum

23. Conservation of Angular Momentum Angular momentun = m x v x r M = mass V = velocity R = radius In the absence of a net torque (twisting force), the angular momentum of a system remains constant

25. Universal Law of Gravitation Every mass attracts every other mass through the force called gravity Newton came up with this formula F = G M 1 M 2 d 2 M 1, M 2 are the masses of the two objects d is the distance between the objects G = constant = 6.67 x 10 -11 m 3 /(kg  s 2 )

26. So what should you know about this formula F = G M 1 M 2 d 2 The force of attraction between any two objects is directly proportional to the product of their masses The force of attraction between two objects decreases with the square of the distance between their centers G is a very small number

27. What is the attraction of two people in this room? F = G M 1 M 2 d 2 Say their masses are both 100 kg Their distances are 10 meters apart F = 6.67 x 10 -11 m 3 /(kg  s 2 ) * 100*100 kg 2 /(10*10 m 2 ) F = 6.67 x 10 -9 N = 0.0000000067 N Remember the person weighs 980 N

28. PRS question F = G M 1 M 2 d 2 How would the force between the two people change if they were only 5 meters apart instead of 10 meters? A) Stay the same B) Double (Increase by a Factor of 2) C) Quadrupul (Increase by a Factor of 4) D) halve (decrease by a factor of 2)

29. PRS question F = G M 1 M 2 = G M 1 M 2 = 4 G M 1 M 2 (d/2) 2 d 2 /4 d 2 How would the force between the two people change if they were only 5 meters apart instead of 10 meters? A) Stay the same B) Double (Increase by a Factor of 2) C) Quadrupul (Increase by a Factor of 4) D) halve (decrease by a factor of 2)

30. Can you use this formula to calculate acceleration of gravity? F = M 2 a = G M 1 M 2 you are M 2 d 2 M 1 is the Earth’s radius a = G M 1 d is the Earth’s diameter d 2 a = 6.67 x 10 -11 m 3 /(kg  s 2 ) * (6.0 x 10 24 kg) (6.4 x 10 6 m) * (6.4 x 10 6 m) a = 9.8 m/s 2

31. Escape velocity Velocity above this will allow an object to escape Earth’s gravity v = square root[(2 x G x M)/R] v = square root[(2 x 6.67 x 10 -11 m 3 /(kg  s 2 ) x (6.0 x 10 24 kg)] (6.4 x 10 6 m) v = square root [1.25 x 10 8 m 2 /s 2 ] v = 11.2 x 10 3 m/s = 11.2 km/s

32. Show animation

33. Why do we have tides?

35. Remember Rock is stretching too However, water is easier to stretch than rock

36. Force due to Moon on side closest to Earth F = G M 1 M 2 d 2 F = 6.67 x 10 -11 m 3 /(kg  s 2 ) * (6.0 x 10 24 kg) * (7.4 x 10 22 kg) (3.84 x 10 8 m) * (3.84 x 10 8 m) F = 2 x 10 20 N

37. Force due to Moon on side farthest from Earth F = G M 1 M 2 d 2 F = 6.67 x 10 -11 m 3 /(kg  s 2 ) * (6.0 x 10 24 kg) * (7.4 x 10 22 kg) (3.904 x 10 8 m) * (3.904 x 10 8 m) F = 1.94 x 10 20 N Difference is 6 x 10 18 N

38. Is the force due to the Sun stronger or weaker on the Earth? F = G M 1 M 2 d 2 F = 6.67 x 10 -11 m 3 /(kg  s 2 ) * (6.0 x 10 24 kg) * (1.99 x 10 30 kg) (1.5 x 10 11 m) * (1.5 x 10 11 m) F = 3.54 x 10 22 N This is approximately 184 times stronger than the force due to the Moon

39. PRS Question Why aren’t the tides due mainly to the Sun than the Moon? A) they are mainly due to the Sun B) the difference in the Sun’s pull on the different sides of the Earth is smaller than the Moon’s C) the forces due to the Moon and Sun contribute equally to the tides D) the tides are not due to forces from either the Sun or the Moon

40. PRS Question Why aren’t the tides due mainly to the Sun than the Moon? A) they are mainly due to the Sun B) the difference in the Sun’s pull on the different sides of the Earth is smaller than the Moon’s C) the forces due to the Moon and Sun contribute equally to the tides D) the tides are not due to forces from either the Sun or the Moon

41. What is the difference in forces on the two sides of the Earth? F = G M 1 M 2 d 2 F = 6.67 x 10 -11 m 3 /(kg  s 2 ) * (6.0 x 10 24 kg) * (1.99 x 10 30 kg) (1.50 x 10 11 m) * (1.50 x 10 11 m) F = 3.53924 x 10 22 N (far side of Earth) F = 3.53954 x 10 22 N (near side of Earth) Difference due to Sun= 3 x 10 18 N Difference due to Moon = 6 x 10 18 N

42. When Sun and Moon are pulling in same direction, strongest tides

43. When Sun and Moon are pulling in perpendicular directions, weakest tides

45. Questions?