1. Survey of the Universe Tom Burbine tburbine@mtholyoke.edu

2. Galileo Galilei (1564-1642) He was able to figure out answers to these arguments 1) Things in motion tend to remain in motion. 2) He used a telescope to see sunspots on the Sun and features on the Moon. 3) Galileo found that stars were more numerous and more distant than imagined

3. He also He discovered the moons of Jupiter and saw that they were orbiting Jupiter –Io –Europa –Ganymede –Callisto Proving that bodies could orbit other bodies besides the Earth

5. Galileo also found that Venus orbited the Sun

6. 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 Mass in metric system is usually measured in kilograms

7. 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 Also came up with calculus Isaac Newton (1642-1727)

8. Force Force – anything that can cause a body to change velocity Velocity – a speed in a particular direction

9. Gravity Gravity is a natural phenomenon by which objects with mass attract one another.

10. Newton http://www.youtube.com/watch?v=_q6CXni6yTE

11. Newton’s 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

12. Why do things on Earth not remain in motion?

13. Friction

14. Objects in orbit Because the planets are moving in elliptical orbits around the Sun and not straight lines, there must be a force acting on the planets This force is gravity

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

16. Acceleration a = ∆v/∆t Car is travelling at 10 m/s Increases its speed to 30 m/s over 5 seconds a = (30 m/s – 10 m/s)/5 seconds a = 4 m/s 2

17. Acceleration due to Earth’s gravity g = 9.8 m/s 2 If something is dropped, it will gain 9.8 m/s in velocity for every second it falls

18. Newton’s 2 nd Law Force = mass x acceleration Units of Force kg  m/s 2 = newton

19. Newton A Newton is equal to the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second per second

20. How much do you weigh? So much do you weigh Say your mass is 100 kg F = 100 kg x 9.8 m/s 2 F = 980 Newtons 9.8 m/s 2 is the acceleration of gravity on Earth This is the acceleration due to the Earth’s gravitational field

21. Newton’s 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. http://www.vshiksha.com/system/files/u1/pslvc6-rocket.jpg

23. Newton’s Universal Law of Gravitation Every mass attracts every other mass through the force called gravity Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses

24. Formula Newton came up with this formula Force is proportional to M 1 M 2 d 2 M 1, M 2 are the masses of the two objects d is the distance between the objects

25. If you want to calculate actual forces 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. assume all mass is concentrated in the center of a body

28. What is the attraction of two 100 kg people in the same 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

29. F = G M 1 M 2 d 2 The value of G was determined by Henry Cavendish between 1797-1798 G = 6.67 x 10 -11 m 3 /(kg  s 2 ) http://blogs.howstuffworks.com/2009/04/13/diy- calculate-the-gravitational-constant-like-cavendish- did/http://blogs.howstuffworks.com/2009/04/13/diy- calculate-the-gravitational-constant-like-cavendish- did/ http://www.makingthemodernworld.org.uk/learning_modules/maths/06.TU.02/illustrations/06.IL.09.gif

30. Any Questions?