1. Announcements Quiz #1 is this Friday. Please pick up study guide Readings: Chapters 1-7 in Ferris Lectures 1-8 (don’t forget planetarium) Planetarium EC show moved to next Monday Please pick up HW #1 Please turn off all electronic devices Don’t forget to sign the attendance sheet

2. a)The meter b)The pound c)The inch d)The kilogram e)The Newton What is the metric unit of force?

3. Lecture 8: Gravity Astronomy 1143 – Spring 2014

4. Key Ideas: Gravity Always attractive Binds gas into stars; stars, gas, dark matter into galaxies Works to slow the expansion of the Universe Newton’s Law of Universal Gravitation force of gravity depends on mass and inversely on distance

5. Key Ideas Gravitational Force used to measure amount of mass Example of Methods Circular velocity Escape velocity Freely falling in gravity resembles weightlessness everything falls at the same rate

6. Universal Mutual Gravitation Isaac Newton, in his Principia, formulated the Law of Universal Mutual Gravitation: Gravity is an Attractive force: Works to bring massive objects closer together. Gravity is a Universal force: Works everywhere in the Universe. Gravity is a Mutual force: Works between pairs of massive objects.

7. Gravitational Force The Force of Gravity between any two objects depends only upon: The masses of the two objects: More massive objects exert a stronger force. The distance between them: The force gets stronger as they move closer. The force gets weaker as they move apart. It does not depend on the shapes, colors, or compositions of the objects.

8. The Law of Universal Gravitation The force of gravitational attraction between any two massive bodies is proportional to their masses and inversely proportional to the square of the distance between their centers. Example of an “Inverse Square Law Force”

9. Newton’s Gravitational Force Law F = Force of Gravity M 1 = Mass of the first object M 2 = Mass of the second object d = Distance between their centers G = “Gravitational Force Constant”

10. M2M2 M1M1 M2M2 M2M2 d d/2 2d The Gravitational Force is inversely proportional to the square of the distance.

11. M1M1 2M 1 M2M2 d 2M 2 The Gravitational Force is proportional to the masses.

12. The Gravitational Force Constant The force constant, G, is a number that gives the size of the gravitational coupling between two massive objects. G is very small. In metric units: G=6.67  10 –11 Newtons meter 2 / kilogram 2 G=6.67  10 –11 meter 3 / kilogram s 2 G has to be measured experimentally.

14. Calculating the Mass of the Sun Let’s use the acceleration needed to hold the Earth in a circle to determine the mass of the Sun To have a circular orbit, Earth must have an acceleration of Therefore, force pulling on Earth is

15. r

16. Calculating the Mass of the Sun Force is force of gravity therefore

17. Calculating the Mass of the Sun What is the speed of the Earth in its orbit around the Sun? From HW  1.072x10 5 km/hr

18. Calculating the Mass of the Sun speed of Earth around Sun radius of Earth’s orbit Gravitational force constant

19. Calculating the Mass of the Sun

20. Escape Velocity Minimum velocity to escape from a gravitating body (go up and never come down): M is the mass of the object you are escaping r is the distance between the centers Does not depend of mass of object that is escaping

21. Calculating escape velocity from Earth G=6.67x10 -11 m 3 /kg s 2 = 6.67x10 -11 N m 2 / kg 2 M=5.97x10 24 kg r=6378 km

22. Escaping from Other Planets Sun617.5 km/s Mercury4.3 km/s Venus10.3 km/s Earth11.2 km/s Moon2.4 km/s Mars5.0 km/s Jupiter59.5 km/s Saturn35.6 km/s Uranus21.2 km/s Neptune23.6 km/s

23. Mass-o-meter The motions that we see in the Universe are very informative about the force of gravity and therefore the amount of matter pulling on a star, planet, etc. If we see orbits – how much matter is needed to keep stars/planets on those orbits? Mass of Sun If we see stars or gas confined to a galaxy – how much matter is needed to keep them? Highest speeds have to be < escape velocity Mach 1 = 0.34 km/s

24. Gravity?

25. “Zero Gravity” doesn’t exist It is a misnomer (though a very descriptive one) to refer to astronauts or spacecraft as experiencing “weightlessness” or “zero gravity” Law of Universal Gravity: Force of Gravity is never zero, no matter how far away you are

26. Feeling Earth’s Gravity

27. Your weight in Space Weight is defined as the force of gravity on an object How much less do you weigh on the shuttle? d earth =6378 km d shuttle =6378+350 km=6728 km

28. Your weight in Space If you weighed 200 lbs on Earth, you would weigh 180 lbs on the space shuttle

29. Force of Gravity still working The force of gravity is truly long-range. This is not true for all forces (such as the strong nuclear force) Collectively, force of many objects can be quite powerful – escape velocity of Milky Way is 600 km/s Everything in the Universe is feeling the force of gravity!

30. Why do you float in space? The force of gravity from the Earth is still pulling on you in orbit (in fact, it’s what keeps the shuttle/space station in orbit) The force of gravity is also pulling on every other part of the spacecraft No air resistance, no surfaces of planets to add an extra force Everything is falling at the same rate, therefore nothing falls relative to each other

31. Everything falling

32. Gravitational Accelerations Acceleration because of Earth’s gravity does not depend on mass of object

33. Weightlessness Movies

34. Falling Objects Everything falls at the same rate in a gravitational field was established by Galileo Took Newton’s laws to understand how the laws of physics explained this Einstein used this idea to lead him to General Relativity

35. Mr Galileo was correct

36. Airplane Weightlessness

37. “Vomit Comet” in Action

38. Weightlessness Movies

39. a)The Gravitational Force Constant b)The speed of light c)The distance between Earth and Sun d)The fifth day of the week e)The metric unit of distance What does G stand for?

40. a)There is no gravitational force b)More massive objects fall more quickly c)The gravitational force from the Earth on objects does not depend on their mass d)Your weight is heavier than it is on Earth e)Everything is falling at the same rate In a space shuttle in orbit

41. a)Star 1 and Star 3 separated by 5 AU b)Star 2 and Star 3 separated by 1 AU c)Star 1 and Star 2 separated by 1 AU d)Star 1 and Star 3 separated by 1 AU e)Star 1 and Star 3 separated by 5 AU Star 1 has a mass of 10 solar masses, Star 2 has a mass of 5 solar masses and Star 3 has a mass of 1 1 solar mass. In which setup is the gravitational force between two stars the largest?

42. a)Sun’s pull on Jupiter is greater b)They are the same c)Jupiter’s pull on Saturn is greater d)You need more information e)The answer depends on the distance between the Sun and Jupiter How does the size of the gravitational force of the Sun on Jupiter compare to the force of Jupiter on the Sun?

43. a)Sun b)Jupiter c)They are the same d)You need more information e)There is no acceleration, just a circular orbit Which has the larger acceleration from the other’s gravitational force, the Sun or Jupiter?

44. Force of Gravity between A & B Equal & Opposite Force of Gravity from Earth on A bigger than Force of Gravity from Earth on B A B