Ch 8 Universal Gravitation

1. Ch 8 Universal Gravitation

2. Black hole- • an extremely massive object that can bend light back to the object

3. Centripetal acceleration • -acceleration toward the center of a circular path

4. Freefall— • accelerating downward b/c of an unbalanced gravitational force

5. General theory of relativity— • Einstein’s theory that mass causes space to be curved, accelerating bodies

6. Gravitational field— • the area around a mass that acts on other masses, causing them to be attracted to each other

7. Gravitational force— • an attractive force that exists between all objects

8. Inverse square law— • a relationship in which one variable is inversely proportional to the square of another variable

9. Kepler’s laws of planetary motion— • Laws that describe the motion of planets and satellites

10. Law of universal gravitation— • The attraction between two bodies depends on the masses of the two bodies and the distance between their centers

11. Newton’s second law— • the acceleration of a body is directly proportional to the net force on it and inversely proportional to its mass

12. Satellite— • a body that is in orbit around another body

13. Universal gravitational constant— • G- needed in calculating the gravitational force between 2 objects

14. Weightlessness- • the apparent loss of gravitational force on an object in orbit or in freefall

15. The force of gravity on a satellite, its weight, provides the centripetal force to maintain its circular motion. • A satellite farther from the earth has a larger velocity • The Velocity of a satellite is independent of its mass

16. Equation; the velocity a satellite must have to orbit the earth • __ • V = V² or V = g r • r

17. g = acceleration of gravity at distance r from the center of the earth • r is the average radius of its orbit from the center of the earth.

18. The mass of the satellite does not affect its orbital velocity. • The orbital velocity is independent of the mass of the satellite

19. A more massive satellite requires a greater centripetal force to keep it in orbit. • However, a more massive satellite also has a greater weight. • The greater weight provides the greater centripetal force.

20. Astronauts are weightless because?_____ • They and the satellite are in free-fall, accelerating toward the earth

21. 1. Calculate the velocity at which a satellite must be launched in order to achieve an orbit about the earth. Use 9.8 m/s² • As the acceleration of gravity and 6.5 X 10³ km as the earth’s radius. • V = gr __________________ • V = (9.8 m/s²) (6.5 X 106 m) • = 8.0 X 10³ m/s

22. 2. During the lunar landings, the command module orbited close to the moon’s surface while waiting for the lunar module to return from the moon’s surface. The diameter of the moon is 3570 km and the acceleration of gravity on the moon is 1.60 m/s². • a. at what velocity did the command module orbit the moon?

23. 2. During the lunar landings, • a. at what velocity did the command module orbit the moon? • V = gr • = (2.9 X 106 m²/s² • = = 1.7 X 10³ m/s • = 1.7 km/s

24. 2. During the lunar landings, the command module orbited close to the moon’s surface while waiting for the lunar module to return from the moon’s surface. The diameter of the moon is 3570 km and the acceleration of gravity on the moon is 1.60 m/s². • b.In how many minutes did the module complete one orbit?

25. 2. During the lunar landings, the • b. In how many minutes did the module complete one orbit? • b. V = 2 r t = 2  r = t V • = 6.6 X 10³s = 6.6 X 10³s 60 S/min • = 1.1 X 10² min

26. 3. Calculate the velocity at which a satellite orbits Jupiter. The acceleration of gravity on Jupiter is 5.8 X 10³ m/s² . The diameter of the planet is 1.422 X 10 5 km. • V = gr • V = (5.8 X 10³ m/s²)(7.11 X 107 m) • = 6.42 X 105 m/s = 642 km/s

27. Greeks used terms levity (rise) & gravity (fall)

28. Galileo & Newton- stated gravity to the force that exists between Earth & objects

29. Newton- stated same force exists between all bodies • Einstein- gave different & deeper description of the gravitational attraction

30. We Still do not know WHY things fall. (only how)

31. Early scientist watched the skies • Notices stars moved in regular paths • Planets (wanderers) had complicated paths • Astrologist claimed the motion of the bodies contolled events in life

32. Comets- erratic movement, appeared w/o warning, w/bright lights.- considered bearers of evil omens • It Took Galileo, Kepler, Newton & others to understand that the all of them follow the same laws that govern the motion of objects on Earth.

33. Tycho Brahe (1546-1601) • Was interested in astronomy After observing eclipse at 14. • Decided to learn how to make accurate prediction of astronomical events when a predicted planets in conjuncture occurred 2 days late.

34. Tycho Brahe • Studied throughout Europe for 5 years then set up observatory on island. (Believed Earth was center of Universe) • Next 20 years spend recording positions of planets & stars. • Moved to Prague where Kepler became one of his assistants.

35. Tycho Brahe • Made very accurate measurements of the positions of planets & stars which were used by Kepler to formulate his laws.

36. Kepler • Believed measurements on number, distance and motion of the planets could be explained with a sun-centered system using geometry & mathematics.

37. Kepler’s theories are no longer considered correct( still describe the behavior of every planet & satellite)

38. Kepler • Was driven to find the true paths of planets after finding that Tycho’s predictions were wrong by eight minutes of arc (1/4 the width of the moon). • Kepler’s Laws are now known to be the result of the conservation of energy and angular momentum.

39. Kepler’s laws • still apply to motion in any conic section (ellipse, parabola, hyperbola and circle. (the behavior of every planet and satellite) even though they are no longer considered correct.

40. Kepler’s laws • 1.The paths of the planets are ellipses with the center of the sun at one focus.

41. Kepler’s laws • 2.An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. Thus, planets move fastest when closest to the sun, slowest when farthest away.

42. Kepler’s laws • 3.The ration of the squares of the periods of any 2 planets revolving about the sun is equal to the ratio of the cubes of their avg distances from the sun.

43. Kepler’s laws • 3. Thus, if Ta & Tb are their periods and ra & rb their avg distances, • [T a ]² = [ r a ] ³ • [T b ] [ r b ]

44. Kepler’s Laws • Or The ration of the avg radius of a planet’s orbit about the sun, r cubed & the planet’s period, • T (the time for it to travel about the sun once) squared, • is a constant for all the planets. This law can be expressed as • or r³ = k • T²

45. Laws 1 & 2 apply to planet, moon or satellite individually • 3rd – movement of satellites about a single body (planets around sun) & compare distances and periods of the moon & artificial satellites around early.

46. Problem Solving • For preciseness keep at least 1 extra digit in your calculations until you reach the end. • You do not need to convert all units to meters & seconds- just use the same units throughout the problem

47. Problem Solving • For 3rd law- to find radium of the orbit- solve for the cube of the radius then take the cube root. • Use cube-root key or Yx or Xy. • Enter the cube of the radius- press the Yx key then enter 0.33333333 and press =

48. Jules Verne- (1828 – 1905) • Wrote about airplanes, submarines, guided missiles and space satellites, accurately predicting their uses.

49. In 1666, Newton • Used math to show that if the path of a planet were an ellipse then the force on the planet must vary inversely w/the square of the distance between the planet and the sun.

50. Newton • the force on the planet must vary inversely w/the square of the distance between the planet and the sun. • F= force: • α = is proportional to: • d = avg distance between the centers of the 2 bodies