Chapter 5 Newton s Universe

Transcription

1 Chapter 5 Newton s Universe Lecture notes about gravitation Dr. Armen Kocharian

2 Units of Chapter 5 The Idea of Gravity: The Apple and the Moon The Law of Gravity: Moving the Farthest Star Gravitational Collapse: The Evolution of the Solar System Gravitational Collapse: The Deaths of More Massive Stars

3 Units of Chapter 5 The Newtonian Worldview: A Democratic, Mechanical Universe Beyond Newton: Limitations of Newtonian Physics

4 The Idea of Gravity: The Apple and the Moon Newton saw a commonality between the motion of the moon and the motion of a falling apple. From this image, we can t really tell what it might be.

5 The Idea of Gravity: The Apple and the Moon But if we think about the direction of the acceleration of the moon the direction of its change in velocity we see it points towards the Earth just as the apple s acceleration does.

6 The Idea of Gravity: The Apple and the Moon How can the same force make one object move in a circle and another fall down? Imagine throwing an apple horizontally. The faster you throw it, the farther it goes.

7 The Idea of Gravity: The Apple and the Moon Now take this to the extreme, remembering that the earth is a sphere. If the apple goes horizontally fast enough, it will be in orbit falling all the time.

8 The Law of Gravity: Moving the Farthest Star Not only does gravity keep the moon in its orbit around the earth; it also keeps the planets in their orbits around the sun, and the stars in their paths. But what about objects that are not astronomical in size? Does gravity have an effect on them as well?

9 The Law of Gravity: Moving the Farthest Star Yes, it does; there is even an experiment typically done in an undergraduate physics lab that measures the gravitational attraction between two small spheres.

10 The Law of Gravity: Moving the Farthest Star Experimentation shows that the gravitational force between masses is larger if the masses are larger, and smaller if the masses are farther apart. Newton put all this together in his law of gravity.

11 The Law of Gravity: Moving the Farthest Star The gravitational force between two masses is proportional to the product of the masses and inversely proportional to the square of the distance between them. F α m 1 m 2 / d 2 Using metric units, the exact expression is: F = m 1 m 2 / d 2

12 The Law of Gravity: Moving the Farthest Star So, the force doubles if either of the masses doubles, and is divided by 4 if the separation doubles. Think about yourself standing on the earth. What is the distance between you and the earth? It s zero, at least for the part you re standing on, but what about the opposite side?

13 The Law of Gravity: Moving the Farthest Star In order to figure this out, Newton had to invent calculus. When he did, he found that distances should be measured from the centers of objects. Since the radius of the earth is about 6500 km, that s how far away from it you are.

14 The Law of Gravity: Moving the Farthest Star As you move away from the center of the earth, the gravitational force on you decreases, although it is never really zero.

15 The Law of Gravity: Moving the Farthest Star But if that s true, why do astronauts experience weightlessness? The answer is that, although the gravitational force on them is not zero, they are falling around the earth. They appear to be weightless because they are in free fall.

16 The Law of Gravity: Moving the Farthest Star This kind of weightlessness can be experienced on earth, but only until you hit bottom!

17 Gravitational Collapse: The Evolution of the Solar System Gravity also plays a major role in the formation, lifetime, and ultimate end of stars and planets. We believe that stars are formed by the gravitational collapse of huge interstellar clouds of gas and dust, and have now seen evidence of star formation in such clouds.

18 Gravitational Collapse: The Evolution of the Solar System Our solar system began as such a cloud. As it collapsed, the speed of the gas molecules became larger and larger the cloud was heating up. Meanwhile, it was also rotating creating such a cloud with no rotation is rather like trying to balance a pencil on its tip and the outer regions flattened into a disk.

19 Gravitational Collapse: The Evolution of the Solar System The center of the cloud continued to collapse and heat; eventually it reached a temperature of millions of degrees hot enough for hydrogen fusion to take place. Meanwhile, the heat and light from the forming sun blew away the gas and dust that had not coalesced into planets, asteroids, meteors, and comets.

20 Gravitational Collapse: The Evolution of the Solar System Once fusion began, the sun settled down as a stable star.

21 Gravitational Collapse: The Evolution of the Solar System In about another 5 billion years, the sun will exhaust the hydrogen in its core. The core will begin to collapse and become even hotter. Fusion will take place in a shell surrounding the core until the core becomes hot enough to fuse helium. As this goes on, the outer layers of the sun heat and expand, eventually engulfing the earth.

22 Gravitational Collapse: The Evolution of the Solar System Finally, the sun exhausts all its fuel; the outer layers blow away and only the core is left, no longer generating energy. Gravity takes over once again, and it continues to contract until it is as small as quantum mechanics will allow it to be about the size of the earth, and incredibly dense. A star in this stage of its existence is called a white dwarf. It will gradually cool off and become invisible.

23 Gravitational Collapse: The Deaths of More Massive Stars A star must have at least 10% of the sun s mass in order for fusion to start; if its mass is much more than 100 times the sun s mass, it will blow apart very quickly. In between, a star s life cycle is determined primarily by its mass. Stars up to about ten times the sun s mass have a life cycle similar to the sun s, ending up as white dwarfs.

24 Gravitational Collapse: The Deaths of More Massive Stars Larger stars suffer a much different fate. They go through multiple cycles of core collapse and heating, fusing in turn helium, carbon, and all the way up to iron. But now the star is in trouble iron will not fuse. The core is no longer generating energy, and gravity takes over once again.

25 Gravitational Collapse: The Deaths of More Massive Stars The star is so massive, and the collapse so fast the iron core only lasts for about 1 second that the star collapses all at once, causing an explosion called a supernova that blasts the rest of the star into space. The last supernova that occurred in our galaxy happened in 1604; it was bright enough to be seen in the daytime.

26 Gravitational Collapse: The Deaths of More Massive Stars In 1987, a supernova occurred in a galaxy near ours; even at that great distance, it was visible to the naked eye. Below are before and after photographs of the galaxy.

27 Gravitational Collapse: The Deaths of More Massive Stars About 10% to 20% of the star remains after the explosion; this remnant collapses quickly. The gravitational force is strong enough that not only are atoms not able to exist, nuclei can no longer exist either. The entire star becomes a solidly packed ball of neutrons, called a neutron star.

28 Gravitational Collapse: The Deaths of More Massive Stars Neutron stars are incredibly dense a neutron star with the mass of the sun would be about 10 km in diameter! The star s rotation also speeds up as the collapse occurs, just as a skater s rotation speeds up as she pulls her arms in. Neutron stars typically rotate between 1 and 1000 times per second.

29 Gravitational Collapse: The Deaths of More Massive Stars This spinning, along with very large magnetic fields, produces very intense radiation, which appears to blink on and off as the star rotates.

30 Gravitational Collapse: The Deaths of More Massive Stars If the original star is more massive than about 30 times the sun s mass, even a neutron star cannot survive the star collapses all the way to a single point. It is then called a black hole, because nothing, not even light, can escape its gravitational pull if it gets too close.

31 The Newtonian Worldview: A Mechanical Universe Before Newton, the Western worldview was a combination of medieval Christianity, earth-centered astronomy, and Aristotle s physics. All were believed to act together, as humankind fulfilled the purpose of Creation.

32 The Newtonian Worldview: A Mechanical Universe Since the Middle Ages, astronomy and physics have contradicted earth-centered astronomy and Aristotle s physics. The earth is no longer believed to be at the center of the universe, and is typical rather than special. This lack of hierarchy had cultural effects as well. The divine right of kings was challenged; Martin Luther split from the Catholic Church.

33 The Newtonian Worldview: A Mechanical Universe Newton and his contemporaries believed in God; they assumed there were two realities, the material world and the spiritual world. Newton s laws implied a perfectly predictable universe, called the mechanical universe. Everything in it was thought to be completely predictable much to the frustration of those who believed in free will!

34 The Newtonian Worldview: A Mechanical Universe Our present understanding of the universe makes it rather less predictable, but the reconciliation of the material and the spiritual worlds remains an issue today.

35 Beyond Newton: Limitations of Newtonian Physics Newtonian physics passed every test of its validity from the time it was formulated until the late 19 th century. It seemed infallible. Then physicists started exploring very high speeds, enormous gravitational forces, vast distances, and tiny distances, and Newtonian physics did not give correct predictions for any of them.

36 Beyond Newton: Limitations of Newtonian Physics Three new theories were developed in the 20 th century to address these shortcomings. Special relativity deals with extremely fast speeds, close to the speed of light. General relativity deals with large gravitational fields and vast distances. Quantum physics deals with the very small.

37 Beyond Newton: Limitations of Newtonian Physics Each of these theories, when applied in situations where Newtonian physics is valid, gives the same result as Newtonian physics does the differences are too small to detect. Therefore, we continue to use Newtonian physics when we can.

38 Beyond Newton: Limitations of Newtonian Physics This diagram shows the regions of validity of the different theories.