1. What is it that we need to understand? 1.How we can use Newton’s theory of gravitation to find the masses of planets, stars, and galaxies. 2.Energy conservation and some of its implications. 3.How gravitational potential energy is liberated when a massive object gets smaller, and where this energy goes. 4.How mass can be converted into energy in other forms. 5.How angular momentum conservation affects the rate of spin as the radius from the rotation axis changes. 6.Quantized energy levels of atoms and molecules, and the implications for spectra. 7.Doppler effect: spectral line shift and/or broadening. 8.Effect of temperature on spectrum.

2. Conservation of Energy: 1.We can formulate the laws of nature as we now know them in terms of conservation laws. 2.The most important of these is the conservation of energy. 3.It says that energy can be transformed from one type to another by physical processes, but it can neither be created nor destroyed. 4.A car at rest at the top of a hill, given a tiny push, can appear to gain energy as it barrels down the hill. 5.But we say instead that it merely converts its gravitational potential energy into kinetic energy of motion in this process. 6.If the car runs back up another hill, it should stop at the same height where it began. This would convert the kinetic energy of its motion back into gravitational potential energy.

5. Conversion of Gravitational Potential Energy into Heat: 1.The example of the car may not seem to have anything to do with astronomy, but it is actually not that far off base. 2.Imagine a star that is held up against gravity by the immense pressure of its hot gases in the central region where heat is being generated through nuclear reactions (we will come back to this presently). 3.Now suppose that the nuclear reactions run out of fuel and therefore cease. 4.Without the pressure they generate, the star will collapse under its gravitational force. 5.Just like the car, all the little chunks of the star will fall toward the star’s center, converting gravitational potential energy into kinetic energy of motion.

6. Nuclear reactions in the stellar core generate heat energy, which produces the pressure that supports the star against gravity.

7. When the nuclear fuel gives out, the pressure support is reduced, and the star collapses inward.

8. The gases rushing inward toward each other collide, and convert the energy of ordered, inward motion into heat, which creates the additional pressure necessary to support the star at a smaller radius.

10. What is it that we need to understand? 1.How we can use Newton’s theory of gravitation to find the masses of planets, stars, and galaxies. 2.Energy conservation and some of its implications. 3.How gravitational potential energy is liberated when a massive object gets smaller, and where this energy goes. 4.How mass can be converted into energy in other forms. 5.How angular momentum conservation affects the rate of spin as the radius from the rotation axis changes. 6.Quantized energy levels of atoms and molecules, and the implications for spectra. 7.Doppler effect: spectral line shift and/or broadening. 8.Effect of temperature on spectrum.

11. Conversion of mass into energy within a star: 1.Before Einstein, people believed in the conservation of mass. 2.But Einstein suggested that the conservation of energy was the most fundamental law, and that mass was just one particular form of energy. 3.Einstein’s famous equation E = mc 2 tells us how much energy is stored in a mass m. 4.In a star like the sun, through a sequence of reactions, hydrogen atoms are converted into helium atoms, and in this process a small fraction (0.7%) of the mass of the original hydrogen atoms is converted into energy in the form of heat and radiation (light). 5.The sun converts 600 million tons of hydrogen into 596 million tons of helium, and a lot of energy, every second.

12. We should all be familiar with the con- version of mass into energy. Here the same process that takes place in the center of the sun is used to liberate energy in an un- controlled fashion.

13. These images and diagrams represent a 3 billion dollar facility in California that generates energy from mass, as in the sun, using lasers and lots and lots of very high-tech gear. The process is controlled, well sort of.

14. These images and diagrams represent a 3 billion dollar facility in California that generates energy from mass, as in the sun, using lasers and lots and lots of very high-tech gear. The process is controlled, well sort of.

15. What is it that we need to understand? 1.How we can use Newton’s theory of gravitation to find the masses of planets, stars, and galaxies. 2.Energy conservation and some of its implications. 3.How gravitational potential energy is liberated when a massive object gets smaller, and where this energy goes. 4.How mass can be converted into energy in other forms. 5.How angular momentum conservation affects the rate of spin as the radius from the rotation axis changes. 6.Quantized energy levels of atoms and molecules, and the implications for spectra. 7.Doppler effect: spectral line shift and/or broadening. 8.Effect of temperature on spectrum.

16. Momentum conservation: 1.Although mass is not conserved, in the absence of applied forces, momentum is. 2.Linear momentum, the momentum associated with linear motion, is just the mass, m, of the object multiplied by its velocity, v. Thus momentum is mass times velocity, or mv 3.The conservation of linear momentum can be easily observed on a pool table.

17. Fig. 6.6: Momentum conservation demonstrated on a pool table No external force acts on the combined system consisting of the two pool balls, and hence the combined momentum of the pair does not change. (An “elastic” collision is shown.)

18. Angular Momentum conservation: 1.Angular momentum is the momentum associated with spinning motion. 2.Angular momentum is conserved in the absence of applied forces. 3.Forces that act to alter spinning motions, and to change angular momentum, are called torques (twisting forces). 4.The angular momentum of a body of mass m executing a circular motion, with speed v, about an axis at a radius r is equal to the product m×v×r 5.In the absence of torques, a reduction of the radius of this spinning motion by a factor of 2 must therefore cause the speed v to double, and both these changes make the number of rotations per second quadruple.

20. This behavior, a result of the conservation of angular momentum, is related to Kepler’s second law (equal areas are swept out in equal times)

22. An Astronomical Example of Angular Momentum Conservation: 1.If the sun formed out of a spinning cloud of gas, then as this gas cloud contracted under gravity, it must have spun faster and faster (unless acted upon by an external torque). 2.The faster and faster spinning of the gas would have created centrifugal forces that would act in the opposite sense from the gravitational forces, reducing the tendency of the gas cloud to collapse further. 3.For the protosun to collapse to form the sun, it may be that a torque must be provided to reduce its spinning. 4.When we come to discuss the formation of the solar system, we will see how this might have happened.