## Lecture Notes:

Day 17, March 11, 1997.
• INERTIA, CURVATURE OF SPACE AND TIME, AND LIGHT

The quiz on March 20 will cover chapters 15, 4,5,6,7
Review questions to look at:

Chapter 4: 1,4,6,7,9
Chapter 5: 3,4,5,7,10
Chapter 6: 2.3.4.6.7.8.9
Chapter 7: 1,2,5,10 The optional projects are due on April 29.

Comet Hale-Bopp is getting to be quite spectacular in the morning, with two tails, a broad dust tail and a sharp, narrow gas tail. It would be a fine topic for an observing project: for example, take photos with a tripod and high speed film on a regular basis to show how it changes from day to day.

Hale Bopp has a period of 4200 years; it is very large as comets go: 10 km by 40 km which is bigger than Halleys comet. It will be closest to the earth on March 22 when it comes within 1.3 au of the earth which is 197 million km. On April 1, the comet comes closest to the sun (reaches perihelion) at which time it will be 0.914 au from the sun, zipping along at 44 km/sec

• INERTIA

Inertia is characterized by Newton's first law of motion, F = Ma, which may also be written a = F/m(inertial). Alternately, change (which is acceleration) equals a force acting on an object divided by the resistance to that force which is inertia or inertial mass. Inertial mass may be defined as that property of matter that resists change.

We did some inertial games in class again today. Kim hit Aaron in the stomach with a hammer when he was lying on his back with a heavy weight on his stomach. Aaron broke a cement block on Kims stomach with a sledge hammer while he was lying on a bed of nails. (Thank God for inertia, both were heard to mutter!)

Curvature of space-time is responsible for our experiences of gravity, which was (incorrectly) described by Newton as a force F = mMG/R^2 where m and M are gravitational masses. Gravitational mass may be defined as "that property of matter that produces a gravitational force of attraction".

Galileo showed that, if one eliminates the effect of the air, all objects on the earth fall with the same acceleration. He dropped fat cats and skinny cats from the leaning tower of Pizza and discovered that they all reached the ground at the same time as the anchovies.

Combining the equations for inertia and gravitational force we get a = F/m = m* M* G/r^2m where m and M are gravitational masses or a = MG/R^2 times[ m/m]. The equation for acceleration only works if m/m = 1 since only then is the acceleration of objects independent of their mass. Newton did not know why these two kinds of mass were equal; it was strange and puzzling because they refer to two entirely different experiences: one of resistance to change and the other of creation of an attractive force of gravity. The unexplained equality of these two kinds of mass remained a deep and disturbing mystery until Einstein came along 200 years later.

Around 1917, Einstein resolved the problem by pointing out that there is no such thing as gravitational mass and likewise no such thing a gravitational force. Everything that we know as gravity is achieved by inertia and curved space-time. Gravity is thus an inertial effect, like the flying out of the baby buggy of a baby when it is brought to a sudden stop; like your face smashing into the windshield of a car that stops suddenly; and like being thrown from a car when it suddenly turns. All these inertial effects appear as fictitious forces.

• CHANGES IN THE COLOR OF LIGHT:

1. Temperature: hot gas produces blue light; cool gas produces red light. The variation of the maximum wavelength with temperature is given by Weins Law: wavelength of maximum times temperature equals 0.3 cm*T

2. Doppler effect: z = v/c. A source of light moving toward you has its wavelength shortened and its color is shifted to the blue. If an object is moving at 1/4th the speed of light, it has a z = 0.25.

3. Gravitational red shift due the curvature of time in the vicinity of mass.

4. Rayleigh scattering: when scattering particles such as molecules and particles have the same size as the wavelength of light blue light is scattered out of a beam of light more than is red light. The result is that when seen directly the beam of light is reddened; when seen perpendicular to the beam, blue light is given off.

Examples of Rayleigh Scattering:

Red sunsets, red fog lights, red lunar eclipses
Blue sky at the earth; blue tails of comets; blue
volcanic eruptions from IO

5. The Relativistic Doppler effect caused by the slowing down of time when an object is moving relative to an observer. Time stops, as seen by an observer, when the object is traveling at the speed of light, relative to the observer. The relativistic Doppler effect applies to galaxies moving close to the speed of light. For example, the most distant quasars in our universe have redshifts of 4, and if one uses the equation for the relativistic Doppler effect, v/c = .924. The universe is filled with ancient light which is very red with a relativistic red shift of 1500 because it was formed in space that was mowing away from us with enormous speeds when the universe was very young.