BELIEVE   ME   NOT!    - -     A   SKEPTICs   GUIDE  

. . . cyclotron.^10.1

You could even imagine examples from ``outside Physics,'' in which the radius and speed were purely metaphorical; but I can't think of one . . . .

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . $\vec{\mbox{\boldmath$\space A $\unboldmath}}'$.^10.2

We write this   $\Delta \vec{\mbox{\boldmath$\space A $\unboldmath }} \parallel \vec{\mbox{\bo . . . . . . ce A $\unboldmath }} \parallel \vec{\mbox{\boldmath$\space A $\unboldmath }}'$  in standard notation.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . $\vec{\mbox{\boldmath$\space A $\unboldmath}}'$.^10.3

We write this   $\Delta \vec{\mbox{\boldmath$\space A $\unboldmath }} \perp \vec{\mbox{\boldmath$\space A $\unboldmath }}$  in standard notation.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . Empiricist^10.4

(who may or may not be the same person as the Experimentalist and/or the Theoretician - these are just different ``hats'' that a Physicist may put on)

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . it.^10.5

Of course, as in Kepler's case, the empirical description is always in terms of some preselected model or paradigm; but the paradigm in question is generally a familiar and widely accepted one, otherwise it is not very helpful in communicating the results to others. Besides, the data themselves are ``collected'' within the context of the Experimenter's paradigms and models about the world. The ``simple'' act of vision employs an enormous amount of ``processing'' in the visual cortex, as discussed earlier . . . .

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . are^10.6

(neglecting perturbations from the other planets, as is assumed in all Kepler's laws)

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . ellipses^10.7

Note that a circle is just a special case of an ellipse in which the major and semimajor axes are both equal to the radius and both foci are at the centre of the circle.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . orbit.^10.8

This feature, unlike the other two LAWS, is true for any ``central force'' (a force attracting the body back toward the centre, in this case the sun). The other two are only true for inverse square laws, $F \propto 1/r^2$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . tiny.^10.9

If the Earth attracts a 1 kg mass with a force of 9.81 N, the gravitational force between two 1 kg masses separated by R_E would be smaller by a factor equal to the number of kilograms in M_E, which is a large number. Fortunately the smaller masses can be placed much closer together; this helps quite a bit, but the force is still miniscule!

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . time.^10.10

If you have a TV satellite dish, it is pointing at such a satellite; note that (if you live in the Northern Hemisphere) it is tipped toward the South. Why?

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . why.^10.11

(The most intuitive explanation for this involves the concepts of kinetic and potential energy, which we will watch emerge from Newton's Mechanics in succeeding Chapters.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . Earth.^10.12

Surely by now you have gotten skeptical of my repeated declarations that the mass of the Earth can be treated as if it were all concentrated at the Earth's centre of gravity (i.e. the centre of the Earth). What about all the bits right next to us? They have a much smaller r² and thus contribute far more ``pull'' than those `way on the other side. Well, hang on to that skepticism! I'm not leading you astray (promise!) but a little later on I will be in a better position to use Gauss' Law to explain in a few quick steps why this works. You should only provisionally accept this notion until you have seen a convincing argument with your own eyes.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . past.^10.13

This motif has been used in several delightful science fiction stories, notably ``Neutron Star'' by Larry Niven. and ? Egg ? by ? .

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

. . . stable.^10.14

Bill Unruh, of the UBC Physics Department, is one of the world's leading experts on this subject.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.