Exploration of the Universe

Lives of the Stars

Two Profound Ideas

• The Sun is a Star• We Are Made of Starstuff

Large Numbers

• 10 x 10 x 10 x 10 = 104

• 10 x 10 x … (n times) = 10n

• To multiply, add exponents–10,000 x 100,000 = 1,000,000,000–104 x 105 = 104+5 = 109

More About Large Numbers

• 1,000,000,000/10,000 = 100,000• 109/104 = 105 = 109-4

• To divide, subtract exponents• 1000/100 = 103/102 = 103-2 = 101 = 10• Anything to the first power equals itself

A “Paradox” of Scientific Notation

• Not really a paradox, but hard for many people to accept

• 100/100 = 102/102 = 102-2 = 100 = 1• Anything to the zero power equals 1

Negative Exponents

• 1000/100,000 = 103/105 = 103-5 = 10-2 = 1/100 = .01

• 10n x 10-n = 10n-n = 100 = 1• 10-n = 1/10n

Does Anybody Need Really Big Numbers?

• 10100 = “googol”• 1010100 = 10googol = googolplex• Statistical Physics: energy distribution of air

molecules in a room–Need to know total possible energy states–Roughly 10number of molecules = 101026

–Not a googolplex, but still pretty huge

Infinity• The symbol ∞ for infinity is not a

number - you can’t calculate with it.• The mathematician Georg Cantor

studied transfinite numbers, denoted by א (Hebrew letter Aleph)– 0א : integers (counting numbers)

– 1א : all numbers, or points on a line

– 2א : all mathematical functions

Forces in Nature

• Long Range– Gravity– Electromagnetism

• Short Range - Only Within Atoms– Weak Nuclear– Strong Nuclear

• Other???

Atoms• Democritus 400 B.C.• Lucretius 1st c. B.C.• Medieval: new elements• Definition of Element• Ratios in Chemical Reactions• Crystallography

Atoms• Nucleus: Almost all Mass in Atom– Protons: Determines Element Identity– Neutrons– Protons repel (electromagnetism) but strong

nuclear force is stronger, holds it together– Too many protons: unstable (radioactive)

• Electrons– The part that engages in chemical reactions

Why Alchemy Didn’t Work

• Atomic energies are measured in units called electron volts (ev - very tiny)

• Energy binding electrons to an atom are a few ev

• Energies binding particles in the nucleus are millions of ev

• Trying to alter elements by chemical means is like trying to crack a safe with a feather

The Heavens Are Not Changeless• The Stars Move– Most of our constellations would have been

unrecognizable to Neanderthal Man

• The Solar System Moves– Very few of our nearby stars would have been

visible to the first humans

• Stars are Born, Live and Die– Many of our brightest stars did not exist in the

days of the dinosaurs