Transcript Explorations of the Universe

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
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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”
100
10
• 10
= 10googol = googolplex
• Statistical Physics: energy distribution of air
molecules in a room
– Need to know total possible energy states
26
number
of
molecules
10
– Roughly 10
= 10
– 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 ‫( א‬Hebrew letter Aleph)
– ‫א‬0: integers (counting numbers)
– ‫א‬1: all numbers, or points on a line
– ‫א‬2: all mathematical functions
Forces in Nature
• Long Range
– Gravity
– Electromagnetism
• Short Range - Only Within Atoms
– Weak Nuclear
– Strong Nuclear
• Other???
Atoms
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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