What's the difference between a scientific law and a
theory?
"A law explains a set of observations; a theory explains a set of laws.
The quintessential illustration of this jump in level is the way in which
Newton's theory of mechanics explained Kepler's law of planetary motion.
Basically, a law applies to observed phenomena in one domain (e.g.,
planetary bodies and their movements), while a theory is intended to unify
phenomena in many domains. Thus, Newton's theory of mechanics explained
not only Kepler's laws, but also Galileo's findings about the motion of
balls rolling down an inclined plane, as well as the pattern of oceanic
tides. Unlike laws, theories often postulate unobservable objects as part
of their explanatory mechanism. So, for instance, Freud.s theory of mind
relies upon the unobservable ego, superego, and id, and in modern physics
we have theories of elementary particles that postulate various types of
quarks, all of which have yet to be observed."
(Quoted from John L. Casti in "Correlations, Causes, and Chance,"
Searching for Certainty: How Scientists Predict the Future (1990))
[Retrieved from http://en.wikiquote.org/wiki/Johannes_Kepler
on 2012 Jan 16]
Teach Yourself #2
Write out the Doppler effect formula. Then plug in the values one by
one.
a) v = c x { (lambdaobserved - lambdatrue) /
lambdatrue}
b) Now lets put in the numbers, starting with the far right hand side.
NOTE: Always include the units! It is not 653.450, it is 653.450 nm.
The "nm" part is vital, as it tells you this is a distance (the length
of the wave). If you leave out the units, you are very likely to get the
incorrect answer. This is one of the most common mistakes students make.
{ (lambdaobserved - lambdatrue) /
lambdatrue }
{ (653.450 nm - 656.255 nm) / 656.255 nm }
{ -2.805 nm / 656.255 nm }
-0.004274
Notice how the units cancel out in the division; we have a pure
number with no units.
b) Now we need to multiply this by the speed of light c:
v = c x {(lambdaobserved - lambdatrue) /
lambdatrue}
v = 3x105 km/s x { -0.004274 }
Now just punch it into a calculator and you've got the answer.
Notice how the units of speed, km/s, come from the speed of light.
The distances in the wavelength part all cancel out.
c) So what velocity do you get? Redshift or blueshift?
Click for the answer and
another example problem using the Doppler effect.
Here is a short but detailed description of the
connection between atoms, light, and discovering exoplanets,
including answers to the questions:
"Why don't we see color changes due to the Doppler effect?" and
"Why can't we use the Doppler effect to find Earth-like planets?"
Did you know:
One of the first persons to accurately measure the mass of the Earth was
Johann Philipp Gustav von Jolly, who did so in the early 1880s.
In a very clever scheme, he used Newton's law of gravity, a balance, a
ball of known mass, and the radius of the earth to measure the Earth's
mass. One of von Jolly's students was a chap named Max Planck.
Wien's Law:
Here are some helpful notes on Wien's
Law (in .pdf format), kindly provided by former astrobio student E.
Ross (and edited by W. Welsh). These notes should help you understand the
importance of Wien's law, and help you understand how to use it.
Teach Yourself #3
In the simplest expanding universe cosmology, the
age of the universe is given by: t = 1 / H0.
(Note that a more sophisticated derivation will include correction
factors, but we can ignore these to get the gist of the idea that you
can get the age from Hubble's constant.)
So start by writing down Hubble's constant.
Then go find the conversion between km and Mpc.
Change all units to either km or Mpc. So you'll have units of
xxx km/s / km (=km/s per km)
or
xxx Mpc/s / Mpc (= Mpc/s per Mpc)
Then the distance units cancel out and you are left with some number with
units of (1/seconds).
Take the inverse and you get the age in seconds.
You can work out how many seconds in a year to get the age in years, or just use
the approximation that 1 year has about 3.16 x 107 seconds.
(For you science/engineer types, a useful approximation to remember is
that 1 year is about ~ pi x107 seconds.).
Now compare your age with the age of the solar system. Is it ok?
Here are some fully worked-out
examples using the Hubble law.
Here is the Hypothetical Dialog
used in class.
Did you know that Mark Twain (Samuel
Clemens) was an avid amateur astronomer? Have a look at some
quotes about astronomy by Mark
Twain.
Teach Yourself #4
A bare helium nucleus moving at very high speed is often called an "alpha
particle", and it is a dangerous form of particle radiation that comes from
radioactivity. Radioactivity is the relase of sub-atomic particles and energy
from the process of nuclear fission. Fission is the sponteneous
breaking apart of a nucleus. Many big nuclei, like uranium, can be unstable
and fall apart. When they do, they can spit out high energy photons (gamma
rays) and/or high-speed particles like protons, electons (called a beta
particles), or He nuclei (called an alpha particles). Fission is the opposite
of fusion, but both can release energy. [ WHY ?]
Now that you know what an "alpha particle" is, why is the creation of
carbon called the "triple-alpha process"?
An alpha particle is a He nucleus, and contains 4 particles:
2 protons and 2 neutrons.
Take three alpha particles and add them together. What do you get?
You get 12 particles total: 6 protons and 6 neutrons.
And what is a nucleus that contains 6 protons?
By definition, it is a carbon nucleus. (If it contains 6 protons, then
it is carbon). Thus the combination of three He will fuse into
one C nucleus.
Teach Yourself #5
Some practice questions from the textbook to help you get ready for the
first exam:
Ch 1 # 15
Ch 2 # 12, 14, 36, 38
Ch 3 #7, 8, 16, 19, 20, 37-40, 43, 44
Ch 4 # 8, (10,) (13,) 16, 20, 37, 38
Ch 10 # 1, (2,) (5,) 7, (10,) 29, 30, 31, (32,) 35
Ch 11 # 1, 2, (5-8), 9, (10-14), 27-29, (30-35), 51
(the ones in parentheses can be skipped until later in the semester).
Teach Yourself #6: Basic Chemistry
The following lecture notes discuss material we would cover in more
detail if we had the time, but we won't get to these this
semester. So you can just enjoy these "gems of wisdom" on your own.
They will help give you a better understanding and appreciation of some
of the topic we cover in the course.
Lecture notes on:
Intro to Basic Chemistry & the
Periodic Table
Intro to Radioactivity