ASTROBIOLOGY Teach Yourself Exercises and Study Aid

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]

Also, please don't confuse the terms "hypothesis" and "theory". As used in science, a theory is a very strong term and only a handful of ideas in all of science qualify as a theory. A hypothesis is an educated guess or explanation, and implies insufficient evidence or comprehension for a more concrete understanding. A theory is a well-tested, well-established hypothesis, able to make far-ranging predictions and connections with other theories, and usually with an elegant mathematical or physical mechanism for its operation. A theory is much stronger than a hypothesis. It has been rigorously tested by many independent people. When speaking in technical terms, don't use the word "theory" when you simply mean speculation or conjecture or idea or educated guess (all of which are synonymous with hypothesis). In science-speak, we don't come up with theories, we come up with hypotheses. But that's not the way the word "theory" is used in common conversation. Keep this in mind so you don't get confused when you hear someone say, "It's only a theory." That theory may encompass the sum total of all of human experience and knowledge! A better way to think of the word theory is to think of it as a "super law". That is closer to the meaning that scientists intend when they call something a theory.

Teach Yourself #2
The observed wavelength of the H-alpha line in a star is 653.450 nm. The true wavelength of the H-alpha line (measured at rest in the lab) is 656.255 nm. What is the radial velocity of the star?

To answer this, first write out the Doppler effect formula. Then plug in the values one by one.
a) v = c x { (lambda_observed - lambda_true) / lambda_true}

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.
{ (lambda_observed - lambda_true) / lambda_true }
{ (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 = 3x10⁵ km/s x { -0.004274 }
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 is it nearly impossible to find Earth-like planets via the Doppler effect RV technique?"

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 this is correct to first order; 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 of the universe 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 the age you computed with the age of the solar system. Is it ok?
Here are some fully worked-out examples using the Hubble law.

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 known radius of the Earth to accurately estimate the Earth's mass. Incidentally, one of von Jolly's better students was a chap named Max Planck.

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"? (Think about this before reading the answer below).

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
Ch 3 #7, 8, 12, 16, 31, 34-36, 39, 40, 48, 56
Ch 4 # 8, (10,) (13,) 16, 20, 37, 38, 39
Ch 10 # 1, (2,) (5,) 7, (10,) 29, 30-33, 35
Ch 11 # 1, 2, (5-8), 9, (10-14), 31, (32-39), 58
(the ones in parentheses can be skipped until later in the semester).
2022 UPDATE: THE NEW EDITION OF THE TEXTBOOK HAS CHANGES MOST OF THE QUESTIONS, SO THESE ARE NO LONGER CORRECT.

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

+ An excellent TED video by Brian Cox: "Why we need the explorers". "In tough economic times, our exploratory science programs - from space probes to the LHC - are first to suffer budget cuts. Brian Cox explains how curiosity-driven science pays for itself, powering innovation and a profound appreciation of our existence." This video contains a lot of the things we covered (or will cover) in this course, so in addition to being a fascinating talk presenting an important view point, it is also a good study aid.

Teach Yourself #7
For some practice and for guidance to help prepare for the second exam, try answering these questions:
Ch 5 # 30, 32
Ch 6 # 34, 35, 37
Ch 7 # 28, 30
Also
Ch 4, Review Questions #8, 10, 20 on page 147
Ch 5, Review Questions #6, 7, 8, 12, 14 on page 189
Ch 6, Review Questions #1, 4, 5, 15 on page 243

+ Here is another excellent short video from TED: Drew Berry "Animations of unseeable biology". It very much helps puts some of the concepts we are learning into a more realistic light.

Teach Yourself #8
Interested in viruses and want to know more about them in the context of astrobiology? Here is a link to some interesting articles from our beloved astrobio new source, Astrobiolog Magazine:
Viruses & Astrobiology

Teach Yourself #9
So you think you know some astrobiology now, eh? Let's see how well you can answer this homework question given to astrobiology students at Princeton University, as seen in the 2008 remake of the movie "The Day The Earth Stood Still":
"So... pompejana, thiobacillus, deinococcus radiodurans... which of these three would most likely survive in the the extreme environment of the Jupiter moon Callisto, - and why? That's your lab report question for this week and its due in my box by midnight on Friday."
Note: Thiobacillus is now known as acidithiobacillus, and they are one of the microbes that create snottites.

Teach Yourself #10
Ready for a challenge? Try doing this problem. Actually it isn't that hard at all, but its a good check to see if you really understand how extrasolar planets are discovered and how transits provide so much useful information. From the Kepler Mission website, here is the transit_problem.pdf. (If you try this excersize, turn it in to see how you did. And if you did a good job, you can earn an extra credit point.)

"We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens. The diversity of the phenomena of nature is so great and the treasures hidden in the heavens so rich precisely in order that the human mind shall never be lacking in fresh nourishment." Johanes Kepler (as quoted in Cosmos (1980) by Carl Sagan).

Teach Yourself #11
For some practice and for guidance to help prepare for the final exam, try answering the questions to a quiz from a previous semester.
I recommend you don't try these if you are behind in the reading. Catch up first, then attempt answering these. Many of these questions come from the biology parts of the textbook and Reader, and from the latter chapters in the textbook.

Teach Yourself #12
Prepare for the final exam: Take a look at the following list Astrobiology A-to-Z and make sure you can define and explain all the terms.
(NB: I need more items for the letters Q, X, Y, and Z. I will reward you 1 extra credit point if you can come up with a few. E-mail the suggestions to me *before the final exam*.)

Thanks for taking this course. I hope you learned some interesting things, and had some fun in the process. We covered a lot of things in this class, but one of the most important things to take away from this course is developing the skill to be able to teach yourself - and the fun and excitement of discovering and learning things on your own. May your life be filled with wonder.

GOOD LUCK ON THE FINAL EXAM!