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Astronomy 100
Name(s):
Exercise 1: A bit of math, chemistry and physics
Astronomy requires a foundation of physics and chemistry. In this exercise, you’ll
go over some of the chemical and physical ideas that recur throughout this course.
Length scales and units
One of the basic aspects of science, in contrast to other “ways of knowing”, is the
measurement of phenomena. This idea of quantifying immediately leads to the
necessity of units; that is, words that describe the measurement and give it meaning.
For instance, one of the crucial distances we’ll be talking about this quarter
is the distance of a planet from its sun. In our Solar System, we can use a variety
of units, from the familiar “kilometers” (abbreviated km) to the more exoticsounding “astronomical units” (AU). The table below shows the planet–Sun
distances using both units:
Planet name
Planet–Sun
Planet–Sun
Steps away
distance (km)
distance (AU)
from Sun
Mercury
57,900,000
0.387
Venus
108,200,000
0.723
Earth
149,600,000
1.00
Mars
227,900,000
1.524
Jupiter
778,300,000
5.203
Saturn
1,427,000,000
9.539
Uranus
2,870,000,000
19.19
Neptune
4,497,000,000
30.06
Pluto
5,916,000,000
39.54
Eris (Xena) (2003 14,511,000,000 97.00
UB13)
1000
One thing I hope you notice is that kilometers are a cumbersome unit to use,
what with all the big numbers. This is the justification for using scientific
notation.
1. In the second-from-the-right blank column on the table, convert the numbers
in the “kilometers” column into scientific notation.
2. Look at the “AU” column and suggest a definition for 1 AU. (I don’t mean “1 AU
= 149,600,000 km”; I can read the table, too. What does a distance of 1 AU
represent?)
3. We are going to make a model of the solar system on the roof of the building.
The roof is about 1000 of my steps in length. If we put the Sun at one end of the
roof and Eris at the other, figure out how many of my steps away each planet will
be, and enter this number into the far right blank column on the table.
4. a. The problem is, I’d like to be able to put the Sun and planets in this model at
the same scale as the distances between objects. Given that the Sun’s diameter
(width) is about one-hundredth (1/100) the distance from the Sun to the Earth,
how many steps “wide” will the Sun be on our model. What common
household object might be used to model the Sun?
b. If you think that’s a problem, then consider that the Earth’s diameter is about
one-hundredth that of the Sun. How many steps “wide” will the Earth be in the
model. Is there any common household object that might be used?
c. So must two different scales be used on our model, one for the distances
between bodies and one for the bodies themselves, in order for objects to be
visible and not take up too much real estate?
5. In this course, we’ll be talking about stars and galaxies, each of which comes
with its own distance scales. Convert the following into “steps” for our model.
Distance to Proxima Centauri, the nearest star = 4.2 light years (ly); 1 ly = 63440
AU
Distance to Andromeda Galaxy, the nearest non-dwarf galaxy = 0.75 megaparsecs
(Mpc); 1 Mpc = 3.24 million light years.
(Extra credit) If one of my steps is 2.5 feet long, and there are 5280 feet in a mile,
how many miles away from the Sun in our model would Proxima Centauri be?
Would Andromeda Galaxy be?
Physics
Physics is the scientific study of energy and motion. Physics uses mathematics as
a tool to develop theories of energy and motion, though many physics principles
can be described without resorting to numbers and equations.
One of these principles is the notion of force, the impetus behind motion. Force
may arise from one of four fundamental sources; the one mentioned in the first
chapter of the text is gravity. The gravitational force is solely attractive (no
such thing so far as anti-gravity).
To illustrate the point that math is not necessarily needed to figure out physical
situations, consider the three scenarios of pairs of astronomical bodies below.
Each body has its mass and volume specified, and the distance between each pair
of bodies is also shown.
Scenario A:
Scenario B:
distance = 2
mass = 5
volume = 10
mass = 5
volume = 10
distance = 2
mass = 10
mass = 5
volume = 10
volume = 10
Scenario C:
distance = 4
mass = 5
volume = 10
mass = 5
volume = 10
6. In each pair, the body on the right feels a gravitational attraction due to the
body on the left. Order the scenarios from most gravitational force felt by the
body on the right to the least (if you think two scenarios exhibit the same amount
of attraction, use an equals sign).
Summarize your findings by filling in the blanks in the statements below with
“more” or “less”:
More mass on the other body means _____________ gravitational force felt.
Greater distance from the other body means _____________ gravitational
force felt.
7. Consider this scenario (Scenario D):
distance = 2
mass = 5
volume = 5
mass = 5
volume = 5
Where does the right body’s attraction to the left body fit in your order for the
previous problem?
It turns out that scenario D exhibits the same amount of attraction as scenario
A; what does this suggest to you about the importance of “volume” in
gravitational attraction?
8. Finally, consider this scenario (Scenario E)
distance = 4
mass = 10
volume = 10
mass = 5
volume = 10
Where does the right body’s attraction to the left body fit in your order for
problem 6?
It turns out that scenario E exhibits more attraction than scenario C but less
attraction than scenario A; which is the more important factor for gravitational
attraction, mass or distance?
Chemistry
Chemistry is the study of matter and its changes, using the rules of physics. Since
ours is a universe of matter, you will need to know a little about these rules of
how matter changes. Atoms are the smallest unit of matter, but most matter is
made of molecules. Therefore, you will need a set of simplified rules to describe
bonding between atoms to form molecules. Obtain a “ball-and-stick” molecular
model kit from the cart.
The rules:
• White balls represent hydrogen atoms
• Red balls represent oxygen atoms
• Black balls represent carbon atoms
• Blue balls represent nitrogen atoms
• The plastic sticks represent chemical bonds (which are merely a
pair of shared electrons between atoms); length doesn't matter
• For a molecule to be "happy" (i.e., have all of its bonding
requirements satisfied), all holes must be filled with bonds
9. a. Using two white balls and one plastic stick, make a model of the simplest and
most common molecule in the universe — the hydrogen molecule. Therefore, what is
the most common element in the universe?
b. So a hydrogen atom can only bond to one other atom, maximum. What is the
maximum number of atoms that carbon could bond to (hint: count holes)? That
oxygen could bond to? That nitrogen could bond to?
10. Why do you suppose there are no helium atoms in the kit? Hint: Helium is a
“noble” gas.
11. Create the following molecules: water (H2O), ammonia (NH3) and methane
(CH4) and carbon dioxide (CO2). Draw the molecules, as best as you can, below.
At high temperatures, like in a star or a nebula, chemical bonds (the sticks) all break,
leaving atoms free. Atoms contain three principal subatomic particles: the
neutron, the proton and the electron.
More rules:
• Atoms of an element all contain the same number of protons, given by the atomic
number on the periodic table; if the number of protons changes in an atom, it
becomes a different element.
• Neutral atoms contain the same number of protons and electrons.
• The total number of protons and neutrons in an atom is called the isotope
number, and distinguishes different isotopes of the same atom.
12. Quick review of atomic structure; fill in the missing information in the table
below:
Atom (isotope) Number of protons Number of neutrons Number of electrons
hydrogen-1
1
0
1
hydrogen-2
(deuterium)
hydrogen-3
(tritium)
helium-3
helium-4
carbon-12
Moreover, electrons from within an atom can be ejected (ionized). The resulting
atom is called an ion, and will contain fewer electrons than protons, resulting in a
net positive charge; this type of ion is called a cation. Meanwhile, the electron that
was ionize can stabilize around a different atom, which will then have more electrons
than protons, resulting in a net negative charge – this is an anion.
Ions therefore have an overall non-zero electrical charge and are thus more
reactive in general than atoms. The overall charge is written as a superscript to the
right of the element symbol, so, for instance, a calcium ion that has two fewer
electrons than protons would be written: Ca2+.
Confusingly, an old astronomical notation for cations uses Roman numerals to
indicate various numbers of missing electrons, but this numbering system starts with
(I) for neutral atoms. For instance, calcium (I) is neutral calcium, but calcium (III) is
the Ca2+ ion given above.
13. Fill in the missing information in the table of ions:
Ion
H (neutral)
Astronomy
# of protons
notation of ion
H (I)
1
H+
He+
He2+
Ca (II)
# of neutrons
# of electrons
0
1