Credit/Permission: For text, © David Jeffery. For figures etc., as specified with the figure etc. / Only for reading and use by the instructors and students of the UNLV astronomy laboratory course.
This is a lab-with/without-observations: see Sky map: Las Vegas: current time and Las Vegas weather.
Status: Lab 4 is under construction and has NOT been beta-tested. Refinements and updates will come as needed.
Sections
We do touch on the following topics:
Prep items:
Some of the Tasks can be completed ahead of the lab period. Doing some of them ahead of lab period would be helpful.
The Lab Exercise itself is NOT printed in the lab ever. That would be killing forests and the Lab Exercise is designed to be a web active document.
You can print a copy on your own printer if you like.
For DavidJ's lab sections, the quiz prep is doing all the items listed here and self-testing with the Prep Quiz if it exists.
Review the parts of the Celestron C8 telescope in the figure below.
You should also review the Observation Safety Rules.
However to complement and/or supplement the reading, you should read a SUFFICIENT
amount of the articles linked to the following keywords etc. so that you can
define and/or understand the keywords etc. at the level of our class:
A further list of keywords which you are NOT required to look at---but it would be useful to do so---is:
CCD image,
crater central peak,
complex crater,
exposure time,
impact crater,
lunar craters
(see Wikipedia: List of craters on the Moon),
lunar geology,
lunar highlands,
lunar mountain range
(see Wikipedia: List of lunar mountain ranges),
lunar phases,
lunar terminator,
mare
(see Wikipedia: List of maria on the Moon),
Moon
(near side of the Moon,
far side of the Moon),
Moon map,
multi-ring crater,
naked eye astronomy,
rayed craters,
rille (AKA rima)
(see Wikipedia: List of lunar rilles),
selenographic coordinates,
selenography,
sinuous rille,
star diagonal,
terraced crater,
walled plain
(see Look Inside).
Hm.
This range is chosen so that there are lots of Moon features to observe and the Moon is high in the sky during the lab period.
If the sky is going to be heavily clouded, then an alternative lab from the Introductory Astronomy Laboratory Exercises should be chosen.
Thin cloud cover is usually OK. The telescopes will usually shoot the Moon through thin cloud cover.
The same instructions as in the last item apply.
The Moon during this lab is usually uncomfortably glaring without Moon filters.
If the sky is hazy or the Moon is still in crescent moon, the Moon filters can/should sometimes be omitted since the haze provides a natural filter.
If you are the last one doing Lab 4: The Moon before other observing labs are done, take off the Moon filters at the end of lab.
All the Tasks are linked here so that you can find them in the context of the lab---which might be useful when completing your Report Form.
The Moon and Earth orbit their mutual center of mass (i.e., mass-weighted average position) in elliptical orbits in the inertial frame of the fixed stars approximately.
The center of mass is one of the focuses of each elliptical orbits.
However, the Earth is about 80 times as massive as the Moon, and so the center of mass is very close to the Earth's center---it's actually inside the Earth at about 3/4 of the Earth's radius (see Wkipedia: Orbit of the Moon).
Thus, to 1st order, we say that the Moon orbits the Earth.
A generic orbital two-body system with a large mass difference between the two bodies is shown in the animation below.
The animation does NOT have the right sizes nor right orbital shapes for the Earth-Moon system.
Below is a table of facts for the
Earth-Moon system.
______________________________________________________________________________________
Table: Earth-Moon System
______________________________________________________________________________________
Earth mass M_⊕ 5.97219*10**24 kg ≅ 81.3 M_moon
Earth radius 6378.1370 km (equatorial radius), 6371.0 (mean radius)
Moon mass M_Moon 7.3477*10**22 kg = 0.012300 M_⊕ ≅ 1/81.3 M_⊕
Moon radius 1738.14 km (equatorial radius), 1737.10 km (mean radius)
≅ 0.273 Earth radii ≅ 1/4 Earth radii
Mean orbital radius of the Moon 384,748 km = 60.3229 Earth equatorial radii
≅ 60 Earth radii
Orbital period 27.321662 days
(AKA sidereal month)
Mean lunar month 29.530587981 days ≅ 29.5 days
Eccentricity 0.0549006 ≅ 5.5 %
Orbital inclination 5.14°
______________________________________________________________________________________
Some of the facts about
Earth-Moon system
are recapitulated in the two figures below.
The formula for the center of mass of
objects along a line is
Answer:
x_cm = (0 + 1*60.3229 )/82.3 = 0.73296 R_Earth_equatorial radii = 4674.9 km
The
center of mass of
a physical system
equals the
center of mass
evaluated from
the center of masses
of any set of subsystems of the physical system.
Proof:
Each member of the group draw
side-view diagram of the Earth-Moon system
similar to the diagram above on a sheet of blank paper.
Draw to-scale
for the Earth,
the Moon,
and the mean orbital radius.
Answer:
The diagram will look like the one above, but will be
to-scale.
The relationship of the lunar month
and the sidereal month
are explicated in the figure below.
The lunar month falls into the class of
synodic periods
and the sidereal month
into the class of orbital periods.
The
sidereal month
can be calculated from the directly observed
lunar month
and the
sidereal year.
The appropriate formula---no derivation given here---is
Calculate the sidereal month.
Answer:
I get 27.321660800585885 days which equals the accepted value 27.321662 days to 5 decimal places.
In the lab exercises,
exponents are usually indicated
by double asterisks.
The figure below explains why.
We oftne have to do
unit conversions in the lab exercises.
Now Unit conversions often seem difficult,
but they are simple with the general approach.
One does unit conversions by multiplying
numbers by 1 and treating units as
algebraic variables (which is
one of the things they are).
For example, say you wanted to convert 10 km into meters.
Well 1 km = 10**3 m.
Therefore 1=(10**3 m/1 km).
You can always multiply a number by 1 without changing its value.
Thus
The dynamical Kepler's 3rd law is
Hint: Do the calculation one step at a time: i.e., Gm_1 = z, then a**3 = y, then y/z = x, then sqrt(x) = w,
then 2*π*w = P. Trying to it all at once on a
calculator usually leads to a
random number.
Answer:
Answer: I get 27.322 days which agrees with the accepted value to 3 decimal places
which is certainly within a few percent.
x_cm = ∑_i (m_i*x_i) / ∑_i m_i = ∑_i (m_i*x_i) / m ,
where m = (∑_i m_i) is the total mass.
As an example, say you had m_1 = 3 at x_1 = 0 and m_2 = 5 at x_2 = 2.
Applying the formula gives
x_cm = (m_1*x_1 + m_2*x_2)/(m_1 + m_2) = (3*0 + 5*2)/(3+5) = 10/8 = 1.25 .
Evaluate the center of mass position of
the Earth-Moon system
in Earth radii
and then convert to kilometers.
Measure the masses in Moon masses.
Take the center of the Earth as the
origin (i.e., x_1 = 0).
m*r_sub_cm = ∑_i m_sub_i*r_sub_i = ∑_i ∑_j m_ij*r_ij
= ∑_k m_k*r_k = m*r_cm ,
and thus
r_sub_cm = r_cm
where
the position variables are all
vectors,
"sub" stands for subsystem,
r_sub_cm is the center of mass
evaluated using the subsystem centers of mass,
r_cm is the center of mass evaluated
from the elementary particles (i.e., the true
center of mass of the system),
the index ij labels elementary particles in subsytem i,
and k labels elementary particles in general.
The division into subsystems is general and the division into elementary particles
(however they are defined) is unique.
QED.
t_2
t_1 = ----------- ,
1+t_2/(± t)
where
t_1 is the sidereal month
(accepted mean value 27.321662 days
probably epoch J2000),
t_2 is the sidereal year
(365.256363004 days
epoch J2000)
t is the lunar month
(mean value 29.530587981 days
probably epoch J2000)
and one uses the upper case of ± t (i.e., t, not -t).
10 km = 10 km * 1 = 10 km * (10**3 m/1 km) = 10**4 m .
The example above, generalizes to all other cases
straightforwardly---'nuff said.
P = 2*π*sqrt[a**3/(G(m_1+m_2))] ,
where P is orbital period,
a is the
semi-major axis (AKA mean orbital radius)
of the relative orbit
(i.e., of one body relative another and not relative to the
mutual center of mass),
G is the gravitational constant G=6.67384(80)*10**(-11) (MKS units),
and m_1 and m_2 are the masses of the two bodies in the two-body system.
(see also Wikipedia:
Standard gravitational parameter: Two bodies orbiting each other
and Goldstein et al. 2002, p. 102).
If m_1 >> m_2, the formula reduces to
P = 2*π*sqrt[a**3/(Gm_1)] ,
Calculate the sidereal month in days
given the data in Table: Earth-Moon System.
You will have to convert kilometers to meters and seconds to days during the calculation (see the subsection
above on unit conversions).
Does the result agree with the accepted value of 27.321662 days to within a few percent?
If not, why not?
The lunar phases are explicated in the figure below.
There are some traditional problems associated with the lunar phases as illustrated in the figure below.
My children beware, the Werewolf transforms on the
on the night of the:
The Moon is
tidally locked
to the Earth.
The tidal force
of gravity---in way that we don't describe here, but
isn't so hard to understand---has caused the
Moon's axial rotation rate to equal its orbital rotation rate on average.
The two rates are virtually never exactly, exactly equal, but any perturbations from exact
equality are damped out by the tidal force
which acts as a restoring force.
In fact, nearly all significant moons
in the Solar System are
tidally locked to their
parent planets because of the
tidal force
of the parent planets.
The animation below illustrates
the actual lunar tidal locking
and the counterfactual case of a non-rotating Moon.
The Moon's
tidal locking and the
lunar libration
as seen from Earth
are illustrated in the animation below.
How long is the Moon's axial rotation period relative
to the
local inertial frame
(which is well approximated for the Solar System
by the reference frame of the
fixed stars)
and the lunar day (which is not the same thing as the
axial rotation period).
Answer:
Since the orbital and axial rotation rates are the same, the
rotation period and the lunar day
must equal, respectively, the
sidereal month (27.3 ... days)
and the lunar month (29.53 ... days).
Complete this task using the
lunar phase simulator
displayed below the task.
in the group must do the task for themselves.
Answer:
The Sun is sufficiently remote that
the sun rays
are parallel to good approximation.
Technically, I'd call this a good
zeroth order approximation
since the angle between rays
is never zero for point source.
Let's do three examples of lunar phase problems.
Phase and time are the knowns. Location on the sky is the unknown.
Glance at the lunar phases calculator diagram
below allows us to find the answer.
The Moon must be on the eastern
horizon. It is just
rising. It is in
opposition
to the
Sun
as it must
be when it is full.
If the time were midnight, then
the Moon would be
transiting the
meridian.
They are the easiest to do.
If there is a full moon,
the Moon is OPPOSITE
Sun on the sky (i.e., on the
celestial sphere).
If a full moon is rising,
the Sun is setting, etc.
Time and location on the sky are knowns. Phase is the
unknown.
Glance back lunar phases
diagram and find the time location
on Earth and identify the eastern direction.
The Moon must be a
waning crescent.
Location in sky and phase are knowns. Time of day is the
unknown.
Glance back at the lunar phases diagram.
It must be sunset.
If the Moon was on the eastern
horizon, it would be noon.
Determine best answer for the time of solar day
(sunrise, noon, sunset, midnight) for following
lunar phase situations.
You should use the Moon Phase Calculator Diagram above.
Actually, it's sort of best to concentrate on
full moon problems first.
Examine the Moon map below.
Without looking back at the moon map
mentally locate in the map in your mind:
Couldn't do it, eh.
Look back at the Moon map and
keeping trying until you can do it.
Have you succeeded at last? Y / N
Answer: I did it first time.
Answer:
For 2015 May26,
waxing gibbous moon.
What is the
lunar illumination at 9 pm today?
Note:
When the instructor gives the signal go to the roof to do the
Moon observations.
The first observation is
naked-eye astronomy.
Before going to the roof, each person should print out one copy of the
blank Moon map shown below.
Also print out one extra copy for the group as whole that is used for
Task 12: Telescopic Observation of the Moon.
Each group member observes the Moon
with the naked eye
and fills in their own blank Moon map
following the instructions in the image caption.
Keep looking for awhile and try to make out the features as best you can.
Every group member should append their own
naked-eye
Moon map to their report.
Have you done this? Y / N
Answer: I've never done this, but do as I say, not as I do.
The second observation is with the
telescope.
Each group
observes the Moon
with the telescope
and fills in the group blank Moon map
following the instructions in the image caption.
All group members should help draw this map---don't let one person hog the
telescope.
Keep looking for awhile and try to make out the features as best you can.
Each group should append
the telescopic Moon map
to the favorite report form.
Have you done this? Y / N
Answer: I've never done this, but do as I say, not as I do.
Take an image of the Moon
your cell phone.
Did you get an image? Y / N
Answer: No.
I'm the last person on Earth
who doesn't have a cell phone.
Don't worry. You get the mark whether you get an image or not
and whether you have cell phone or not.
After completing this task you can return to the lab room to continue with
the inside parts of this lab.
Answer:
For 2015 May26, 8 pm PST,
the illumination is
0.56 + (20/24)*0.09 = 0.56 + (5/6)*0.09 ≅ 0.64.
From the information in the reference Moon maps laid on the tables by the instructor OR from the detailed Moon map shown below, label all the Moon features from the checklist below that you can reasonably identify on the telescopic hand-drawn Moon map.
On the checklist, check off the Moon features you identified.
Checklist for Moon features:
Have you done this? Y / N Answer: I've never done this, but do as I say, not as I do.
Let's do a little processing on a canned
CCD image
of the Moon.
We will just process one of the old images:
Choose the image that is closest in
lunar phase
to the lunar phase of today.
Download the image to the desktop
and process as described below.
The ordinary windows image opener will NOT work since the image is a
FITS file.
Print out one copy of the processed image and append it to the
favorite report form
which also has the telescopic hand-drawn Moon map.
Have you done this? Y / N
Answer: I've never done this, but do as I say, not as I do.
If the AIP4WIN icon is NOT on the
desktop do the following:
Any that are semester-section-specific will have to added as needed.
Comments: