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 exercise with observations which are essential: see Sky map: Las Vegas: current time and weather.
Sections
We do touch on the following topics:
Some of the
Tasks can be completed ahead of the lab period.
Doing some of them ahead of lab period would be helpful.
However, you can print a copy ahead of time if you like especially if
want to do some parts ahead of time.
You might have to compensate for updates in this case.
The Lab Exercise itself is NOT printed in the lab ever.
That would be killing forests
and the Lab Exercise is designed to be an active web document.
General remarks about quiz prep are given at
Quiz Preparation: General Instructions.
For DavidJ's lab sections, the quiz prep is doing all the items listed here and self-testing with the
Prep Quizzes and Prep Quiz Keys
if they exist.
Review the parts of the
Celestron C8 telescope
in the figure below
(local link /
general link: telescope_c8_diagram.html).
You should also review the
Observation Safety Rules.
However to complement and/or supplement the reading, you should at least
read the intro of a sample of the articles
linked
to the following keywords etc.
so that you can define and/or understand some 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:
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 last 2 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 a 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 during a week,
you should usually take off
the Moon filters at the end of lab.
Sub Tasks:
Sub Tasks:
Couldn't do it, eh?
Look back at the
Moon-map figure above
(local link /
general link: moon_map_side_near.html),
and
keeping trying until you can do it.
Sub Tasks:
There are 3 ways to find the
illumination for today:
(1) the super easy way---which you are NOT to use,
(2) the easy way,
(3) the hard way.
Choose one way out of way (2) and (3), and calculate the
illumination for today
or the day you are doing this lab.
Note that (today's date) - (last new moon date) = (day count for the
plot).
To find the last
new moon
date,
see Date & Time: Lunar phase: Current
or
google
"new moons this year".
Use the table to calculate the
illumination
Example calculation:
The Apr01 start of the day
illumination
Do the preparation required by your lab
instructor.
Keywords:
CCD image,
crater central peak,
complex crater
(which is sometimes also a
walled plain,
walled plain (defn. 2)),
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
(walled plain (defn. 2)),
werewolf.
Hm.
Task Master:
EOF
In this lab, we do three kinds of Moon observations outside.
For a general dicussion of
lunar observations,
see Wikipedia: Lunar observation.
But before we go out, we can do a little preparation.
Note that the USNO
provides the illumination
Say it is
2019
Apr10
8 pm PST
(9 pm PDT).
See
USNO Table 2019: lunar fractional illumination.
What is the illumination
So one finds by linear interpolation
Sub Tasks:
Sub Tasks:
The observations may have to wait awhile depending on
weather
and which laboratory sections have observing time when.
So you may have to wait for the
weather
to be good, either on the night you choose first or on a later night.
Each group member observes the Moon
with the naked eye
and fills in their own blank Moon map
following the instructions in the caption that goes with
the blank Moon map
(local link /
general link: moon_map_blank.html).
Keep looking for awhile and try to make out the features as best you can.
For naked-eye observations,
note that the Moon
can be glaring when your eyes
are dark adjusted
(i.e., set to scotopic vision).
So sunglasses might help.
Have you done this? Y / N
Have you done this? Y / N
Sub Tasks:
For telescopic observations,
the telescopes should have
Moon filters
on the eyepieces since otherwise the
Moon will usually be
too glaring to observe.
The instructor
should have put Moon filters
before the lab period.
All group members should help draw this map---do NOT let one person hog the
telescope.
Keep looking for awhile and try to make out the features as best you can.
Have you done this? Y / N
Have you done this? Y / N
Sub Tasks:
Did anyone get an image? Everyone. / Some did. / None did.
Do NOT worry about your answer. You get the mark for any answer.
Did you have a look? Y / N
From the information in the reference
Moon maps
(laid on the
tables by the instructor),
the Moon map shown in the figure above
(local link /
general link: moon_map_side_near.html),
the
detailed Moon map in figure below
(local link /
general link: moon_map_side_near_topographic.html)
AND/OR
the Moon globes
(laid on the
tables by the instructor),
LABEL all the Moon features
in the checklist below that you can reasonably identify
on the telescopic HAND-DRAWN Moon map
from Task 6: Telescopic Observation of the Moon.
On the checklist, check off the
Moon features you
identified and LABELED.
Checklist for Moon features:
Have you done this? Y / N
Let's do a little processing on a canned
CCD image
of the Moon.
Sub Tasks:
Choose the image that is closest in
lunar phase
to the lunar phase of today.
Nota bene:
The ordinary windows image opener will NOT work since the image is a
FITS file.
Have you done this? Y / N
If the AIP4WIN icon is NOT on the
desktop do the following:
Note a center of mass
(which is used in the discussion below) is
a mass-weighted
average position for an
object or
a physical system.
Task 11: Center of Mass Question below
gives more insight into the concept of
center of mass.
Now in the
Earth-Moon system,
the Moon
and Earth
orbit
Earth-Moon system
center of mass.
To be a bit more precise, they orbit in
elliptical orbits to
1st order.
There are small deviations from exact
elliptical orbits
due
astronomical perturbations---which
we will NOT discuss further in this lab.
The eccentricities of
elliptical orbits are actually small
in the Earth-Moon system.
The mean eccentricities
= 0.0549006 ≅ 5.5 % deviation from a circle.
So to a crude
1st order,
the orbits
are circular orbits.
Sub Tasks:
Have you watched and read?
Y / N
The center of mass of the
Earth-Moon system
is one of the focuses of both of
the elliptical orbits
of the Earth-Moon system.
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 ∼ 3/4 of the
Earth's radius
(see Wkipedia: Orbit of the Moon;
Wikipedia: Earth radius: Equatorial radius:
R_eq_⊕ = 6378.1370 km).
Thus, to 1st order, we say that the
Moon orbits
the Earth.
The figure below
(local link /
general link:
orbit_circular_large_mass_difference.html)
shows an
animation
of a generic orbital two-body system
with a large mass difference between the two bodies.
Note that the animation does NOT
have the right sizes NOR right orbital shapes
for the Earth-Moon system.
Sub Tasks:
Have you understood this example.
Y / N
The calculation will give the
center of mass position
in Earth equatorial radii.
Then convert the answer to
kilometers.
SHOW your calculation or at least its setup.
Each member of the group draws
a side-view diagram of the Earth-Moon system
SIMILAR to the figure above
(local link /
general link: moon_orbit_view_side.html)
on a sheet of blank paper, but following the Directions below.
Or if your
instructor so directs, draw only
one diagram and append it to the
favorite report form.
Sub Tasks:
Read the figure. Have you done so?
Y / N
The
sidereal month
can be calculated from the easily directly observed
lunar month
(which is the Moon's
synodic period)
and the
sidereal year.
How this done is explicated in the second figure below
(local link /
general link: synodic_period.html).
Read the figure. Have you done so?
Y / N
In the lab exercises,
exponents are usually indicated
by double asterisks.
The figure below
(local link /
general link: alien_fortran.html)
explains why.
We often have to do
unit conversions in the lab exercises.
The general approach to
unit conversions is
given in the figure below
(local link /
general link: unit_conversion.html).
The
Newtonian Kepler's 3rd law
is
For example, when they
try to calculate the
sidereal month in DAYS
given the relevant data in
List: Earth-Moon-System Facts above
(also at
local link /
general link: moon_facts.html):
i.e.,
the gravitational constant,
the Earth mass,
and Moon mean orbital radius.
Sub Tasks:
Procedures:
Why is the exact formula NOT
exactly correct?
It is exact for an ideal
gravitationally-bound
2-body system.
The real
Earth-Moon system
is affected by
astronomical perturbations:
most importantly
gravitational perturbations.
The lunar phases are explicated in the
figure below
(local link /
general link: moon_lunar_phases.html).
My children beware,
the Werewolf transforms
on the night of the:
Sub Tasks:
In this task,
we study lunar phase problems
and study 3
examples of them.
Sub Tasks:
Have you done so and understood it?
Y / N
Phase and time are the knowns. Location on the sky is the unknown.
A glance at the
Moon Phase Calculator Diagram below
(local link /
general link: moon_phases_calculator.html)
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.
Time and location on the sky are knowns. Phase is the
unknown.
A glance again at the
Moon Phase Calculator Diagram below
(local link /
general link: moon_phases_calculator.html),
shows us where eastern direction on
Earth is
at sunrise.
Then, clearly, Moon must be a
waning crescent.
Location in sky and phase are knowns. Time of day is the unknown.
We glance again at the
Moon Phase Calculator Diagram below
(local link /
general link: moon_phases_calculator.html).
It must be sunset.
If the Moon was on the eastern
horizon, it would be noon.
Determine best answer for
--- lunar phase / location in the
sky / time of solar day --- for the following sub tasks.
You will probably need
Moon Phase Calculator Diagram
shown in the figure above
(local link /
general link: moon_phases_calculator.html.html).
But with a little practice, the answer usually just leaps into your mind.
Sub Tasks:
The tidal force
of gravity---in way that we do NOT
describe here, but is NOT so hard to understand---has caused the
Moon's
axial rotation rate
to equal its orbital rotation rate
EXACTLY ON AVERAGE.
The two rates are virtually never exactly, exactly equal at any one time, but any perturbations from exact
equality are damped out by the tidal force
which acts as a restoring force.
In fact, most significant moons
in the Solar System are
tidally locked to their
parent planets because of the
tidal force
of the parent planets
(see Wikipedia: Tidal locking: Moons).
The animation in the figure below
(local link /
general link: tidal_locking_moon.html.html)
illustrates
the actual lunar tidal locking
and the counterfactual case of a non-rotating Moon.
Sub Tasks:
Have you done so?
Y / N
However, since the 1970s,
the giant impact hypothesis
has become the well established theory
of origin of the Moon.
Sub Tasks:
Sub Tasks:
We can do a little post-observing observation work.
How to Process the CCD Image of the Moon:
In this section, we consider the
Moon's orbit
after an explication of the
inertial frames
used to analyze
gravitationally bound systems
of astro-bodies.
EOF
EOF
For the Earth-Moon system,
we give below
List: Earth-Moon-System Facts
(local link /
general link: moon_facts.html).
Some of the facts about
Earth-Moon system
are recapitulated in the two figures below
(local link /
general link: moon_orbit_view_side.html;
local link /
general link: moon_node_line.html).
x_cm = (m_1*x_1 + m_2*x_2)/(m_1 + m_2)
= [(3 M_Mo)*0 + (5 M_Mo)*(2 R_eq_⊕]/(3 M_Mo + 5 M_Mo)
= (10 R_eq_⊕)/8 = 1.25 R_eq_⊕
= 1.25 R_eq_⊕ * 1
= 1.25 R_eq_⊕ * [ (6378.1370 km) / (1 R_eq_⊕ )]
≅ 80,000 km ,
where you note that some units
cancel out like
algebraic symbols since there are
algebraic symbols
and we have used the
factor of unity (i.e., conversion factor)
to do a
conversion of units
since you can always multiply by
1.
Directions:
End of Task
t_1 = t_2*t/(t_2 + t) = t/(1 + t/t_2) ,
Calculate the sidereal month
and DISPLAY calculation and the answer.
Does it agree with the accepted value given above to 3 or more digits?
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 = 6.67408(31)*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
the approximate formula
P = 2*π*sqrt[a**3/(G*m_1)] .
Students often find it very hard to calculate
the orbital period
using this formula.
In fact, when they try to do so in ONE nonstop calculation on a
calculator, the probability
of going WRONG approaches 100 %---usually the order of operations is somehow mixed up.
print*
print*,'Sidereal Month calculation using'
print*,"the Newtonian Kepler's 3rd law in a Fortran program."
pi=3.14159265358979323846264338327950288419716939937510e0_np
! ! http://en.wikipedia.org/wiki/Pi#Approximate_value
g=6.67408e-11_np ! gravitational constant
a=384784.e+3_np ! Moon orbital radius in meters
xm1=5.9722e24_np ! Earth mass in kilograms
xm2=7.342e22_np ! Moon mass in kilograms
x1=a**3 ; x2=x1/g ; x3=x2/(xm1+xm2) ; x4=sqrt(x3)
x5=2.0_np*pi*x4*(1.0_np/86400.0_np) ! From multiple steps.
x6=2.0_np*pi*sqrt(a**3/(g*(xm1+xm2)))*(1.0_np/86400.0_np) ! From one step.
! Where we have used the exact Newtonian Kepler's 3rd law formula.
x7=2.0_np*pi*sqrt(a**3/(g*xm1))*(1.0_np/86400.0_np) ! From one step with the approximate
! ! Newtonian Kepler's 3rd law formula.
print*,'x1,x2,x3,x4,x5,x6,x7'
print*,x1,x2,x3,x4,x5,x6,x7
! 5.69706290776023039979E+0025 8.53610221597618008718E+0035 141194818992.52979988 375758.99056779705995
! 27.325964914076566062 27.325964914076566062 27.493419442226445430
write(*,'(4e14.6,4x,3f10.6)') x1,x2,x3,x4,x5,x6,x7
! 0.569706E+26 0.853610E+36 0.141195E+12 0.375759E+06 27.325965 27.325965 27.493419
xacc=27.321661547e0_np ! The accepted sidereal month value (J2000).
print*,'The calculated sidereal month in days is ',x6 ! 27.325964914076566062 days
print*,'The calculated approximate sidereal month in days is ',x7 ! 27.493419442226445430 days
print*,'The accepted value is ',xacc ! 27.321661547 days
print*,'The relative error in the exact calculation ',(x6-xacc)/xacc ! 1.59383965798743016043E-0004
print*,'The relative error in the appr. calculation ',(x7-xacc)/xacc ! 6.36140352690538626232E-0003
One can see that the exact
formula is accurate to 4 digit places
and ∼ 0.015 %, but the approximate formula
is accurate to only 2 digit places and ∼ 0.63 %.
P = 2*π*sqrt[a**3/(G*m_1)] ! Using the approximate Newtonian Kepler's 3rd law.
= 2*π*sqrt[(384784*10**3 m)**3/(6.67408(31)*10**(-11)*5.9722(6)*10**24 kg)]
with all digits
= 6.3*sqrt[(4*10**8)**3/(6.7*10**(-11)*6*10**24)] rounding off to ∼ 2-digit values
= 6.3*sqrt[6*10**25/(4*10**14)]
= 6.3*sqrt(1.5*10**11) = 6.3*sqrt(15*10**10)
= 6.3*4*10**5 = (25*10**5 s)*(1 day/(0.9*10**5 s))
= 27 days
which is correct to 2 digits.
Now for the lunar phases---everything you ever
wanted to know about lunar phases, but were afraid to ask.
The lunar phases in action are shown
in the animation in the figure below
(local link /
general link: moon_lunar_phases_animation_2c_html).
There are some traditional problems associated with the
lunar phases
as illustrated in the figure below
(local link /
general link: alien_werewolf.html).
In this section, we consider
tidal locking
and the lunar libration.
The Moon's
tidal locking and the
lunar libration
as seen from Earth
are illustrated in the animation
in figure below
(local link /
general link: moon_lunar_phases_animation.html.html).
The origin of the Moon was
once a much vexed question.
There might be more here on
lunar geology
sine die------but maybe on
Greek Kalends
(Augustus (63 BCE -- 14 CE)
quote).
Goodnight all.
Post mortem comments that may often apply specifically to
Lab 4: The Moon: