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.
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:
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EOF
php require("/home/jeffery/public_html/course/c_astint/ast_remote_ipi_rmi.html");?>
End of Task
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
?
The Apr01 start of the day illumination
= 0.24 and the end of day illuminationSo 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:
Sub Tasks:
Have you watched and read?
    Y / N
   
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
   
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.
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:
Sub Tasks:
Have you done so?
    Y / N
   
Sub Tasks:
Sub Tasks:
How to Process the CCD Image of the Moon:
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.