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).
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:
It can be done without observations at any time, but it is educationally best with them.
If the sky is going to be heavily clouded, then
an alternative lab from the
Introductory Astronomy Laboratory Exercises
should be chosen or you could do
Lab 6:
Galilean Moons of Jupiter without observations.
Thin cloud cover is usually OK. The
telescopes will usually shoot through
thin cloud cover.
Patchy cloud cover may be OK if you observe when
Jupiter is in the clear.
Here we explicate the Kepler's 3 laws a bit
and make use of them to understand
orbits of the
Galilean moons.
Kepler's 1st law
states that
in a gravitationally-bound
two-body system, the
two bodies orbit their mutual center of mass
in elliptical orbits,
where center of mass
is at the mutual ellipse focus of
the two elliptical orbits.
A simple real case obtains when all of the following are true:
The figure below
(local link /
general link: orbit_circular_large_mass_difference.html)
illustrates
the simple real case except that the mass difference is NOT enough to make the
smaller body's mass negligible.
Sub Tasks:
Kepler's 2nd law
is explicated in the figure below
(local link /
general link: kepler_2nd_law.html).
The closest point of approach of an orbiting body to the
center of force is
generically called periapsis.
Special case names exist for particular
centers of force: e.g.,
perigee
for the Earth,
perihelion
for the Sun,
periastron
for a star,
etc.
For Jupiter as the
center of force, the special
case name is _____________ . HINT: What is the alternate
name for the Roman god Jupiter.
The
Kepler's 3rd Law
is somewhat explicated in the figure below
(local link /
general link: kepler_3rd_law.html).
Some data
for the Galilean moons
is given in
Table: Galilean Moons of Jupiter
below
(local link /
general link: galilean_moons_table.html).
Sub Tasks:
Kepler's 3rd law
for a fixed center of force
(e.g., Jupiter for the
moons of Jupiter
to high accuracy/precision)
can always be written p**2 ∝ r**3, where
p is orbital period
and r is mean orbital radius.
For the moons of Jupiter,
we can rewrite the law as p_d = C * r_j**(3/2), where
p_d is orbital period
in days,
r_j is mean orbital radius
in equatorial Jupiter
radii,
and C is a constant.
Sub Tasks:
The 3 innermost Galilean moons exhibit
a 1:2:4 Laplace resonance
which is explicated in the figure below
(local link /
general link: jupiter_galilean_moons_resonance.html).
By following with your eye 2 adjacent-orbit
Galilean moons in the
animation verify
that the animation does
display the
1:2:4 Laplace resonance.
Did you verify it? _________ .
We CANNOT set up real gravitational
orbits in the classroom to demonstrate
their behavior.
Gravity is just far, far too weak between human-sized objects.
However, the conical pendulum gives
a somewhat analogous case to a gravitational
orbit.
The period of the conical pendulum
obeys P ∝ r**(1/2), where r is the horizontal radius.
This is different from
Kepler's 3rd law
P ∝ r**(3/2), where r is the
mean orbital radius.
Still the
2
formulae are a bit alike.
The conical pendulum
is explicated in the figure below
(local link /
general link: pendulum_conical.html).
Omit this task if NO
conical pendulum
is available.
The formulae given in the figure above
(local link /
general link: pendulum_conical.html)
predicts that the period of
conical pendulum
with r ≅ 0.25 m and θ ≅ 45° will be P ≅ 1 s.
Swing the conical pendulum
with r ≅ 0.25 m and θ ≅ 45° and time it for for 10 periods.
Divide the swinging time by 10. Is the experimental
result consistent with the predicted 1 s to within 25 %?
We'll have to do some angle
measurement with a protractor.
Behold:
Obviously the Galilean moon
can't be observed at this time.
These kind of eclipses are
total solar eclipses on the
Galilean moons.
Galilean moons
shine by reflected light mainly from the Sun,
and so they are nearly invisible during an
eclipse even though there is usually
an unobstructed line of sight
from the Earth
to the Galilean moon.
Occultations
and eclipses
coincide when Jupiter is
in opposition.
They will sometimes also coincide near
oppositions.
A shadow transit is
a total solar eclipse on that
small region of Jupiter where the
umbra touches it.
Transits
and shadow transits
coincide when Jupiter is
in opposition.
They will sometimes also coincide near
oppositions.
The triple transit
and shadow transit
is explicated in some detail in the figure below
(local link /
general link: galilean_moons_transit.html).
Estimate and
then (if you have a protractor)
measure the astronomical phase angle
illustrated in the figure below
(local link /
general link: phase_angle_astro_jargon.html).
Each group should follow the instructions given with the figure below
(local link /
general link: galilean_moons_orbits.html)
and append the
completed diagram to favorite group member's report.
Sub Tasks:
Launch
TheSky.
Prepare and print a diagram of the
Solar System
for today.
Remember
TheSky date has to be set each time
(at least for the
TheSky6).
The diagram should be looking straight down from the
north ecliptic pole.
It should show only out to the orbit
of Jupiter.
Draw a triangle
with vertices
at the Sun,
the Earth,
and Jupiter.
You may need to consult List of Tricks for TheSky
to carry out the operations.
Measure the elongation
and astronomical phase angle
for Jupiter.
Do the values agree with those determined in
Task: Galilean Moon Orbits to within a few degrees.
____________ . If NOT, you've done something wrong.
Append the diagram to the favorite group member's report.
Tidally locked means that
the moon
(or any astro-body)
always turns nearly the same side to the
parent planet
(or whatever other astro-body
it orbits).
For tidal locking to happen, the
moon's
axial rotation rate to equal its orbital rotation rage exactly on average.
At almost all moment,
the tidal force
(which effected
tidal locking
in the first place)
acts as a
restoring force
to maintain
tidal locking.
See the figure below
(local link /
general link: tidal_locking_moon.html).
Sub Tasks:
The tidal force is explicated in
the figure below
(local link /
general link: tidal_force.html).
Sub Tasks:
How does the tidal force cause
tidal locking?
The figure below
(local link /
general link: tidal_locking_origin.html)
will completely satisfy your curiosity.
Something like the figure below
(local link /
general link: galilean_moons_sky.html).
The Galilean moons
are quite bright and could easily be observed with the
naked eye
if they were NOT lost in the glare of
Jupiter.
In fact, if you mask out Jupiter
(e.g., with building edge),
you can see the Galilean moons
(see Wikipedia: Galilean moons: Visibility).
It's possible that they were observed occasionally long before the
invention of the telescope.
In fact, it is possible
that Chinese astronomer
Gan De (4th century BCE)
observed Ganymede
in 365 BCE
(see Wikipedia: Gan De: Observations).
However, Galileo (1564--1642) is correctly
credited with the discovery of the Galilean moons
since he is the first recorded person to certainly see them and
he is certainly first person to identify them for what they were:
moons of Jupiter.
Sub Tasks:
Galileo's observations
of the Galilean moons
showed their sinusoidal motion
on the sky.
Sub Tasks:
Magnification
and
field of view (FOV) are
two parameters of a
telescope.
They can be varied by
changing the eyepiece used.
Magnification
is the ratio of angular size seen through the
telescope to the
angular size seen without the telescope.
Magnification is, in fact,
determined the focal lengths
of the primary
and eyepiece---the formula is
M = f_primary / f_eyepiece.
FOV has two meanings:
As usual, context tells you which meaning applies.
I don't think there is a simple general formula for
FOV.
However, FOV is at least approximately
inversely proportional to magnification.
Table: C8 Telescope Magnification and Field of View
below
(local link /
general link: telescope_c8_mag_fov_table.html)
gives the magnification and
FOV
data for
the Celestron C8 telescopes
and
the eyepieces we have available.
You should review the parts of the
Celestron C8 telescopes
in the figure below
(local link /
general link: telescope_c8_diagram.html).
You should also review the
Observation Safety Rules.
When the instructor
gives the word, everyone goes to the roof.
You can leave your stuff safely.
The instructor will lock the door.
Each group member should find a
Celestron C8 telescope.
The sky alignmet is set, so don't destroy it by moving the
C8's
by hand or
by turning off the power.
Always use the
LCD
keypad to
slew the
C8's.
Put Jupiter
in the field of view (FOV)
either by just finding it by eye or using the find menu on the
LCD
keypad.
Each PERSON in the group should draw their own
sky map
of the FOV
(using our standard 40 mm eyepieces) centered on
Jupiter.
Use the FOV figure below
(local link /
general link: field_of_view_blank.html)
for your sky map
and draw approximately to-scale.
Given the FOV
data given in
Table: C8 Telescope Magnification and Field of View
above
(local link /
general link: telescope_c8_mag_fov_table.html),
estimate the angular diameter of
Jupiter and put that value
on your sky map in brackets
near Jupiter's label.
To help identify which
Wikipedia: Galilean moon is which
and transits,
occultations,
eclipses,
and shadow transits
use Javascript Jupiter when you get back inside.
Figuring out the
NSEW is a a bit of trick.
You can find them on the
sky pretty easy since
the great circle path
through Jupiter
to the
north celestial pole (NCP)
(almost exactly at Polaris) is easy to find.
Then remember that the
telescope
point inverts the
FOV
and the star diagonal
mirror inverts
the FOV through the line
perpendicular its symmetry plane.
Repeat Task 16: Your Own Sky Map Centered on Jupiter
using a 9-mm eyepiece.
Sub Tasks:
Do the preparation required by your lab
instructor.
Keywords:
C8 telescopes,
Galilean moons
(Io,
Europa,
Ganymede,
Callisto),
Jovian solar eclipses,
Jupiter,
Kepler's 3 laws of planetary motion,
Kepler's 3rd law,
occultation,
opposition,
orbit
(orbital period,
mean orbital radius,
orbital resonance),
shadow transit,
TheSky
(TheSky6,
TheSkyX,
List of Tricks for TheSky,
TheSky Orientation),
tidal locking,
umbra,
Wikipedia: Moons of Jupiter: List.
Hm.
Task Master:
EOF
The Galilean moons orbit
Jupiter in nearly
circular orbits.
For tabulated data on the
Galilean moons see
Wikipedia: Moons of Jupiter: List.
The Galilean moons, in fact, obey
Kepler's 3 laws of planetary motion
to high accuracy: the Galilean moons being the
"planets" in this context.
Each Galilean moon and
Jupiter are examples of this simple real case.
EOF
In this section, we consider
transits,
occultations,
eclipses,
and shadow transits
involving
the Galilean moons.
The video
Triple transit by the Galilean moons, 2015 Jan23
| 1:12
shows a rare triple transit
and shadow transit
by the Galilean moons.
View it.
EOF
_________________________________________________________________________
Table: Transit Times for the Galilean Moons
_________________________________________________________________________
Galilean Orbital Orbital Δθ ω Δt Δt_h
Moon Period p Radius r ≅d/r =2π/p =Δθ/ω =Δt*24
(days) (mm) (radians) (rads/day) (days) (hours)
Io 1.7691
Europa 3.5512
Ganymede 7.1546
Callisto 16.689
_________________________________________________________________________
As mean orbital radius
increases,
angular velocity ω
decreases which tends to increase
transit time,
but transit orbital arc length θ
decreases which tends to decrease
transit time.
Which trend wins out?
Most significant
moons
in the
Solar System
(including the Moon
and the Galilean moons)
are tidally locked
to their parent planet
(see Wikipedia: Tidal locking: Moons;
Wikipedia:
Tidal locking: List of known tidally locked bodies).
We are going to observe
Jupiter
(planet symbol
♃)
and the Galilean moons---if
Jupiter
is in the night sky
and were NOT clouded out.
EOF
This is the observing section.
Include all the details you can see and label them if possible: i.e.,
Jupiter,
Jovian band structure,
Great Red Spot,
all Galilean moons,
transits,
shadow transit,
stars,
the astronomical NSEW approximately.
Under construction until
sine die---but maybe on
the Greek Kalends
(Augustus (63 BCE -- 14 CE)
quote).
This section is only
for remote instruction.
End of Task
Goodnight all.
Post mortem comments that may often apply specifically to
Lab 6: Galilean Moons of Jupiter: