- Objectives (AKA Purpose)
The main objective is to learn something about planets including exoplanets.The main focus is on planets as astronomical objects in the old-fashioned sense: i.e., astronomical objects as seen on the sky and their orbits. We are NOT much concerned with their internal structure (e.g., with planetary geology and planetary atmospheres).
We touch on the following topics:
- Planet apparent motions on the sky. Remember, in astronomy "apparent" does NOT mean illusionary: "apparent" means as seen from the Earth.
- A bit about the history of the geocentric Ptolemaic system and heliocentric solar system.
- Planet physical motions: i.e., their motions relative to the local inertial frame (which is well approximated for the Solar System by the reference frame of the fixed stars).
- A little celestial mechanics: mostly just an intro to Kepler's 3 laws of planetary motion.
- The discovery and characterization of exoplanets.
- Las Vegas weather permitting, we make observations with the telescope of the planets currently available in the sky.
- Preparation
Do the preparation required by your lab instructor.- Prep Items:
- Read this lab exercise itself: Lab 5: Planets.
Some of the Tasks can be completed ahead of the lab period. Doing some of them ahead of lab period would be helpful.
- It is probably best to print out a copy of
Report Form
on the lab room printer when you get to the lab room since updates to the
report forms are ongoing.
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.
- Do the prep for quiz (if there is one) suggested by your
instructor.
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 Quiz if it exists.
- This is an observing lab. So you should review
Telescope Operation
and List of Tricks for the Telescope as needed.
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.
- There are are many keywords that you need to know for this lab. Many of these you will learn sufficiently well by reading over the Lab Exercise itself.
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.
-
Keywords:
Celestron C8 telescopes,
conjunction
(inferior conjunction and
superior conjunction),
elongation
(greatest eastern elongation and
greatest western elongation),
exoplanet,
Kepler's 3 laws of planetary motion,
naked-eye astronomy,
opposition,
planets
(Mercury,
Venus,
Earth,
Mars,
Jupiter,
Saturn,
Uranus,
Neptune,
ex-planet Pluto,
inner planets,
outer planets,
inferior planet,
superior planet),
planetary configuration,
planetary system,
quadrature,
Solar System,
synodic period,
syzygy,
transit method.
A further list of keywords which you are NOT required to look at---but it would be useful to do so---is:
-
Hm.
- There are are many keywords that you need to know for this lab. Many of these you will learn sufficiently well by reading over the Lab Exercise itself.
- Prep Items for Instructors:
and its Tasks 22--25.- From the General Instructor Prep, review as needed:
- You need to put out
rulers and
protractors.
- This is an observational lab. However, the observations are only a small part and can
be omitted if the seeing is bad.
The sky alignment on the telescopes may NOT needed if the students are only going to make quick sketches.
However, if you are going to larger telescope magnification than provided by the 40-mm eyepieces, sky alignment is probably a good idea.
- The complete lab exercise is too long for the one night. Yours truly recommnends that you omit sections:
- Read this lab exercise itself: Lab 5: Planets.
If observations are NOT done, then Section Exoplanets (Optional at the discretion of the instructor)
could be done.The lab exercise was planned to a complete lesson on planets as astronomical objects in the old-fashioned sense. That plan made the lab exercise too long---but I'm NOT cutting it down---so there.
-
Task Master:
- Task 1: Planetary Configuration Definitions.
- Task 2: Planetary Configurartion Simulator Questions.
- Task 3: Angle Measurement with a Protractor (IPI only).
- Task 4: Solar System Diagrams Made Using TheSky (IPI only).
- Task 5: Measuring Elongations (IPI only).
- Task 6: The Ptolemaic System Simulator.
- Task 7: The Ptolemaic System and Uniqueness.
- Task 8: Inferior Planet Oscillation and Ptolemy.
- Task 9: Copernicus Questions.
- Task 10: Copernicus' Form of the Universe.
- Task 11: A Touch of Pure Algebra. Optional at the discretion of the instructor.
- Task 12: Planet Motion During a Synodic Period. Optional at the discretion of the instructor.
- Task 13: Orbital Period Formulae. Optional at the discretion of the instructor.
- Task 14: Orbital Period Calculation. Optional at the discretion of the instructor.
- Task 15: The Mean Orbital Radius of an Inferior Planet.
- Task 16: The Mean Orbital Radius of a Superior Planet. Optional at the discretion of the instructor.
- Task 17: Good Theories.
- Task 18: Simple Astronomical Unit Questions. Optional at the discretion of the instructor.
- Task 19: The Determination of the Astronomical Unit. Optional at the discretion of the instructor.
- Task 20: The Planetary Orbit Simulator.
- Task 21: The Planetary Orbit Simulator and a Logarithmic Plot.
- Task 22: The Doppler Effect Explicated a Little.
- Task 23: The Exoplanet Radial Velocity Simulator. Optional at the discretion of the instructor.
- Task 24: The Exoplanet Transit Simulator. Optional at the discretion of the instructor.
- Task 25: Exoplanet Mean Orbital Radius and Year of Discovery. Optional at the discretion of the instructor.
- Task 26: Exoplanet Mean Orbital Radius and Orbital Period. Optional at the discretion of the instructor.
- Task 27: Print Sky Map and Observable Planets.
- Task 28: Planet Observations (IPI only).
EOF
Before the advent of the heliocentric solar system, the actual 3-dimensional arrangements and motions in space of the planets were NOT known.
However, there were still special APPARENT arrangements that were obviously important in determining those arrangements and motions of the planets. Wrong models were used in determining the arrangements and motions, and those arrangements and motions were determined, NOT surprisely, wrongly.
-
Recall that in astro jargon,
APPARENT does NOT mean false or seeming; it means as
seen from Earth.
The special apparent arrangements are the planetary configurations. They and related items are part of ancient astronomy lore that everyone should know.
Since the advent of the heliocentric solar system, the correct 3-dimensional space arrangements that create the planetary configurations have also been known.
In this section, we consider the planetary configurations themselves and related items.
In the 2 sections below (i.e., Determination of Orbital Periods (Optional at the discretion of the instructor) and Determination of the Mean Orbital Radii), we consider how planetary configurations are used to determine orbital periods and mean orbital radii for the planets in the Solar System.
- Apparent Retrograde Motion Illustrated:
Apparent retrograde motion occurs at the time of the planetary configuration inferior conjunction for inferior planets and at the time of the planetary configuration opposition for superior planets.
Apparent retrograde motion is explained and illustrated in the figure below (local link / general link: apparent_retrograde_motion.html).
- Planetary Configurations Illustrated:
Planetary configurations are defined and the most important ones are displayed in the figure below (local link / general link: planetary_configurations.html).
- Task 1: Planetary Configuration Definitions:
Complete the following short definitions in complete sentences in your own words. Read the definition or explanation from some source, think about what it means, and then formulate your own version.
Sub Tasks:
- Apparent retrograde motion is:
the angular motion
of an astronomical object
in a plane
in a direction of motion opposite at least approximately to a reference direction
all as seen from a particular observing point.
The reference direction can be the
astronomical object's usual direction of motion,
the usual direction of motion of other
astronomical objects in the
the astronomical system,
or a defined reference direction.
The usual convention is that the Earth is the observing point and the reference direction is eastward in the equatorial coordinate system on the celestial sphere.
Apparent retrograde motion (often abbreviated to retrograde motion) in the usual convention is the westward motion exhibited by inferior planets near inferior conjunction and superior planets near opposition.
- A conjunction is: generally speaking when 2 or more astronomical objects are aligned or nearly aligned on the sky. In the category of planetary configurations, a conjunction is when a planet's position projected onto the ecliptic plane is aligned with the Sun.
- The ecliptic is:
- Elongation is:
- A greatest elongation is:
- Inferior and superior conjunctions are:
- Inferior and superior planets are:
- An opposition is:
- A planetary configuration is:
- A quadrature is:
- A syzygy is:
- Task 2: Planetary Configuration Simulator Questions:
Complete this task using the planetary configuration simulator shown in the applet figure below (local link / general link: naap_planetary_configurations.html).
in the group must do this task for themselves.
Sub Tasks:
- Push all the buttons to see what they do. Did you do this? Y / N Answer: Yesss!
- Can you see apparent retrograde motion in the lower simulation panel? Y / N Answer: Yesss!
- Can you make the simulator show the elongation angles? Y / N Answer: Yesss!
- Can you make the target planet an inferior planet? Y / N Answer: Yesss!
- Can you make the target planet orbit at exactly 1 AU if the observer is on Earth? Y / N Answer: Noooo! I thought the answer was yes at first, but I was wrong.
- Planetary Configurations Illustrated:
In this section, we will consider the elongations of the planets as of today and planetary configurations nearest to those elongations.
- Task 3: Angle Measurement with a Protractor
(IPI only):
- EOF
- Task 4: Solar System Diagrams Made Using TheSky (IPI only):
Sub Tasks:
- Launch TheSky
(TheSky6 to be precise).
-
Go Toolbar/File/AST105 which is probably
unnecessary
since AST105 should be the normal setting, but sometimes people leave
TheSky in funny modes.
-
Set the date to today's date & time:
Go Toolbar/Data/Time.
-
To view the Solar System appropriately,
go Toolbar/View/3D Solar System Model.
Then check out the List of Tricks for TheSky: Solar System Tricks (i.e., item 18) which tells you how to do some of the things we have to do tonight.
- We a view of the Solar System
the north end of the ecliptic axis
pointing straight out of the screen:
i.e., we want
the ecliptic plane (i.e., the plane
of the Earth's orbit) perpendicular to the
line-of-sight with
eastward being
counterclockwise.
Usually, the 3D Solar System Model will just come up in this orientation. If NOT, use the Tricks (item 18) to find out how to get it.
-
The direction of the red line is the vernal equinox which
is the zero point of the
right ascension (RA) in the
equatorial coordinate system.
-
Zoom in to see the
inner Solar System
out to Mars.
If some inner Solar System planets are turned off, you must turn them on using the button menu with Display Explorer. See List of Tricks for TheSky: Solar System Tricks (i.e., item 18.1).
- Go Toolbar/File/Print Preview.
Try to get the Mars
orbit as large as possible and still be all
visible in the Preview---you'll have to go back to
TheSky to adjust
the size.
The larger the Mars
orbit, the easier the measurements on the
printout will be.
- Go Toolbar/File/Print Preview/Print
to get a printout of the
Solar System diagram.
Get one printout per group to append to
the
favorite report form---unless your
instructor
asks for every group member do to a
Solar System diagram.
If you don't want to print after seeing the Preview, go Toolbar/Close.
- Now zoom out to show
Jupiter
and Saturn,
click off
Mercury,
Venus,
and Mars, but NOT
Earth.
- Get a printout of this Solar System diagram following the
same procedure as for the first one.
- We probably won't use TheSky again tonight,
but you can leave it open just in case.
But when you do close TheSky,
do NOT save changes.
- Task 5: Measuring Elongations (IPI only):
Sub Tasks:
- If the astronomical objects are NOT named
already, write in their names (i.e., label the Earth,
Sun
and all the shown planets)
on your Solar System diagrams.
- Draw lines from the
Earth to the Sun
and all the shown planets
and extend the lines well beyond the astronomical objects
so that you can measure the elongations
to the planets easily with
a protractor.
- Remember elongation is
measured
east/west
from the
Earth-Sun line
from 0° to 180°.
- Measure the
elongations
of the planets
and put the elongation values
on the diagrams showing to which angle they apply as best you can.
- You should attach the diagrams to the
favorite report form---or, if
every student printed diagrams as requested by the
instructor,
to every group member's report form.
- For today's date (see Date & Time),
complete the table below
(local link /
general link: Table: Elongations and Nearest Planetary Configurations).
By nearest "planetary configuration", we mean the planetary configuration nearest to today's elongation just approximately.
You'll need to know that the greatest elongations for Mercury and Venus are, respectively, 18--28° and 45--47° (see Wikipedia: Elongation). There is a range of greatest elongations since the orbits are NOT exact circles.
_______________________________________________________________________________________ Table: Elongations and Nearest Planetary Configurations: For today, right now. _______________________________________________________________________________________ Planet Elongations Nearest Planetary Configuration (degrees,E/W) (e.g., opposition, quadrature, etc.) _______________________________________________________________________________________ Mercury Venus Mars Jupiter Saturn _______________________________________________________________________________________ - Task 4: Solar System Diagrams Made Using TheSky (IPI only):
In this section, we consider the Ptolemaic system (AKA the geocentric Ptolemaic solar system).
-
Task 6: The Ptolemaic System Simulator:
Complete this task using the Ptolemaic System Simulator shown in the applet figure below (local link / general link: naap_ptolemaic_system_simulator.html.html) after this task.
in the group must do the task for themselves.
Sub Tasks:
- Push all the buttons to see what they do. Did you do this? Y / N Answer: Yesss!
- Can you see apparent retrograde motion in the 2 simulation panels for a superior planet? Y / N Answer: Yesss!
- Can you make simulator show the motion of an inferior planet? Y / N Answer: Yesss!
- Can you see apparent retrograde motion in the 2 simulation panels for an inferior planet? Y / N Answer: Yesss!
- Can you identify your zodiac constellation by using the NAAP Applet: Seasons and the Zodiac Simulator? Y / N Answer: Yesss!
- Can you change the epicycle size and the equant eccentricity, and show the Earth-Sun line and the epicycle center-planet line? Y / N Answer: Yesss!
- Task 7: The Ptolemaic System and Uniqueness:
The Ptolemaic system was NOT the uniquely good geocentric epicycle system---many roughly equally good geocentric epicycle systems were developed in the centuries after Ptolemy (c.100--c.170 CE).
After reading the caption with Ptolemaic System Simulator (which is given above), discuss whether or NOT Ptolemy should have been aware of the non-uniqueness problem of geocentric epicycle systems and what might a modern scientist conclude about the geocentric epicycle theory from the non-uniqueness problem. Remember that the Ptolemaic system was worked out in great detail by Ptolemy, and so he spent a lot of time devising its particular epicycle orbits.
Answer: Since this is a discussion problem, there is NO right answer.
My answer is that Ptolemy was such a clever builder of epicycle orbits/models that he must have been aware of the non-uniqueness problem. But it probably was NOT as glaringly obvious as ∼ 14 centuries later when Nicolaus Copernicus (1473--1543) presented his Copernican heliocentric solar system which still used epicycle orbits, but was much more contrained because Copernicus' heliocentrism fixed the relative distances of the Solar System.
A modern scientist would conclude from the non-uniqueness problem that geocentric epicycle theory was an inadequate theory to account for the Solar System and was possibly completely wrong.
- The Full Ptolemaic System:
The full Ptolemaic system is displayed in the cartoon below.
- Task 8: Inferior Planet Oscillation and Ptolemy:
Was the fact that the inferior planets exhibit an apparent oscillation around the Sun's position on the sky (see the figure above (local link / general link: ptolemy_system.html) and the Ptolemaic System Simulator in the applet figure below (local link / general link: naap_ptolemaic_system_simulator.html.html) a clue to good old Ptolemy? Discuss. HINT: You might consider what happens in the Tychonic system and the Copernican system.
Answer: This is a discussion question, and so there is NO absolutely right answer.
One could answer that Ptolemy was so fixed in his geocentrism and a basically Aristotelian outlook that he unable to see the oscillation as a clue. Geocentrism said the basic motion of the planets had to be around the Earth and the Aristotelian outlook made all the planets separate entities and NOT interacting.
But, on the other hand, you could say "What the Heck". It's obviously a clue that the inferior planets orbit the Sun. And if you say that then why NOT all the planets. If Ptolemy had picked up the clue, he would have been well on his way to the Tychonic system in which all the relative Solar-System distances are just as in the Copernican system. Maybe Ptolemy would even have had to face the power of the Copernican system and become convinced of its truth.
But Ptolemy did NOT pick up the clue. Maybe his geocentrism incapacitated him. Maybe he said "enough is enough" when he finished the Almagest---his big book on the Ptolemaic system. Either way, astronomy ended up spinning its wheels for ∼ 14 centuries until Nicolaus Copernicus (1473--1543).
The students deserve full marks for anything showing some insight or even less is you need to be generous.
Copernican Revolution was the establishment of the heliocentric solar system as the accepted model of the Solar System.
The Copernican Revolution was started by its eponym, Copernicus.
- Nicolaus Copernicus (1473--1543):
Nicolaus Copernicus (1473--1543) was the first person to put into recorded history the heliocentric solar system as a well supported hypothesis. The qualification is "well supported hypothesis" is necessary and important.
- Task 9: Copernicus Questions:
Sub Tasks:
- Approximately how long after Ptolemy was
the lifetime of
Copernicus? _______________
Answer:
About 14 centuries.
- What is the main difference between the
Ptolemaic system
and the heliocentric solar system?
Answer: In the Ptolemaic system, the physical motion of the planets is about the Earth and in heliocentric solar system, it's about the Sun. Note that by "physical", we mean as directly determined caused by physical law. A second main difference is that in the Ptolemaic system, the Earth is a unique object, but in the heliocentric solar system, it's just a planet.
- Discuss why would people in the
16th century found the
heliocentric solar system
hard to accept.
Remember, they thought motion and rest were absolutely different states and
thought of the Heavens
as being unchanging and eternal unlike the
Earth.
Answer: In the 16th century and earlier, almost everyone thought that motion and rest were absolutely different states and that if you were in motion you would notice from all kinds effects like bumping along or flying off. Those effects were NOT noticed relative to the Earth, and so the Earth was at rest absolutely and the heavenly bodies (which were moving relative to the Earth) were in motion absolutely. So the Earth was special because it was at rest, but also because the heavenly bodies mostly did seem to going around it (with some complications) or, in the case of the fixed stars, the celestial axis, and the Heavens seemed unchanging and therefore perfect unlike the Earth. All of these reasons were WRONG if the heliocentric solar system were RIGHT. And they were WRONG, but they looked RIGHT before a lot more data was analyzed and theorizing was done.
- Task 10: Copernicus' Form of the Universe:
Sub Tasks:
- Read the figure below
(local link /
general link: copernican_system.html)
which is from Copernicus'
own book on heliocentric solar system.
Have you read it? Y / N Answer: Yesss!
- Since heliocentrism gave the
relative radii for the
planets
(which now included the
Earth),
the structure of the Solar System
was revealed to Copernicus:
-
... the chief thing, that is the form of the universe and the clear
symmetry of its parts.
Unfortunately, Copernicus never makes that completely explicit it seems. He certainly thought of it as a major argument. Retrospectively, it clearly is the main argument.
Now Copernicus could NOT measure absolute distances beyond the Moon. No one could until the 17th century (see Wikipedia: Astronomical unit: History).
So how could Copernicus get the correct order and correct relative orbital radii of planets or as he put it "form of the universe". HINT: The short answer is expected.
Answer: Copernicus had the right theory for the Solar System (i.e., the theory of heliocentrism) and sufficient constraints from observations (most importantly planetary configurations) in order fit the relative radii and thereby also obtain the correct order.
- Task 9: Copernicus Questions:
In this section, we determine approximate orbital periods of the planets.
We are following in crude way the footsteps of Nicolaus Copernicus (1473--1543).
- Assumptions:
We assume the heliocentric solar system model, of course.
But we will simplify our work by assuming (a) circular orbits centered on the Sun, (b) the circular orbits are aligned with the ecliptic plane and (c) constant revolution rates for the planets.
We also assume the planets revolve counterclockwise (a direction we also call eastward) as viewed from the north celestial pole (NCP)---our Space Ghost view of the Solar System.
We also neglect the distinction between solar orbital periods and sidereal orbital periods---for the Earth, this is the difference between the solar year and sidereal year.
- Direct Observables and the Synodic Period:
The Earth's orbital period---the year---is a direct observable with heliocentric solar system model.
But the other planet orbital periods are NOT direct observables.
The direct observable for the planet is the synodic period.
The synodic period is the time it takes for a planet to return to the same angular position relative to the Sun.
To give a concrete picture, the synodic period is the time between, e.g.,
- Task 11: A Touch of Pure Algebra:
Now for the a touch of pure algebra.
Sub Tasks:
- Given 0 =1/a + 1/b + 1/c, solve for a in terms of b and c.
1/a = - 1/b - 1/c a = -bc/(b+c) - Show that your solution can be written a = -b/(1+b/c).
a = -bc/(b+c) a = -b/(1+b/c) - Now, mutatis mutandis, solve for b and c.
HINT: Proof by symmetry and cycling the variables suffices.
Answer: Obviously by symmetry and just cycling the variables, we have
b = -ca/(c+a) = -c/(1+c/a) c = -ab/(a+b) = -a/(1+a/b)
- Synodic Period to Orbital Period:
Say you have 2 planets: planet 1 and planet 2
Say they are aligned at time zero.
The next time they are aligned is 1 synodic period later.
During that 1 synodic period one planet has lapped the other one.
-
Task 12: Planet Motion During a Synodic Period:
Draw a diagram illustrating inner planet 1 lapping outer planet 2 during 1 synodic period.
Answer: Behold, outer planet 2 goes X° < 360° while inner planet 1 goes 360°+X°. The angles are about the Sun. You will have to imagine the apppropriate diagram.
- Task 13: Orbital Period Formulae:
The relative difference in angle after 1 synodic period is ±360, where the upper case if for leading planet and the lower for the trailing planet.
Thus,
±360 = R_1*t - R_2*t , where R_1 is the angular velocity of planet 1, R_2 is the angular velocity of planet 2, and t is the synodic period.Sub Tasks:- Now R_1=360/t_1 and R_2=360/t_2.
Show that 1/(±t) = 1/t_1-1/t_2 .
Answer: Substitute in the formulae for R_1 and R_2 to get ±360 = 360*t/t_1 - 360*t/t_2 and get ±1 = t/t_1 - t/t_2 and then divied by t to get the formula to be proven.
- Now making use of the algebra you did above in
Task 11: A Touch of Pure Algebra: Sub Task 2,
derive the orbital period
formulae:
t_2 t_1 t_1 = ----------- and t_2 = ----------- . 1+t_2/(±t) 1-t_1/(±t)Answer: Let a=t_1, b=-t_2, and c=-(±t) using the variables of Task 11: A Touch of Pure Algebra: Sub Task 2. The first formula to be proven follows at once. Then let a=-t_2, b=t_1, and c=-(±t) again using the variables of Task 11: A Touch of Pure Algebra: Sub Task 2. The second formula to be proven follows at once.
- Task 13: Orbital Period Formulae:
- Task 14: Orbital Period Calculation:
Using the orbital period formulae derived just above in Task 13: Orbital Period Formulae, complete the following table by filling in the 2 blanks.
____________________________________________________________________________ Table: Planet Orbital Periods and Synodic Periods in Julian years (Jyr) ____________________________________________________________________________ Planet Orbital Period Synodic Period (sidereal years) (sidereal years) ____________________________________________________________________________ Mercury 0.240846 0.317 Venus ________ 1.599 Earth 1 - Mars ________ 2.135 Jupiter 11.86 1.092 Saturn 29.46 1.035 Uranus 84.01 1.012 Neptune 164.8 1.004 Pluto (ex-planet) 248.1 1.002 ____________________________________________________________________________Answer: Let Venus and Mars be planet 1 and Earth be planet 2. For Venus, t_1 = 1/(1+1/1.599) ≅ 8/13 ≅ 0.6 with accepted value being 0.615198 Jyr. For Mars, t_1 = 1/(1-1/2.135) ≅ 2 with accepted value being 1.88082 Jyr. - Direct Observables and the Synodic Period:
In this section, we determine approximate mean orbital radii of the planets.
We are following again in crude way the footsteps of Nicolaus Copernicus (1473--1543).
We make the same assumptions as in the Section Determination of Orbital Periods: see Assumptions.
- Planetary Configurations Redux:
Planetary configurations are NOT just observational curiosities---which were probably used in astrology---but I don't know.
The are/were useful in determining the orbital parameters.
We've already used planetary configurations as a mental aid in determining orbital periods
Just have a look again at the common planetary configurations in the figure below (local link / general link: planetary_configurations.html).
- Task 15: The Mean Orbital Radius of an Inferior Planet:
Sub Tasks:
- Take a good look at the greatest eastern elongation of an inferior planet in the planetary configuration figure above (local link / general link: planetary_configurations.html). Have you done this? Y / N Answer: Yesss!
- What is the closed geometric shape marked out by the inferior planet, the Sun, and the Earth? Be as specific as possible. HINT: At greatest eastern elongation, the Earth-planet line is tangent to a circle. ___________________ Answer: A right triangle.
- Let the Earth-Sun distance be A, the Sun-planet distance be R, the Earth-planet distance be D, and the angle at the Earth vertex be θ. Recalling the sine function of trigonometry, we have R/A=sin(θ). Solve for R. ___________________ Answer: R=A*sin(θ)
- What is the name of distance A in astro jargon? ___________________ Answer: The astronomical unit (AU).
- Is θ a direct observable? Y / N Answer: Y = Yes. You can just measure it on the sky.
- So can R be determined by simple measurements? Y / N Answer: Obviously, yes.
- Could Copernicus have obtained the distance to the inferior planets in astronomical units (AUs) using the method just explicated above? ___________________ Answer: Yes because he had the heliocentric model of the Solar System.
- Can the orbital radius R for
superior planets be found by
the method just explicated above? Explain.
HINT: What
planetary configuration
corresponds to a
greatest elongation
for a superior planet?
Answer: No. For superior planets, it is the Earth vertex of the right triangle formed at quadrature by Earth, Sun and superior planet which has the right angle. NEITHER of the other 2 angles of the right triangle are direct observables.
For a superior planet, the planetary configuration corresponding to greatest elongation is quadrature as implicitly knew in answering the first part of this task. ! Answer space is in the Report Form, NOT in the lab itself. >
- Task 16: The Mean Orbital Radius of a Superior Planet:
Sub Tasks:
- Take a good look at the easstern quadrature of a superior planet in the planetary configuration figure above (local link / general link: planetary_configurations.html). Have you done this? Y / N Answer: Yesss!
- What is the closed geometric shape marked out by the superior planet, the Sun, and the Earth? Be as specific as possible. HINT: At quadrature the Earth-planet line is tangent to a circle. ___________________ Answer: A right triangle.
- Let the Earth-Sun distance be A, the Sun-planet distance be R, the Earth-planet distance be D, and the angle at the Sun vertex be φ. Recalling the cosine function of trigonometry, we have A/R=cos(φ). Solve for R. ___________________ Answer: R=A/cos(φ)
- What is distance A in astro jargon? ___________________ Answer: The astronomical unit (AU).
- Is φ a direct observable. ___________________ Answer: No. There is no direct way of measuring φ from the Earth.
- So can R in astronomical units be determined by one simple observation? Y / N Answer: No. See the question and aswer above.
- Draw a diagram below showing the
superior planet at
opposition and a time t later
when the superior planet
is at eastern quadrature.
Note that both
Earth and
superior planet move during time t.
Label φ on this diagram.
Answer: You will have imagine the diagram.
- What the angular velocity ω of the Earth RELATIVE to the superior planet as seen from the Sun given that the superior planet's synodic period t_syn (which is among other things the time period between oppositions). HINT: Remember, there are 360° in a circle. ___________________ Answer: ω = 360°/t_syn .
- Now solve for R in terms of A, ω and t. ___________________ Answer: R = A/cos(ωt) .
- Could Copernicus have determined the
mean orbital radii
of the superior planets
in terms of astronomical units
given data available to him? Explain.
Answer: Obviously yes. t and t_syn are simple direct observables easily measured since ancient times and well known to Copernicus.
- Task 17: Good Theories:
Given that Copernicus could predict (or deduce) the mean orbital radii of the planets from the heliocentric solar system model, would the heliocentric solar system model have been a good scientific theory even if it had turned out to be wrong? Discuss.
Answer: Since this is a discussion question, there are no right or wrong answers: there are better and worser answers. However, a good answer is that in modern science a good theory is one from which important testable predictions can be derived, even if testable only prospectively with improvements in experimental or observational technique. Having important testable predictions means a theory can be confirmed to a degree or falsified: either way science is advanced. A bad theory in modern science (though maybe NOT in other fields) is one that CANNOT be tested in principle or CANNOT be tested in practice in any way we can conceive of. Such bad theories are futile in modern science. Since Copernicus' predicted mean orbital radii could in principle and conceivably in practice be compared to observations at least in some indirect sense, the heliocentric solar system model would be judged a good theory in modern science even if had been shown to be wrong: i.e., falsified.
Note an indirect test of the predicted mean orbital radii would be a proof that were correct from a valid physics theory. In fact, they were proven to be correct first by Newtonian physics. - Task 15: The Mean Orbital Radius of an Inferior Planet:
The astronomical unit (AU) is the natural unit for distances in Solar System and, since the Solar System is our reference planetary system, it is the natural unit for other planetary systems too.
Addtionally, the astronomical unit is the baseline for parallax measurements to extrasolar astro-bodies as illustrated in the figure below (local link / general link: parallax_stellar.html).
But to use Solar System distances
and other distances given in astronomical units
for physical understanding, we need
to know the astronomical unit
in terms of the standard distance units which in modern times are distance units used in the
metric system.
-
Physics is strongly
based on fundamental physical constants and nowadays the
metric system
is mostly based on those fundamental physical constants.
So relating natural units
(like the astronomical unit)
to metric system units
is of immense importance in physically understanding systems for which
natural units are used.
- Pre-Modern Astronomical Unit Determinations:
The ancient Greek astronomers came up with range of values some of which were order-of-magnitude correct and others wildly wrong. Clearly, they did NOT really have a conclusive method of determination.
In the 17th century, determinations accurate to 10 % were achieved. Since the 1970s, determinations accurate to 9 significant figures has been achieved (see Wikipedia: Astronomical unit: History)
- Modern Astronomical Unit Determinations
:Modern accuracy in determination of the astronomical unit is achieved by direct radar measurements. One measures, the travel time for a radar pulse to return from an inner Solar System planet, divides that time by 2, and multiplies by the vacuum light speed to get the distance to the planet in meters.
The distance to the planet is accurately known by astrometry in astronomical units. Using the distance accurately in both meters and astronomical units, the astronomical unit in meters can be found.
- The Exact Modern Astronomical Unit:
Historically, the astronomical unit was defined as Earth-Sun---which in turn is the sum of the aphelion and perihelion center-to-center distances divided by 2.
However, in there are actually many finicky small effects that have to be accounted for in order to make exact determinations using the historical definitions. These effects had to be included in the definition making it rather complex and always making the determination of the astronomical unit subject to change.
In 2012, International Astronomical Union (IAU) decided to simply define the astronomical unit as 1.49597870700*10**11 m exactly (see Wikipedia: Astronomical unit: Development of unit definition).
This modern definition gives a value very, very close to the historical definition determinations and is fixed for good. No need to change all the distances given in astronomical units when the determination of the astronomical unit changed a smidgen.
Note:
1 parsec = 3.08567758*10*16 meters = 3.26379772 ... light-years = 206264.806 ... astronomical units 1 light-year = 9.454254955*10**15 meters = 0.3063915365687 ... parsecs = 63197.7909 ... astronomical units- Understanding the Solar System with the Astronomical Unit:
Because the astronomical unit (AU) is the natural unit for the Solar System, it is easy to comprehend Solar System distances in astronomical units.
This point is illustrated in the figure below (local link / general link: solar_system_inner.html).
- Task 18: Simple Astronomical Unit Questions:
Sub Tasks:
- Why does one divide the radar travel time by 2 to get the distance to a planet?
- What is the formula for the astronomical unit in terms the planet in x meters (x * 1 meter) and the planet distance in y astronomical units (y * 1 AU)? HINT: Equate x * 1 meter and y * 1 AU and solve for 1 AU.
- What is the conversion factor for converting a distance in astronomical units to one in meters? HINT: Any number can be multiplied by 1 and 1 = A/B where A and B are the same quantity in different units.
- Task 19: The Determination of the Astronomical Unit:
Sub Tasks:
- Consider your printed diagram of the
inner Solar System
from Section Elongations and Planetary Configurations Today.
Draw a triangle with vertices at Earth, the Sun and Venus.
We neglect the slight eccentricity of the Earth's orbit, and just take the Earth-Sun distance on the diagram to be the astronomical unit.
Measure 2 angles and determine the Earth-Venus distance in astronomical units using the law of sines.
-
The law of sines is given and proven in
subsection just below.
- Now we need the
Earth-Venus distance
in meters for today's date:
Click on Earth-to-Venus to get that distance approximately in light-minutes. The value is: _____________________
Convert the distance in light-minutes to meters. The value is: _____________________
Work space:
- Now give your determination of the astronomical unit
in meters: _____________________
Work space:
- What is the relative difference
as a percentage
of your determination of the
astronomical unit from the
exact modern astronomical unit 1.49597870700*10**11 m?
Work space:
- The Law of Sines:
In order to make our own determination of the astronomical units from the diagram of the inner Solar System generated by TheSky, we need the law of sines.
The law of sines is given and proven in the figure below (local link / general link: law_of_sines.html).
Johannes Kepler (1571--1630) originally derived his eponymous 3 laws of planetary motion by a semi-empirical analysis of the planetary data accumulated by Tycho Brahe (1546--1601).
The 3 laws are now understood as consequences of Newton's laws of motion and Newton's law of universal gravitation.
- Kepler's 3 Laws of Planetary Motion Illustrated:
Kepler's 3 laws of planetary motion are illustrated in the 2 figures below (local link / general link: kepler_1st_2nd_law.html; local link / general link: kepler_2nd_law.html).
- Task 20: The Planetary Orbit Simulator:
Complete this task using the planetary orbit simulator in the applet figure below (local link / general link: naap_planetary_orbit_simulator.html) after this task.
in the group must do the task for themselves.
Sub Tasks:
- First, read the subsection
Kepler's 3 Laws of Planetary Motion Illustrated
including 2 figures above
(local link /
general link: kepler_1st_2nd_law.html;
local link /
general link: kepler_2nd_law.html)
illustrating
Kepler's 3 laws of planetary motion.
Have you read it? Y / N Answer: Heck no. Look, I wrote it, so I don't have to read it, right?
- Push all the buttons of the planetary orbit simulator to see what they do. Did you do this? Y / N Answer: Yesss!
- Start the animation. Can you find the allowed range of eccentricity? Y / N
- Can you make the simulator show the planets, orbits, and orbit names out to Mars? Y / N
- With parameters set for Mercury (remember to click OK) and using the Kepler's 1st law tab, can you show the empty focus, the semi-major axis, the semi-minor axis, the geometric center, and the radial lines? Y / N
- Using the Kepler's 2nd law tab, can you see or hear equal areas being swept out in equal times qualitatively? There's no real right answer---just make your best judgment. If there's no speaker, you can't hear the ticking sound. Y / N / Maybe
- Using the Kepler's 3rd law tab, can you make all the planets (including ex-planet Pluto) show up on the logarithmic plot? HINT: Push all the buttons. Y / N
- Does the logarithmic plot show a line? Y / N
- With parameters set for Mercury (remember to click OK) and and using the Newtonian features tab, can you make the velocity and acceleration vectors appear? Y / N
- What is the range of Mercury's velocity? ___________________________
- Kepler's 3rd Law:
The Kepler's 3rd Law is somewhat explicated in the figure below (local link / general link: kepler_3rd_law.html).
- Power Laws and Logarithmic Plots:
Kepler's 3rd law is an example of power law---a function relationship in which one variable varies as a power another variable.
Power law are quite common and are often displayed on log-log plot, where they form lines.
Say we have power law y = a*x**p, where p is a general power. If we take the logarithm of both sides we get log(y) = log(a) + p*log(x) which is a linear relation for log(y) and log(x). The slope is power p and the y-intercept is log(a).
On a log-log plot, the axes are scaled to take the logarithm automatically.
The tick marks are separated by powers of 10 and NOT fixed amounts.
So one often just says "power laws are linear on log-log plots.
See the examplein the figure below (local link / general link: log_log_plot_wik.html) of an power-law function plotted on a log-log plot.
Note that plots where only one axis is logarithmic are called semi-log plots.
Semi-log plots cause exponential functions to be displayed as linear.
- Logarithmic Plots in General:
below.Collectively, log-log plots and semi-log plots are called logarithmic plots or log plots.
Besides their use in displaying and identifying power-law functions and exponential functions, logarithmic plots have a more general use.
The explanation of this general use is given in the figure below (local link / general link: log_log_plot_dj.html).
Note that log plots turn up all the time in astronomy We see some examples in section Exoplanets (Optional at the discretion of the instructor)
- Task 21: The Planetary Orbit Simulator and a Logarithmic Plot:
Sub Tasks:
- Read the above subsections
Kepler's 3rd Law,
Power Laws and Logarithmic Plots,
and Logarithmic Plots in General
including their embedded figures.
Have you read them? Y / N Answer: Yesss!
- Go back to the
planetary orbit simulator
in the applet figure above
(local link /
general link: naap_planetary_orbit_simulator.html).
Using the Kepler's 3rd law tab,
can you make all the planets
(including ex-planet Pluto) show up on the
logarithmic plot?
Y / N
Answer: Yesss!
What is the slope of the curve on the plot? _________________ Answer: 3/2 as shown in the figure above (local link / general link: kepler_3rd_law.html).
- Task 20: The Planetary Orbit Simulator:
Many astronomers, maybe most, had believed since the time of Isaac Newton (1643--1727) and even somewhat earlier that planets outside of the Solar System (i.e., exoplanets) were abundant.
However, before 1995, there were NO confirmed exoplanets around ordinary stars (see Wikipedia: Exoplanets: Confirmed discoveries).
This was just due to observational limitations as people had long believed.
Now thousands of exoplanets are known---see The Extrasolar Planets Encyclopaedia for current statistics.
Exoplanets are now known to be as common as stars to order-of-magnitude.
There are many methods of discovering exoplanets.
The 2 main methods Doppler spectroscopy and the transit method.
In this section, we learn a bit about discovering exoplanets with the 2 main methods and a bit about the current statistics of exoplanets.
- The Doppler Effect:
The Doppler effect/shift is the change in frequency of a wave phenomenon depending on the motion of source and receiver.
It's a common phenomenon in everyday life for sound. For example, the pitch (which is the psychophysical response to frequency) of sirens depends on whether they are coming or going.
In fact, the Doppler effect is rather different between mechanical waves for which a medium is needed and electromagnetic radiation (EMR) which require NO medium.
We will NOT elaborate on mechanical waves here.
For EMR in vacuum, only the line-of-sight relative velocity between source and receiver determines the Doppler shift.
-
There are, however, effects related to the
Doppler effect which
which have different behaviors: i.e.,
cosmological redshift
and the gravitational redshift.
Some people refer to these effects as
Doppler effects too, but
yours truly they are distinct---thought related.
Note redshift/blueshift is astro-jargon for decreased/increased frequency which is also increased/decreased wavelength.
- Task 22: The Doppler Effect Explicated a Little:
In this lab, we do NOT want to expand much on the Doppler effect/shift, but a little explication is needed to understand it for our purposes.
Sub Tasks:
- Read the subsection above
The Doppler Effect
(local link /
general link:
The Doppler Effect).
Have you read it? Y / N Answer: Yesss!
- Watch all the
Doppler effect videos
below
(local link /
general link:
Doppler effect videos).
Have you watched them? Y / N Answer: Yesss!
- EOF
- The Discovery of Exoplanets by Doppler Spectroscopy:
Using Doppler spectroscopy, one measures the time varying Doppler shift of spectral lines in stellar spectra. They redshift, then they blueshift, then they redshift, then they blueshift ...
The Doppler shift varies because the stars have small orbits about the centers of mass (i.e., barycenters) of their planetary systems.
From the behavior of the Doppler shift, the orbital parameters of the stars can be determined to some degree.
And from the orbital parameters of the stars, details about the planetary systems can be extracted, and, in particular, exoplanets can be discovered.
Doppler spectroscopy had been in use for decades before the first exoplanet was discovered by it. It was used to study binary systems of stars where the Doppler shifts, due to mutually orbiting stars, are much larger than for a single star its planetary system.
Making Doppler spectroscopy work in practice (for planetary systems) required the ability to detect Doppler shifts corresponding to velocities of order of magnitude 1 meter per second or less.
This ability only developed since circa 1990.
- Task 23: The Exoplanet Radial Velocity Simulator:
Complete this task using the NAAP: Exoplanet Radial Velocity Simulator shown in the figue below (local link / general link: naap_radial_velocity_simulator.html). in the group must do the task for themselves.
Sub Tasks:
- First, read the subsection
The Discovery of Exoplanets by Doppler Spectroscopy above
(local link /
The Discovery of Exoplanets by Doppler Spectroscopy)
Have you read it? Y / N Answer: Yessss!
- Push all the buttons of the NAAP: Exoplanet Radial Velocity Simulator to see what they do. Did you do this? Y / N Answer: Yesss!
- Can you start the animation, change the animation speed, and show multiple views of the planetary system? Y / N Answer: Yesss!
- What happens to the radial velocity
as the inclination is increased from
0° to 90°?
Answer: The amplitude of radial velocity increases from 0 to its maximum value.
- Does the radial velocity curve change with longitude of observation? Y / N
- How does changing the stellar mass affect the overall radial velocity? Why does it have this effect?
- How does changing the planet mass affect the overall radial velocity? Why does it have this effect?
- How does changing the planet mean orbital radius (AKA semi-major axis) affect the overall radial velocity? Why does it have this effect?
- How does changing the planet eccentricity affect the overall radial velocity? Why does it have this effect?
- Can you show the simulated measurements? Y / N
- Can you change the signal noise? Y / N
- More signal noise should make the observations worse? Y / N
- Task 24: The Exoplanet Transit Simulator:
In the transit method for the discovery of exoplanets, one just observes the light curve of a star.
Dips in the light curve of the right kind show that planets are transiting the star and partially eclipsing it.
Only stars with inclination near 90° will exhibit planet transits.
EVERYONE in the group must do this task for themselves.
Sub Tasks:
- Push all the buttons on NAAP: Exoplanet Transit Simulator shown in the figure below (local link / general link: naap_exoplanet_transit_simulator.html) this task to see what they do. Did you do this? Y / N Answer: Yesss!
- What happens as you change the planet mass?
- What happens as you change the planet radius?
- What happens as you change the mean orbital radius (AKA semi-major axis) with inclination NOT equal 90°?
- What happens as you change the mean orbital radius (AKA semi-major axis) with inclination equal 90°?
- What happens as you change the stellar mass?
- What happens as you change the inclination?
- Can you show the simulated measurements? Y / N
- Can you change the signal noise? Y / N
- More signal noise should make the observations worse? Y / N
- Task 25: Exoplanet Mean Orbital Radius and Year of Discovery:
Sub Tasks:
- Click The Extrasolar Planets Encyclopaedia: Diagrams.
- Select x axis
semi-major axis (AKA mean orbital radius)
and log scale.
- Select y axis
year of discovery
and linear scale (i.e., non-log scale).
- What kind of plot is shown:
linear scale plot,
semi-log plot,
log-log plot?
______________________________
Answer:
Semi-log plot.
- What is the
semi-major axis (AKA mean orbital radius)
range for known exoplanets to
order of magnitude?
For example, 10**(-1) to 10**2 AU.
Answer: ______________________________
Answer: 10**(-3) to 10**4 AU spans of all confirmed exoplanets as of circa 2020.
- Discounting the 1988 discovery (which was a tentative
and only confirmed later)
and 1992 discoveries
(which were pulsar planets
which orbit pulsars),
the first exoplanet discovered
was in ________________ .
Answer:
1995.
- Do most discovered exoplanets
have mean orbital radii less than 1 AU?
Yes / No / Maybe
Answer:
Yes tending to maybe.
The main reason (perhaps the only reason)
for this is selection bias.
Both Doppler spectroscopy
and the transit method
favor the discovery
of large planets close to their
parent star.
- As Time Goes By (1931),
this plot is likely to grow into a pointy-bottomed column (solid black at the center and speckly at the
edges). Yes / No / Maybe
Answer: Yesss!
- Task 26: Exoplanet Mean Orbital Radius and Orbital Period:
Sub Tasks:
- Click The Extrasolar Planets Encyclopaedia: Diagrams.
- Select x axis
semi-major axis (AKA mean orbital radius)
and log scale.
- Select y axis
orbital period
and log scale.
- What kind of plot is shown:
linear scale plot,
semi-log plot,
log-log plot?
______________________________
Answer:
Log-log plot.
- The fact that most points on
the The Extrasolar Planets Encyclopaedia: Diagrams
log-log plot lie nearly on a straight line agrees
approximately with
the dynamical Kepler's 3rd law
which has the formula
P=[2π/(GM)**(1/2)]*R**(3/2) ,where P is orbital period, M is the parent star mass (assumed much larger than the planet mass), gravitational constant G = 6.67430(15)*10**(-11) (MKS units), and R is the mean orbital radius (AKA the semi-major axis). On the log-log plot, one gets the linear relationship between logarithmic period and logarithmic radiuslog(P)=(3/2)*log(R) + constant .What is the slope of the line on a log-log plot of the dynamical Kepler's 3rd law? HINT: Reread subsection Power Laws and Logarithmic Plots above (local link / general link: Power Laws and Logarithmic Plots). ______________________________ Answer: 3/2 = 1.5 . - The set of points on the
The Extrasolar Planets Encyclopaedia: Diagrams
log-log plot
is a band, NOT a line because 1) ________________________________ ,
2) ________________________________________ .
Answer: Actual, there are 4 answers, but the most important one by far is the first one given below:
- The parent star mass varies.
- Gravitational perturbations in non-two-body systems.
- Observational uncertainty.
- If the planet to star mass ratio is NOT negligibly small, then dynamical Kepler's 3rd law does also depend on the planet mass
- Task 22: The Doppler Effect Explicated a Little:
The planets in the Las Vegas sky at the current time are shown in the sky map below.
If there are any planets in good position and weather permitting, we will observe one or more planets.
-
Task 27: Print Sky Map and Observable Planets:
Sub Tasks:
- IPI only:
Print out the sky map figure below
(local link /
general link: sky_map_current_time_las_vegas.html)
following the
instructions in the figure and updating the time to your approximate observing time if necessary.
- IPI only:
Print out one sky map per group
or per group member as your instructor directs.
-
If there is only one sky map per group,
append it to the
favorite report form.
- IPI only:
Did you succeed in getting a printout of the
sky map? Y / N
Answer: Yessss!
- RMI only:
Go to
Sky Maps by Ordinal Date
for your observing day and
print out the white background sky map.
You will have update the
Universal Time (UT) to your
observing time.
For how to do this, see
General Task: Naked-Eye Observations.
- The
planets
on the sky map are identified by
the planet symbols---the
planet symbols
are elucidated in the figure below
(local link /
general link: sky_map_current_time_las_vegas.html)
- What planets can we possibly
see tonight (or your observing night) because
they are above the horizon
NOT counting Earth?
- What planets can we see for sure tonight
(or your observing night)
because they are sufficiently high in the sky,
they are sufficiently bright,
and the weather permits?
- RMI qualification:
Since you are an RMI student,
you can wait a few days at least for a night with good enough
weather for the observing
planets.
- What planets can we possibly
see tonight (or your observing night) because
they are above the horizon
NOT counting Earth?
- Read over the planet
write-ups
in the subsection Observable Planets below
(local link /
general link: Observable Planets)
about the observable and possibly observable
planets.
Have you read them? Y / N Answer: Heck no. Look, I wrote them, so I don't have to read them, right?
- IPI only:
Do
General Task: Naked-Eye Observations at link
General Task: Naked-Eye Observations
and in particular look for the
observable planets
that can be seen with the
naked eye.
- Observable Planets:
Here is the rundown on the planets we can observe:
- Mercury ☿
is an inferior planet
with greatest elongation
in the range 18--28°
(see Wikipedia: Elongation).
Thus, Mercury is always close
to the Sun.
If it is east of the Sun, it can visible in
western sky at or just after sunset.
Mercury
is a
naked-eye
astronomical object.
Observations for our lab are only possible for Mercury near greatest eastern elongation if the class goes out as soon or maybe earlier than the class start time 7:30 pm.
Yours truly doesn't know if we can see the phases of Mercury with our Celestron C8 telescopes even with our highest magnification eyepiece.
- Venus ♀
is an inferior planet
with greatest elongation
in the range 45--47°
(see Wikipedia: Elongation).
Thus, Venus is always NOT so far
from the Sun.
If it is east of the Sun, it can visible in
western sky at or just after sunset.
Venus
is a very bright
naked-eye
astronomical object.
Observations for our lab are only possible for Mercury near greatest eastern elongation if the class goes out as soon or maybe earlier than the class start time 7:30 pm.
The phases of Venus can be observed with our C8 telescopes, but you probably require a higher magnification than obtainable with our standard 40-mm eyepieces.
- Earth ⊕ is at
nadir.
- Mars ♂
is a superior planet,
and so can have any elongation
from the Sun.
Thus, if Mars is in the
night sky and does NOT set too early or rise too late,
it should be available for observations.
Mars
is a bright and reddish
naked-eye
astronomical object---it is
the Red Planet.
Superior planets do NOT show full planetary phases since from the Earth, since we always see at least part of the day side. In fact, the Earth is so close to the Sun relative to Jupiter and further out planets will appear virtually full all the time except to super precise measurements. Mars can appear gibbous at times (see Wikipedia: Planetary phases).
With ideal seeing and Mars in opposition (when it is closest to the Earth), it may be possible to marginally see surface features on Mars with our C8 telescopes. But maybe light pollution rules that out. In any case, ideal seeing and opposition are relatively rare events.
The Martian moons are probably to small to be seen with our setup under any conditions.
Maybe long-exposure imaging could pick them out.
- Jupiter ♃
is a superior planet,
and so can have any elongation
from the Sun.
Thus, if Jupiter is in the
night sky and does NOT set too early or rise too late,
it should be available for observations.
Jupiter
is a very bright
naked-eye
astronomical object.
Jupiter is always full because of its remoteness from the Sun.
The Jovian band structure and Great Red Spot (if it is on the day side of Jupiter) should be readily observable.
The four Galilean moons should also be readily seen as bright star-like objects. They will be on a line which is rougly aligned with the Jovian band structure. One or more might be invisible if they are being eclipsed by Jupiter. One or more might be hard to see if they are transiting Jupiter.
- Saturn ♄ is a superior planet, and so can have any elongation from the Sun. Thus, if Saturn is in the night sky and does NOT set too early or rise too late, it should be available for observations. Saturn is a very bright naked-eye astronomical object.
Saturn is always full because of its remoteness from the Sun.
The Saturnian band structure may be somewhat observable.
The rings of Saturn should be obvious.
Saturn biggest moon Titan is probably observable. It orbits in the equatorial plane (where the Saturn's rings are too), but it might be hard to identify from background stars.
- Uranus ♅ (with more common symbol
which in html
can be fudge-up as ↑☉)
is a superior planet,
and so can have any elongation
from the Sun.
Thus, if Uranus is in the
night sky and does NOT set too early or rise too late,
it should be available for observations.
Uranus is marginally a
naked-eye
astronomical object under ideal conditions---which
means never in Las Vegas.
Finding Uranus is tricky. The sky alignment on the C8 telescopes may NOT good enough to put Uranus in the field of view (FOV) finderscope. And even if it does, you still have to hunt among several possible astronomical objects.
It's NOT impossible. It's been done.
Uranus should appear as a bluish star Under high magnification it should look a little disky. The 9-mm eyepieces have FOV approximately 10' = 600'' and Uranus' angular diameter is 3.3--4.1'' ≅ 0.05'.
-
Recall
arcminutes
are symbolized by the prime '
and
arcseconds
are symbolized by the double prime ''.
- Neptune ♆ is a superior planet, and so can have any elongation from the Sun. Thus, if Neptune is in the night sky and does NOT set too early or rise too late, it should be available for observations. Neptune is NOT a naked-eye astronomical object.
Finding Neptune is tricky. The sky alignment on the C8 telescopes may NOT good enough to put Uranus in the field of view (FOV) finderscope. And even if it does, you still have to hunt among several possible astronomical objects.
It's NOT impossible. It's been done.
Neptune should appear as a bluish star Under high magnification it should look a little disky. The 9-mm eyepieces have FOV approximately 10' = 600'' and Neptune angular diameter is 2.2-2.4'' ≅ 0.03'.
The main thrill in seeing Neptune is just the finding of it.
- Ex-planet Pluto ♇; is NOT observable by us.
Maybe long-exposure imaging with the C8 telescopes could pick out Pluto. But you would have to put the C8 telescope right on it---which is hard to do if it CANNOT be identified by visual astronomy with the C8 telescope.
- Saturn ♄ is a superior planet, and so can have any elongation from the Sun. Thus, if Saturn is in the night sky and does NOT set too early or rise too late, it should be available for observations. Saturn is a very bright naked-eye astronomical object.
- IPI only:
Print out the sky map figure below
(local link /
general link: sky_map_current_time_las_vegas.html)
following the
instructions in the figure and updating the time to your approximate observing time if necessary.
We will go outside in a moment and observe best available planet or planets.
- Celestron C8 Telescope Review:
A schematic diagram of the Celestron C8 telescope is in the figure below (local link / general link: telescope_c8_diagram.html). You should be able to name the parts.
The range of angular diameters in arcseconds (symbolized by the double prime '') for the planets are:
- Mercury 4.5--13''.
- Venus 9.7--66.0''.
- Mars 3.5--25.1''.
- Jupiter 29.8--50.1''.
- Saturn 14.5--20.1'', excluding rings.
- Uranus 3.3--4.4''. Seeing Uranus as disky takes a bit of confidence/imagination since it's of order 1/200th of the field of view with the 9-mm eyepiece.
- Neptune 2.2--2.4''.
- ex-planet Pluto 0.065--0.115''.
- Task 28: Planet Observations (IPI only):
Sub Tasks:
- Read over
subsection Celestron C8 Telescope Review
above
(local link /
general link: Celestron C8 Telescope Review)
Have you read it? Y / N Answer: Heck no. Look, I wrote it, so I don't have to read it, right?
- Print out as many
field of view (FOV) diagrams
(see below) as your
instructor
requires and append them to the
Report Form as your
instructor directs.
-
Yours truly suggests 2 diagrams per group both to be appended to the
favorite report form.
- Take the diagrams outside with you with something solid to hold the diagrams on when you sketch on them.
- Now observe the planets
your instructor
chooses and draw diagrams of those he/she chooses with
whatever focal length
eyepieces he/she chooses.
-
Yours truly suggests
you observe the best observable planet---which is usually
the most interesting to look at---which if they are in the sky
are Jupiter or
Saturn.
Your truly suggests using the standard 40-mm eyepiece for one diagram and a 18-mm eyepiece for the second diagram.
Consult Table: C8 Telescope Specifications for Available Eyepieces as needed.
- Before you use an eyepiece
smaller than the standard 40-mm eyepiece
you have to center the planet
in the FOV of
standard 40-mm eyepiece.
Then you switch to the smaller eyepiece.
- For the sketches of the FOV,
sketch the planet and accompanying detail: e.g.,
moons,
band structure,
planetary rings,
and stars in the
FOV on the
FOV diagram.
- Outside the circle of the FOV area,
mark down the
eyepiece focal length,
telescope magnification,
and the FOV diameter.
See Table: C8 Telescope Specifications for Available Eyepieces.
- Also outside the circle of the FOV area,
label the sky (i.e.,
celestial sphere) directions:
north,
south,
east,
west.
Remember the C8 telescopes does a point inversion and the star diagonal does an plane reflection through the line perpendicular to its symmetry plane. So you can approximately figure out north, south, east, and west.
- Take a cell phone image of the observed planet for fun. There are no marks whether you do this or NOT.
Goodnight all.
Post mortem comments that may often apply specifically to
Lab 5: Planets: