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. The observations can be dropped if necessary since the lab exercise can be made sufficiently challinging without them. For the observations, see Sky map: Las Vegas: current time and weather.
Sections
We 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:
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.
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,
TheSky
(TheSky6,
TheSkyX,
List of Tricks for TheSky,
TheSky Orientation),
transit method.
Hm.
EOF
We are following in crude way the footsteps of Nicolaus Copernicus (1473--1543).
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.
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.,
Now for the a touch of pure algebra.
Sub Tasks:
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.
Draw a diagram
illustrating inner planet 1
lapping outer planet 2 during 1
synodic period.
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,
Show that 1/(±t) = 1/t_1-1/t_2 .
Using the
orbital period
formulae derived just above in
Task 3: Orbital Period Formulae,
complete the following table by filling in the 2 blanks.
It is just the time it takes the Sun
to move once around the ecliptic from
a geocentric point of view.
±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:
t_2 t_1
t_1 = ----------- and t_2 = ----------- .
1+t_2/(±t) 1-t_1/(±t)
_________________________________________________________________________
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:
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 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).
Sub Tasks:
Answer:
! Answer space is in the Report Form, NOT in the lab itself. >
Sub Tasks:
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.
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 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.
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:
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).
Sub Tasks:
Sub Tasks:
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.
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:
Work space:
Work space:
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).
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
The law of sines is given and proven in
subsection just below.
The angles and the
Earth-Venus
in astronomical units are:
For RMI, the General Task: Naked-Eye Observations can only be done with naked-eye observations, unless the RMI student happens to have access to telescope in which case the naked-eye observations can be supplemented by telescopic observations if the RMI student so wishes.
For IPI, the instructor should set up C8 telescopes for opportunistic telescopic observations in lieu of naked-eye observations, weather permitting.