CL - Orbits (remote)
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School
California State University, Bakersfield *
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Course
110
Subject
Astronomy
Date
Apr 3, 2024
Type
docx
Pages
15
Uploaded by bh314014
Computer Lab – Orbits
(Virtual Lab Remote Version)
Moon’s Orbit
Launch the Voyager 4 program from the Virtual Computer Lab. Select the File/Open
Settings… menu, click on the 110 Settings folder in the Quick access (or open the folders
Local Disk, Program Files, Carina Software, Voyager 4, 110 Settings), and open the Settings
File called "Moon Orbit". This is a view of Earth and Moon (at the proper scale) from 5 AU
above the Sun. The blue-green line is Earth's orbit around the Sun and the white circle is the
Moon's orbit.
Actually, the white circle is just the Moon's average orbit. The Moon's real orbit is
distinctly elliptical, you should see that the Moon appears either inside or outside of the
white circle.
Start the animation (you might get a better display by first changing the
zoom to 8’ and the Time Step to 1 hour). Watch how the Moon's distance
varies as it completes an orbit. Stop the animation. In the Location Panel,
drag the Latitude arrow from 90° to 0°. Note how the Moon's orbit is tilted (5°) relative to
the ecliptic plane, you'll probably see that the Moon is above or below the ecliptic at the
current moment.
Animate and watch the Moon vary its position above and below the ecliptic as it
orbits. Does the Moon ever get exactly between Earth and Sun? Yes, but not very often,
usually once or twice a year. When this happens, we have a solar eclipse. Slightly more
common is the Earth getting between the Sun and Moon (more common because the Earth
is bigger than the Moon). Earth blocks sunlight from reaching the Moon and a lunar eclipse
results.
Orbital Eccentricity
Select the File/Open Recent Settings/Startup menu. Close the Time Panel, select the
Tools/Planet Report… menu, select the "Distance to the Moon" option from the pop-up
menu. This display plots the Earth-Moon distance every day for a
year, each blue square dot is one day's value.
That the distances go up and down is typical of any elliptical orbit. The farthest-from-
Earth distances are called apogees (the equivalent of aphelion for orbits around the Sun)
and the closest-to-Earth points are called perigees (equivalent of perihelion). What's very
unusual about the Moon's orbit is that the perigees vary so much, you'll probably see
perigees ranging from about 356,000 km to about 370,000 km.
Estimate the average apogee and perigee distances just by eyeballing the average
level of the peaks and troughs. Note the numbers listed are in 1000s of kilometers.
Apogee = ________________
Perigee = _________________
Orbits–1
Calculate the ratio of these two numbers, I'll call that value s
, your answer should be a
little less than 1, if you get an answer a little more than 1, you likely reversed the perigee
and apogee values.
s
= = __________________
= ___________________
The eccentricity of the Moon’s orbit can be determined from your data. The
eccentricity (
e
) of an orbit tells how circular the orbit is; e
= 0 is circular while e
approaching
1 is extremely elongated. You need to use the value s
you just calculated above. Calculate
the eccentricity using this:
e
= = = = ____________
In textbooks, the Moon’s eccentricity is usually listed as 0.05. But because the Moon's
perigee (and apogee) values vary, the Moon doesn't actually have a single constant
eccentricity value, the 0.05 is just an average value. If you got a value a lot different than
0.05, double-check that you did the calculation correctly.
The reason why the Moon's orbit varies so much is the Sun. The gravita-
tional pull of the Sun on the Moon is comparable to that of Earth on the Moon.
Because Earth and Moon are sometimes closer and sometimes further from the
Sun, the Sun exerts a varying influence that has caused this extra variation in
the Moon’s orbit.
Fun fact: Mars has two tiny moons. The closer of the two, Phobos, is in a
decaying orbit, it will crash into Mars in 10.4 million years.
Apogee Period
How much time does it take, on average, for the Moon to go from one
apogee to the next? Estimate the date of the first January apogee that you see on
the screen for the year shown, just estimate the day of the month. For example,
if your chart looked like the one shown to the right, you might estimate the date
as maybe Jan. 15.
First Apogee:
Approx. Date: _______________________
Now do it again for the next apogee, probably in February.
Next Apogee:
Approx. Date: _______________________
Remembering that January has 31 days, how many days was it from one
apogee to the next? This is the Moon’s orbital period. Your answer should be a
little under one month of time.
Orbital Period = _________ days
Sorry, but I don’t trust your result. That estimating of dates was too inaccurate. One
way to improve accuracy is to make multiple measurements and average them. So, I want
Orbits–2
you to repeat this measurement three more times and then you’ll average the values. You
can click Next Interval and again do the measurements for January to February (but for
different years) or you can stay in the original year and estimate days from some other
apogee peak to the following peak.
You can show all your work here:
#2)
Dates: _____________ to _____________
Period = _________ days
#3)
Dates: _____________ to _____________
Period = _________ days
#4)
Dates: _____________ to _____________
Period = _________ days
Now average your four results to get a better estimate of the Moon’s orbital period
(add the four values together then divide that total by four). Note that all four of your
periods should have been very nearly the same, and your average should be nearly the
same as them as well. If any of the periods was something other than 20-some days, or if
your average wasn’t 20-something, you have made some error(s).
Average orbital period = ____________ days
[Answers to some questions can be found at the end of the lab.]
1. Can you think of a more accurate way we could measure the Moon’s orbital period
using Voyager? How?
2. Why did we use apogees instead of perigees?
Period of Moon Phases
Select the "Phases of the Moon" option from the Planet Report pop-up menu. You will
calculate the average number of days for the Moon to repeat its phase in the same way we
did above for apogees. Looking at the New Moon column (the other phases could be used
instead), record the first January New Moon date (or start wherever you want) and the date
of the next New Moon (probably in February if you started in January). Calculate the
elapsed days between these dates.
First New Moon Date: ______________________
Next New Moon Date: ______________________
Elapsed Days = ______________
Okay, you’ll now do the repeat-three-more-times-and-average procedure.
Orbits–3
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#2)
Dates: _____________ to _____________
Phase period = _________ days
#3)
Dates: _____________ to _____________
Phase period = _________ days
#4)
Dates: _____________ to _____________
Phase period = _________ days
Average phase cycle period for the Moon = ____________ days
The amount of time it takes the Moon to go through its cycle of phases is not
the same
as the time for it to go from one apogee to the next. We'll return to this topic shortly.
Drunken Moon
Open the Settings File called "Drunken Moon ". Start the animation, watch how the
Moon moves faster and slower and also weaves slightly up and down. The computer is
also leaving a "trail" of Moon positions that also show the Moon's varying speed and path.
This surprising behavior is called the “Drunken Moon”. The Moon is not actually
behaving erratically. The reason for the apparent extra motions is that we are viewing it
from a rotating Earth. Earth is carrying us back and forth as it spins; the parallax due to our
changing viewpoint causes the Moon’s apparent wandering.
Moon's Orbital Period
Stop the animation, click the small "Now" button in the Time Panel to
reset the demo. The Moon at this time appears at a particular spot on the
celestial sphere, how long until it returns to that same spot? Write down the
Julian Day (JD) number listed in your Time Panel:
JD: _________________________________________
Animate, stop when the Moon gets back to approximately its starting
spot as indicated by the trail markers. You can use the single time step
forward and backward buttons if you stop the animation early or late.
Write down the Julian Day value for this time.
JD: _________________________________________
Calculate the difference between the two Julian Day numbers. This is the elapsed days
for the Moon to circle the celestial sphere once, which is the time for the Moon to orbit once
about the Earth.
Moon's Orbital Period = __________________ days
Orbits–4
Remember that the stars and Moon whirl overhead every day, rising in the east and
setting in the west. The view that we are using is a view of the stars you would have from
Earth if it didn't rotate. The Moon's motion across the celestial sphere is due to the fact that
the Moon is actually moving in an orbit around Earth. Moon Periods
You just found that Moon phases repeat in about 29.5 days. Apogees of the Moon and
the Moon’s position on the celestial sphere both repeat in about 27.3 days. The Moon also
shifts its position further north and south in our skies, it does this with an average period of
27.3 days. The Moon rises at a later time with each passing day, it returns to the same rising
time every 29.5 days. Why does the Moon do some things in 27.3 days and others in 29.5
days?
Open the Settings File called "Moon and Sun", this is a view of the entire celestial
sphere. Click the Constellation Lines Display button along the edge of the window (the
button has a Little Dipper constellation on it) to turn on constellation lines (only
Zodiacal constellations are being shown). Advance the time in single steps until the
Moon appears close to the Sun, note which constellation is behind the Moon. If you
click another 27 times (go ahead), you'll find the Moon returns to the same spot among the
stars. The Moon does one orbit around Earth in 27.3 days, this is why its apogee distance,
position on the celestial sphere, and north-south position all vary in 27.3 days.
So why do the phases repeat in 29.5 days even though the Moon completes an orbit
(returns to the same constellation) in 27.3 days? One way to understand this was just seen
on screen. While the Moon moved from constellation to constellation, the Sun moved as
well (the Sun more slowly, making a complete trip around the zodiac in 365 days).
We started with the Sun and Moon close together in the sky, this corresponds to the
Moon being in the New phase (do you understand why that is?). After 27 days the Moon
completed its orbit but was not back together with the Sun. It will take two more days, two
or three more clicks (go ahead and do it) until the Moon and Sun are back close together in
our sky. It takes 29.5 days (on average) for the phases to repeat.
3. Starting with the Sun and Moon together, how many clicks is it until the Moon
appears Full?
Why do Moon rising times repeat in 29.5 days? Our clocks run on 24-hour time, they
track the Sun, so measuring the time of an event is comparing it to the Sun's position. For
the Moon to repeat its position relative to the Sun takes 29.5 days. Note the phases of the
Moon and the Moon's rise/set times are correlated. The New Moon always rises around 6
in the morning (the New Moon appears in the same area of the sky as the Sun, so it will rise
at about the same time that the Sun does). The Full Moon is opposite in the sky from the
Sun, the Full Moon always rises around sunset, about 6 or 7 pm.
Orbits–5
Lunar Libration
Open the Setting file called "Lunar Libration". Read the Settings File Info then close it;
start the animation. The Moon pulses bigger and smaller on screen due to its elliptical orbit;
appearing bigger when it is closer to the Earth.
The Moon is famous for always keeping the same face towards the Earth. It does this
by rotating once every 27.3 days, what is called "synchronous rotation." But, according to
Kepler's second law, the Moon will move fastest in its orbit when closer to Earth and slower
when further away. Meanwhile, the Moon's rotation keeps a constant pace. So, sometimes
the Moon rotates faster than it orbits and sometimes slower. On screen you can see the
Moon turning slightly left and right, allowing viewing of a small part of its far side.
The inclination (tilt) of the Moon's orbit also allows us to alternately view the Moon
from slightly above and below. The Moon appears to tilt forwards and backwards on
screen, again this allows viewing of some of the normally hidden back side.
The twisting of the Moon which allows some of the far side to be seen is called
"libration". From Earth, 59% of the lunar surface can be seen at one time or another.
4. Explain the difference between the far side and dark side of the Moon.
Lunar Eclipse
Occasionally (about twice a year), the Moon isn't too far north or south when it's Full
and the Moon can pass through the shadow cast by Earth. This is called a lunar eclipse, see
section 4.7 of the text for more information about eclipses.
Open the Settings File called "Lunar Eclipse - 4 views". The four windows are showing
four different views of the same event – the lunar eclipse of 2/21/08. If the windows pile
atop each other, press the button in the title bar to tile the windows. The upper-left view
is from the Sun, there you will see the Moon move behind the Earth.
The upper-right view shows the Earth and the shadow it is casting along with the
Moon and its orbital path. There you will see the Moon pass through the shadow.
The lower-left view is from the Moon towards the dark (night) side of the Earth
(although it is not being shown as dark on purpose). The part of the Earth you can see there
are the places that will be able to see the eclipse (everyone on the night side of Earth). When
animated, you will see the Earth turning and you should see the Earth eclipse the Sun.
The lower-right view is from Bakersfield and shows a close-up of the Full Moon.
There are also two circles near the Moon in that view, those are the umbral and penumbral
shadow cones cast by the Earth.
The inner circle is the "umbra", the 'true' shadow of Earth. Any object or point inside
the umbra receives no direct sunlight, it's all blocked by Earth. The outer circle is the
"penumbra", within the penumbra Earth partially blocks the sunlight. The Moon only
appears very slightly dimmed while in the penumbral shadow and profoundly darkened
when in the umbral shadow.
Orbits–6
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Sun
Earth Moon Umbra Penumbra
Animate and watch the eclipse.
Done? Fine, but I bet you'd be more interested if this
were a future eclipse rather than one from the past. Here
is
a list of future lunar eclipses; pick one and set the Voyager
program to its listed date and time. Do that by selecting
the Chart/Set Time… menu, clicking on the Universal
tab
, entering the listed date and time, and then clicking
OK.
Date
Time
2022 5/16
1:39
2022 11/8
8:14
No total lunar eclipses in 2023 or 2024
2025 3/14
4:10
2025 9/7
15:35
Whichever eclipse you chose, the time given shows the Moon already slightly into the
penumbral shadow (if you don’t see an eclipse starting, maybe you entered the date and
time wrong or didn’t set universal time). That's the pink shading. But in real life, the
penumbral shadow is all but unnoticeable – the Moon does not look dimmed at all and
there are no obvious shadow boundaries.
The real eclipse is when the Moon enters the inner umbral shadow, that is what
everyone can see.
When the umbra first "touches" the Moon is called 'first contact', when the umbra
completely engulfs the Moon (when the umbra reaches the far side of the Moon) is called
'second contact'. When the Moon is completely inside the umbra is called 'totality', 'third
contact' is when the totally dark Moon first gets sunlight again, and 'fourth contact' is when
the Moon has totally emerged from the umbra. Totality starts at second contact and ends at
third contact.
Start the animation and watch the eclipse; then go back to the middle period of the
eclipse. Estimate the start and end times during which the Moon was totally within the
(inner) umbral shadow, then take the difference between them to get the duration of
totality.
Start Time:
______________
End Time:
______________
Duration of Totality:
__________________
Orbits–7
Aristotle saw this shadow and realized Earth must be round to cast a round shadow.
He correctly gave this as evidence for a spherical Earth. Later, another ancient Greek,
Aristarchus took this further. By comparing the curvature of Earth's shadow to the
curvature of the Moon, he could estimate the relative sizes of the two. Assuming the Earth
was the same size as its shadow, Aristarchus estimated that the Earth was about three
times wider than the Moon. Actually, Earth's shadow is smaller than the Earth when it
reaches the Moon, and the correct result is that the Earth is 3.67 times wider than the Moon.
Nevertheless, this was an important discovery. Still later, Eratosthenes measured the size of
Earth, which when combined with the Aristarchus result allows a calculation of the true
size of the Moon.
By the way, the upper-left window is showing Earth and Moon in their proper
relative sizes. For instance, you may be able to tell that the Moon is much smaller than the
Pacific Ocean; in fact, the Moon has about the same surface area as Africa and Australia
combined.
5. As seen from the Moon, which should appear larger, the Earth or the Sun?
Inner Planet Orbits
Open the Settings File called "Inner Planets". Animate and watch the planets orbit the
Sun.
6. Do all the planets shown orbit the Sun in the same direction?
7. Do all the planets take the same amount of time to orbit the Sun once? If not, is
there a pattern to the times?
8. Which planet moves the fastest on the screen?
9. Of the four planets, which two most clearly do
not have circular orbits with the Sun at the center?
Stop the animation. Select the Window/Planet Panel
menu and click on the Lock button next to the Earth. Click
on the "Moon" button to turn on the Moon. Close the
Planet Panel and zoom to 1' (One minute of angle, not one
degree or one second). Change the Time Step to 1 hour
and resume the animation.
10. Does the Moon orbit Earth in the same direction
that Earth orbits the Sun?
Orbits–8
11. Push the zoom "+" button until you can clearly see the rotating Earth. Does Earth
rotate in the same direction that it orbits the Sun?
All the planets orbit the Sun in the same direction. All the planets rotate in that same
direction (except Venus which is backwards or upside-down, and Uranus which spins on
its side). All the major moons (except one) orbit their planets in this same direction, and the
Sun spins in this direction as well.
The explanation of why most everything in the solar system spins or orbits in the
same direction is that the solar system formed out of a spinning cloud and objects in the
solar system inherited that same spinning direction. The exceptions are believed to be due
to collisions between objects.
Select the File/Open Recent Settings/Inner Planets menu, animate. Drag the Latitude
arrow in the Location Panel from 90° to 0°. The blue line is the ecliptic plane seen edge-on;
the ecliptic plane is the plane of Earth's orbit. Earth moves exactly along the ecliptic line by
definition. You should clearly see that Mercury, Venus, and Mars all move slightly above
and below the plane of Earth's orbit.
Why do all the planets orbit in the same horizontal plane? Because the original cloud
out of which the solar system formed was a flattened disk, and planets naturally formed
and moved in that disk. Fun fact: Every solid object that astronomers have discovered in
the universe is rotating, the body with the slowest rotation that we know of is … Venus!
Outer Planet Orbits
Open the Settings File called "Outer Planets", animate and observe for a while. We
have displayed Pluto even though it is no longer considered a major planet by astronomers.
12. How often do the Sun, Jupiter, Saturn, Uranus, and Neptune lie along a straight
line?
Without stopping the animation, vary the Latitude control in the Location Panel. In
particular, set the Latitude to 0° to get a side-view and see how much the outer planets
move above and below the ecliptic plane. Wow, look at Pluto's orbit!
The planets are usually very close to the ecliptic except for Pluto which is way off.
Pluto does not orbit in the same plane as the other planets. Try playing with the Latitude,
Longitude, and Distance controls in the Location Panel to get used to them.
Comet Orbits
Open the Settings File called "Six Comets". In addition to the outer planet orbits, six
comets and their orbits are displayed. Three of the comets are "short-period comets"
(Halley's, Encke, and Temple); short-period comets have orbital periods of 200 years or less.
The other three are "long-period comets" (LINEAR, Hale-Bopp, and Hyakutake).
Orbits–9
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Use the Longitude, Latitude, and Distance controls in the Location Panel to vary the
view. You can also animate. The following questions can be answered from watching the
display or else by clicking on a comet and searching its Info Panel.
13. Is Halley's comet usually above the ecliptic plane or below it? (Set the Latitude to
0°, locate Halley's orbit, and the answer should be clear).
Set the Latitude to 90°.
14. Does Halley's comet ever get further from the Sun than Neptune (blue orbit)?
15. What is the furthest that comet Hyakutake ever gets from the Sun? (Use the Semi-
major Axis length given in its Info Panel.)
16. What is the orbital period of Hyakutake?
Halley's comet actually comes very close to the Earth's orbit. Astronomers believe that
Halley's was once a long-period comet but a close encounter (probably with the Earth) de-
flected it into its current orbit.
Could Halley's comet ever hit the Earth? There is no chance of that for as far into the
future as astronomers can calculate. But perturbations do constantly alter the orbits of
comets (the Voyager 4 program contains dozens of slightly different versions of Halley's
comet, one for each orbit) and over thousands or millions of years become unpredictable.
So, the ultimate fate of the comet is unknown.
In a way, though, Halley's comet collides with Earth every year! Comets are loose
collections of ice, dirt, and dust. They're also litter bugs, specks of dirt and dust from
Halley's comet have spread out all along Halley's orbit. Every year when Earth passes the
orbit of Halley's comet, we get a meteor shower on Earth as particles from Halley's comet
crash into Earth and burn up in the atmosphere. Section 14.1 of the textbook will tell you
more.
Stop the animation when Halley's comet is close to Jupiter's orbit. Drag the Distance
slider in the Location Panel to something in the 12-20 range. Change the Time Step to 1 day
and resume the animation. As Halley's rounds the Sun you will see its on-screen icon
sprout a tail.
The tails of comets consist mainly of tiny specks of ice particles. When the comet is
near the Sun, the Sun's heat causes particles to evaporate into a cloud surrounding the
comet (called the "coma"). Pressure from sunlight and particles coming from the Sun (the
"solar wind") pushes the cloud of particles away from the Sun forming the comet's "tail".
The tail of a comet always points away from the Sun no matter which direction the comet is
moving.
More About Pluto
Orbits–10
Pluto's perihelion distance is about 30 AU and aphelion distance is about 50 AU.
From 1979 to 1999, Pluto was actually closer to the Sun than Neptune. Halley's comet is
often further from the Sun than Neptune and sometimes further away than Pluto. It may
look like these orbits cross and they could hit each other but that's not the case. Play some
more with the Longitude and Latitude controls to convince yourself of that. Fun fact: Pluto
actually comes closer to Uranus that it ever does to Neptune!
Open the Settings File "Pluto's Discovery in 1929". To make this more realistic, select
the Display/Planets and Moons… menu and click off
Show Name, Show Path, and Dash
Path for Pluto. Click OK.
Pluto is there on-screen, an insignificant star-like dot at the center of the screen. How
did Clyde Tombaugh decide that it was a planet? Animate and you'll see. Planets (along
with other solar system bodies) move relative to the background stars.
Pluto has a large moon (some would call the pair a double dwarf planet) named
Charon (the "Ch" can be pronounced like either "Sh" or "K"). Charon was discovered as a
tiny smudge on a photographic plate by James Christy in 1978.
Open the Settings File "Pluto and Charon" and read the Settings File Info. Animate.
These occultations (eclipses) greatly increased astronomer's knowledge about Pluto.
Asteroids
Open the Settings File called "Largest Asteroids", start the animation. Set the Latitude
control to 0° to see how close to the ecliptic plane the asteroids are. There may be millions
of asteroids, most in the asteroid belt, yet the total mass of all the asteroids is only about
1/1000 the mass of Earth. This demo shows the 1000 largest asteroids.
Despite the large number of asteroids, asteroids are very small and the space between
them very large. If the contiguous 48 states of the U.S. represented the entire asteroid belt
area, asteroids would be fist-sized rocks on average about 2.5 miles apart. The real asteroid
belt looks nothing like how asteroid belts are portrayed in the movies. Not all asteroids are in the asteroid belt, asteroids are grouped according to their
orbits. For example, the Apollo asteroids have orbits which take them from the asteroid belt
inward past Earth’s orbit and then back out to the asteroid belt. One interesting group of asteroids is the Trojans. Open the Settings File "Trojan
Asteroids" and read the Info. These asteroids follow the same orbit as Jupiter – more or less.
Animate.
The East Trojans (red) are ahead (leading) Jupiter while the West Trojans trail Jupiter.
Q. How do we decide what directions are east and west in space?
A. The direction the Earth spins is what we call east, that gives us a direction around
the celestial sphere that we call east. Jupiter orbits in the same direction that Earth rotates so
ahead of it would be further east.
Kuiper Belt
First hypothesized by the astronomer Gerard Kuiper (Kigh-purr), the Kuiper Belt is a
wide ring of small, icy worlds beyond the orbit of Neptune. These are comets-in-waiting,
Orbits–11
the Kuiper Belt is like the asteroid belt except it’s colder, icier, and much more distant from
the Sun.
Pluto and its moon Charon are large members of the Kuiper Belt and Neptune’s large
moon Triton was probably captured from the Kuiper Belt (part of the reason for believing
this is that Triton orbits Neptune backwards, like an object that was captured rather than
one that formed there naturally).
Discoveries of smaller Kuiper Belt Objects started in 1992 when Jewitt and Luu dis-
covered 1992 QB1 (their name of “Smiley” didn’t stick). Over 1000 Kuiper Belt objects have
been discovered so far, the largest being Eris (formerly known by its catalog number 2003
UB313). Eris was discovered Oct. 21, 2003 and confirmed in 2006 to have a diameter larger
than Pluto. This prompted the demotion of Pluto from planet to "dwarf planet", a
classification it shares Eris.
Open the Settings File named "Kuiper Belt". Animate and play with the Latitude
control in the Location Panel. Kuiper Belt objects (KBOs) are dirty snowballs. Occasionally
close encounter may deflect one towards the Sun, this is the origin of most short-period
comets.
Some of the KBOs, notably Sedna, Buffy (2004 XR 190), and maybe Eris have such odd
orbits compared to other KBOs that some astronomers speculate that they may have
wandered into our solar system from a different star!
Get the Orbital Period and Semimajor Axis length for Eris from its Info Panel.
Period:___________________
Semimajor:______________________
Planets, asteroids, comets, and KBOs all obey the same orbital rules – Kepler’s laws.
For instance, the period squared for Eris is 312,000 and the semimajor axis length cubed for
Eris is 312,000; Kepler’s third law P
2
= a
3
is right again.
Orbital Speeds
How fast do planets, like the Earth, travel? That’s easy enough to calculate. Take the
Earth’s orbit to be circular with a radius of 149,600,000 km, the circumference of the orbit is
calculated as
circumference = 2 π r
= 2 π (149,600,000 km) = __________________ km
The Earth travels this distance in one year, convert that into seconds.
1 y = 1 y (365 d / 1 y) (24 h / 1 d) (60 min / 1 h) (60 s / 1 min) = ________________ s
Divide the circumference distance by the time to get the Earth’s orbital speed in km/s.
Earth’s orbital speed = _________________ km/s
This is equivalent to 18.5 mi/s or about 67,000 mph.
Orbits–12
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Planets closer to the Sun go faster, further from the Sun slower. An object in an
elliptical orbit will not travel at a constant speed, it will speed up when closer to the Sun
and slow down when further (that’s Kepler’s second law). All these speeds are relative to
the Sun, the entire solar system is moving together in an enormous orbit about the center of
our Milky Way galaxy. The radius of the orbit is about 27,000 light-years and each orbit
takes over 200 million years.
Eclipses
Select the File/Open Recent Settings/Startup menu. Remember today's date and
select the Tools/Planet Report… menu. Select "Phases of the Moon" from the pop-up menu
and find the date and time of the next New Moon after today’s date, write these down,
Date:________________
Time:_________________
This is Universal Time, basically the same as Greenwich time. Close the Planet Report
window (careful, don’t close the whole Voyager program). Select the Chart/Set Time…
menu, click on the "Universal Time" tab, and enter the above date and time. Select the
Center/Planets/Sun menu, zoom to 5°.
The Sun and Moon are closest together as seen in our skies when the Moon is New
(can you explain why?). You should be able to see both the Sun and Moon on the computer
screen (if not, zoom your view out or try closing the Info Panel if open).
Usually the Sun and Moon “miss” each other as they pass in the sky. This is because
the Moon’s orbit is not in the ecliptic plane, it is usually above or below the ecliptic plane
enough that it doesn’t get exactly between the Earth and Sun as needed to cause an eclipse.
This is the origin of the name for the ecliptic plane, we can only have an eclipse when the
Moon lies in this plane. If the Moon partially or totally covers the Sun, we have a partial or
total eclipse.
Is there going to be a solar eclipse within the next month? You can zoom in if you are
unsure whether the Moon is covering any of the Sun. It is a rather painstaking process to
look for eclipses by setting the time to each successive New Moon; there is an easier way.
Conjunction Search
Select the Tools/Conjunction Search... menu. A conjunction is when two objects in the
sky appear close together. Type in 2020 for "Starting Year", tab, 2040, tab, and then "0.6".
The Sun and Moon are both about 0.5° wide as seen from Earth, so if they were barely
“touching” their centers would be 0.5° apart. We use 0.6° to make sure we don’t miss any
eclipses. Click the "Search" button.
All the close conjunctions the computer finds are listed on the screen. The date, time,
the angle of separation when closest, and a "yes" or "no" for whether the event is visible
from Bakersfield (that Voyager says 'yes' for every conjunction appears to be a bug in the
program).
A nice feature of the Voyager program is that we can jump to any of these events
quickly. Click on the line that reads "Oct 14, 2023 16:16 0.102 yes" and then click the Set
Orbits–13
Time button. The Conjunction Search window will go away, and you should have a view of
the Moon almost totally covering the Sun. Zoom to 1° for a close-up view of the eclipse, this
is the closest the two get together as seen from Bakersfield.
Zoom to 90° to see better where this is in the sky. To make this appear more realistic,
select the Display/Natural Sky/Show Natural Sky menu. As seen from Bakersfield, this
eclipse is occurring late in the morning (around 9:16 am) and low in the eastern sky
(altitude around 25°).
Click the Lock button for the "Sun" at the bottom of the chart window.
Set the time to about 6:50 am (one way of doing this is to carefully drag a
hand on the Time Panel clock). Set the Time Step to 30 sec, zoom to 4°, and animate. Stop
when the eclipse is finished.
We did not see a total eclipse from Bakersfield. Because the Moon at this time is fairly
far from Earth, it appears smaller in our sky than the Sun. No one on Earth will see this
eclipse as total, though some will see an "annular eclipse" – where the Moon blocks out all
but an outer ring of sunlight.
If you now return to the Conjunction Search window, you will find all our search
results are still there. The Conjunction Search works for whatever was your last viewing
location. If you do a search after setting your viewing location to Mars, the search will be
for conjunctions as seen from Mars! We will do additional conjunction searches in a later
lab, but feel free to play around with the options now.
Eclipse Demos
Open the Settings File "American Eclipse - 3 Views", read and close the text window.
Animate. The two concentric circles in the view from the Moon are the penumbral and
umbral shadow boundaries. You are watching the Moon’s shadow cross Earth from the
Moon. Areas in the penumbral circle are places on Earth that would be seeing a partial
eclipse. Locations in the path of the inner umbral shadow are locations that would see a
total eclipse. Bakersfield was in the penumbral – partial eclipse – area. The lower view
shows the Moon's umbral shadow spearing towards Earth.
Open the Settings File "African Eclipse June 2001" and animate. Now open "China
Eclipse" and animate.
Answers to selected questions:
1. Here are some ideas:
We could advance the time while watching the Moon’s distance in its Info Panel.
We could find the times of apogee down to the second rather than guessing at days.
We could carefully count dots (days) on the graph rather than guessing at dates.
We could get an apogee date, then get the date of the 20
th
apogee after that and
divide those total days elapsed by 20.
We could watch the Moon following its orbital path and find the time to complete
an orbit. You will
do this later in this lab.
2. No special reason, perigees should work just as well.
3. Fourteen or fifteen, half of the 29.5-day cycle of phases.
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4. The far side is the side away from the Earth, the dark side is the side away from the Sun.
As the Moon orbits the Earth, we sometimes see the lit side and sometimes the dark
side (usually some of both) but we never see the far side (except for that fraction due to
the libration).
9. Mercury and Mars
12. Uh … never?
14. Yes
15. 951 AU
Today’s fun facts brought to you via Bob Berman, Astronomy Magazine
, April 2011.
Orbits–15
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