Activity 8.2
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111
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Astronomy
Date
Dec 6, 2023
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4
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Conceptual Astrophysics Activity #8-2
Planetary Rings
Purpose
To explore how ring systems remain stable
Objectives
•
To simulate how several tiny objects orbit a larger object
•
To note the effects of elliptical vs. circular orbits for tiny objects
•
To note the effects of different masses on orbits for tiny objects
Materials/Resources
•
“My Solar System”
simulation at
http://phet.colorado.edu/
•
Conceptual Astronomy
by Sirola, Chapter 8
Introduction
As one of the original “planets”, Saturn has
been known throughout history. However, its
most famous feature wasn’t discovered until the advent of the telescope. The rings of Saturn
were first seen by Galileo in 1610, but he couldn’t make sense of them because of the lack of
resolution of his telescopes. In 1655, a Dutch astronomer, Christian Huygens, realized that they
were rings, and that they didn’t touch Saturn at any point. And it wasn’t until 1859 that James
Clerk Maxwell demonstrated that the rings could not be solid but had to consist of innumerable
tiny particles instead. Saturn has been explored by various spacecraft since the 1970s, and much
effort has been made to understand the rings and their origins. All other Jovian planets are now
known to possess rings, though none of them are as spectacular as those of Saturn.
Computer simulations that show the development and behavior of ring particles are
difficult to construct, so we will use a (very) restricted simulation to model ring particle motions.
Our task is to see how ring particles orbit Saturn, under which conditions they remain stable, and
how they might eventually break apart.
Kira
Charles
Part #1: Ring Particle Simulations
Go to
http://phet.colorado.edu
. Follow the
“physics” and “motion” links
and look for the
“My Solar System” simulation.
The default setting for the sim shows a large object at the center and a planet ready to
orbit it. We are interested in seeing many tiny objects in orbit rather than one large one, so go to
the tab at upper
right labeled “Select Presets” and choose the “Trojan Asteroids”. This isn’t
intended directly to model particles in a ring, but we will adapt it for our purposes.
Leave the sim as “system centered” but remove “show traces”, at least to start with. Note
th
at you need to “stop” and “reset” the sim each time you wish to change any parameters.
Each object in the sim has a separate color to help us keep track of them as they move.
You can adjust parameters for each object in the table at the bottom of the scree
n under “Initial
Settings.”
The “Trojan Asteroids” preset has three small objects orbiting one large central object.
We will pretend the central object is Saturn and the three small objects are ring particles.
1.
Let’s start with the simplest case, where the
ring particles
(“bodies”)
are equal in
mass and orbit in the same fashion. The preset has one of the bodies (#2) too large, so
change its mass to the same as the others (which should be 0.001). Note what happens
to the dot that represents body #2
–
does it get smaller, larger, or remain the same
size? How does it now compare to the other ring particles?
2.
Set the speed to “fast” and
start the simulation. Allow the sim to go for at least 1
minute (it can run indefinitely) in order to see all the results. Note you can stop the
motion at any point and restart it or reset as need be.
(a)
Do the particles appear to move in circular paths, elliptical paths, or something
else?
(b)
Do the particles remain separated from each other, or do some of them approach
each other?
(c)
Reset the sim. Adj
ust the “y” velocity of body
#2 to 120 rather than 119, then start
the sim. Run for at least 1 minute. Do the particles remain separated from each
other, or do some of them approach each other?
•
The
dot
gets
smaller
.
similar
to
the
other
particles
•
circular
paths
•
they
remain
close
.
particles
#
2
and
#
3
separate
a
bit
✓
now
the
new
velocity
.
(d)
Did it take much of a change of velocity to change how the ring particles behave?
(And were you surprised by the result?)
(e)
Allow the sim to continue running. Do particles stay near each other, or do they
separate again?
(f)
Are these orbits perfectly circular? To check this, reset the sim and turn on the
“show traces” command.
(g)
Now let’s change the velocity in a significant way. Reset the sim and c
hange the
y-velocity of body #2 to 130. Start the sim. What happens to the orbit (shape and
speed) of body #2?
(h)
Next, let’s change the ma
ss (and therefore size) of body #2. Reset the sim, change
the mass of body #2 to 5, and change the y-velocity of particle #2 to 120. Allow
the sim to run for at least 1 minute. Do all the particles remain in circular orbits?
Do all of the particles even survive?
(i)
Reset the sim and change the y-velocity of body #2 to 130 (keep its mass at 5).
i.
Before running the sim, predict what you expect to happen.
ii.
What does in fact happen to the other ring particles?
-
yes
over
it
was
surprising
to
see
how
the
movements
differed
•
particles
#
3
&
#
4
intersect
•
the
particles
seem
to
get
closer
•
particle
#
4
is
circular
•
the
rest
are
elliptical
•
It
increased
the
orbit
but
the
shape
stayed
the
same
•
no
,
the
orbits
change
completely
•
only
#
I
and
#
2
survived
•
the
orbit
would
increase
greatly
and
affect
a
H
the
other
particles
•
#
3
eventually
gets
out
of
the
orbit
.
#
4
collides
with
#
2
and
doesn't
survive
•
#
I
get
affected
because
of
the
velocity
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Part #2: Conclusions
1.
In order for the orbits of ring particles to remain stable, what should be the case?
Specifically,
(a)
Should ring particles have nearly circular orbits or can they have very elongated
elliptical orbits?
(b)
Should ring particles be nearly the same size (mass) as each other, or can their
masses be very different?
2.
In 1989, Voyager II discovered rings surrounding Neptune. The rings did not make
complete circles, but instead showed as ring “arcs”. What migh
t you conclude about
Neptune’s ring arcs, given the simulations?
3.
Saturn as a planet formed at the beginning of the solar system, about 4
½
billion years
ago, but the rings are likely much younger (researchers estimate no more than 100
million years). Why might this be the case, given the simulations?
4.
What are three possible fates of a ring particle, if it does not remain within its ring?
•
the
orbits
don't
really
affect
the
ring
particles
•
the
mass
can
vary
,
as
shown
in
the
experiment
.
There
might
be
some
with
higher
mass
.
the
rings
might
be
made
of
debris
from
aestvoids
,
moons
,
and
other
things
.
it
will
either
collide
with
something
,
orbit
into
space
or
changes
the
orbit
completely