Volcanoes, Geysers, and Extra Planetary Explosions
Terms to know/learn: Plinian eruption, plume, ejecta, elliptical orbit, friction, volatile
gases, superheated. (see bold for context definition, or appendix for definition)
Volcanoes help to change the surface through their deposits, lava flows, and of course
eruptions. Volcanoes are formed by molten material breaking the surface and interacting
with its new environment. On Earth, this molten material is rock, and is brought to the
surface through convection of this molten rock below the surface, as well as other
mechanisms. Because of this convection, one could relate volcanoes to Earth letting off
some built up pressure.
Geysers are another display of the awesome and intriguing power of nature. They may
not change the area around them much, but they expel material that was once within the
earth to the surrounding area, and usually in a quite dramatic fashion.
Differences in Volcanoes and Volcanic Eruptions:
One might think that because volcanoes are made of the same basic stuff, that they should
look similar, but this is far from what is actually observed in nature. This becomes
obvious when one compares Mt. St Helens to Mauna Loa in Hawaii. Not only the size
and shape of volcanoes differ, but the color of their ejected material (ejecta) as well.
What could cause these differences? (T: What about differences in composition of the
molten material?)
Non-Earth Volcanoes and Io:
There are also many volcanoes throughout the solar system. Exploration of Venus and
Mars has uncovered volcanoes. Our own moon shows volcanic activity through massive
lava flows that can be seen from Earth. There are other volcanoes in the solar system as
well. The most volcanically active body in the solar system is one of Jupiter’s moons: Io.
This moon has a volcanic mechanism different from that of Earth. While Earth’s
volcanic activity is powered by the heat producing decay of radioactive elements beneath
the surface, Io is being tugged upon by the gravity of the extremely massive Jupiter
(Jupiter’s gravitational force is 318 times greater than Earth’s!) as well as Jupiter’s other
moons. Io’s orbit around Jupiter is also highly elliptical, meaning that it is very close to
Jupiter in some parts of its orbit, and far away in others. All of these forces pull on Io,
creating massive amounts of heat from friction, just like when you rub your hands
together. Io is being smashed out of its spherical shape into an ellipsoidal (like an oval);
more like an ellipsoid when it is close to Jupiter, and more like a sphere when it is farther
away. All of the solid contents of the moon are therefore smashed into each other over
and over, which creates huge amounts of heat. This mashing generated heat is what
drives the volcanic activity on Io. If this concept seems odd, think again of rubbing your
hands together. If you add more force, more heat is generated. Using the same logic, Io
has a lot of heavy/massive rocks rubbing together, much more force than rubbing your
hands, which yields much more heat. Photographic evidence of Io’s volcanic activity
was gathered during the Voyager, Galileo, and Cassini space exploration missions. We
will be using images from these missions to explore the volcanic activity of Io.
Behind the Eruptions of Volcanoes and Geysers:
Both Volcanoes and Geysers eject material from below to the surrounding surface, but
both the mechanisms behind these eruptions and the material ejected are vastly different.
Volcanoes on Earth are the result of molten rock rising through the Earth’s crust to the
surface. The composition of the rising material, though, is not purely molten rock; there
are amounts of volatile gases, such as H20 and CO2. This combination, better termed
magma, can erupt quite violently. This type of eruption is termed a Plinian eruption,
which are explosive like Mt. St. Helens. When the magma and volatiles erupt, the
pressure decreases, and this allows the volatiles within the magma to expand and
fragment the lava explosively.
Unlike Volcanoes, Geysers’ main driving force is water and heat. Geyser eruptions come
forth because of the mixture of water with the heat of much hotter magma. Magma can
heat water to extreme temperatures, even above the boiling temperature of water at the
surface; in these cases the only thing keeping the water from turning into vapor is the
massive pressure always pushing down on it. The higher pressure water is under, the
higher its boiling point becomes. When such superheated water is supplied to a cooler
pool of water, it wants to rise because it is less dense than the colder water above. At
first, the colder and denser water above acts like a cap and doesn’t allow the warmer and
less dense water to penetrate to the surface. As the warmer water continues to flow, the
temperature and pressure rises, much like trapped magma before a volcano erupts, and
the superheated water’s temperature can rise above the boiling point of water for the
current pressure. When this happens, vapor bubbles can penetrate the dense water cap.
When this happens, the less dense, superheated water can escape, which decreases the
pressure, and the water (now far above its boiling point for the current pressure)
vaporizes almost at once and shoots up just like Old Faithful in Yellowstone.
Plumes!
When observing an erupting volcano on Earth, one may expect to see ash, lava, lava
bombs, and other particulates spewing from the volcano. The upwelling of molten
material out of the volcano is termed a plume. Take a look at the images below of
Earthly eruption plumes, and those of geysers:
Now that we know a little about Volcanoes, Geysers, and Io, let’s get a feel for how high
Io’s volcanic plumes are and then how fast these volcanoes eject material. You will be
using an imaging program called ImageJ. This program can be used to adjust brightness
and contrast of an image and measure distances.
Section 1 – Taking Measurements
-First open ImageJ
-Click on File and Open and select Image1
-Scan the perimeter of Io and look for volcanic plumes. Look over the rest of the moon
as well to see if you can notice any other plumes.
-Use ImageJ to open Image1F. This image shows where the two plumes are in this
image. The plume towards the middle of the moon doesn’t directly show its height like
the one on the outside of the moon picture; do you know of any ways that this plume’s
height can be measured? If not, do you think that there is a way? Describe what you
know:
Answer:
-Use ImageJ to open Image2. This is a bigger and higher resolution version of Image1.
-Now that the image is opened, you can create a line on the image to set the scale.
-First, click on the straight line tool on the ImageJ toolbar.
This tool will let you
draw a line on the image. Use this tool to make a line from the top of the moon to the
bottom.
-After the line has been made, go to the ImageJ
toolbar and click on Analyze and then Set Scale;
a box will appear.
-The distance in pixels will be calculated and
displayed for you, and the diameter of Io is
3635 Kilometers. Put this value into the
“known distance” box. You can also change the
“Unit of Length” to Kilometers to be consistent.
-Click OK.
This has set the distance scale for the image.
You can now use the Straight line tool to
measure how tall or how long objects on the
image are.
Pillan
Locate the plume on the limb (outside edge) of Io. This plume comes from the volcano
Pillan.
-Place the cursor over the plume, and click the +/= button to zoom in until the plume
taking up most of the window. (you can use the – button directly to the right to zoom out
if you zoom too far). Use the Scrolling tool
to move the plume to the center of your
window. After this select the straight line tool.
Use the straight line tool to measure the height of this plume.
-Place the cursor over the highest point of the plume, click and hold.
-drag the line to the surface of Io, making sure to have the line perpendicular to the
surface. When this has been attained, release the mouse. Because you have set the scale,
the program has calculated how long this distance really is.
-Hit Ctl M, and a table will appear. The value registered in the length column will be the
measured height of the plume. Once you have done this, you will have the height’s
plume in kilometers.
Height of Pillan’s Plume:
Images of Io were taken just after this plume erupted, and in these images the deposit can
be seen. Open Image3 using ImageJ. Set the scale the same way as before. Pillan left a
blackish deposit that covers part of a reddish ring deposit that had been deposited before
this eruption. Measure the maximum radius of Pillan’s deposit by taking the diameter
from the top section, through the middle, to the bottom and dividing by two.
Pillan’s Plume Deposit Radius:
Prometheus
Now we will measure the height of the plume in the center of Io. This volcano is
Prometheus. This can be done using the length of the plume’s shadow, as the diagram
below shows. The brightness and contrast tool will also be used in order to make the
plume’s shadow is clearly visible.
Height equals shadow length/Tangent (incidence angle)
H = L / Tan (ø)
Brightness and Contrast
ImageJ
To obtain the best view of the shadow, on the ImageJ toolbar go to Image  Adjust 
Brightness and Contrast. Move the brightness and contrast bars so that you get a good
view of the plume’s shadow. Use the straight line tool to obtain the length of the shadow.
The incidence angle for this plume is about 76o. Use the equation above to calculate the
height.
Shadow Length:
Calculated Plume Height:
On this plume, the radius of the plume deposit can also be measured. The plume’s
circumference is shown as a white deposit on the image. Find the radius to the plume by
measuring the diameter of the white deposit, divide them by two to get the radius, and
average them.
Prometheus’ Deposit Radius:
Pele
Now we are going to look at a plume of much greater size. Pele’s deposit is actually the
red ring in Image3, the one you used to measure Pillan’s deposit radius. Using ImageJ,
open the image Pele2. Set the scale as done before, and measure the plume’s height.
Height of Pele’s Plume:
To measure the plume’s deposit radius, use ImageJ to open Pele3. This shows the plume
ring just after the eruption. Set the scale for this image. Because the ring for this deposit
is so thick, we will take the measurement from the middle of the ring. Measure the
diameter from the top portion of the ring to the bottom portion of the ring and divide by
2.
Pele’s Deposit Radius:
How does this plume height compare to the heights for Pillan and Prometheus?
Answer:
Section 2 – Finding Relationships
Now that we have taken plume height and deposit radius measurements of the Ionian
volcanoes Pillan, Prometheus, and Pele, we can relate some of the characteristics of these
different volcanoes. First, let’s compare the height of the plumes to their deposit radius.
List the plume heights and the deposit radius for each volcano in the space below. Then
take the height of a plume and divide it by the radius to form a ratio.
Pillan
Prometheus
Pele
Height:
Radius:
Height/Radius:
Did you find any similarities in the height/radius ratio between the volcanoes?
Answer:
Now let’s compare the plume deposits of Pillan and Pele. Using the information
collected in your height and radius table above, list the radius of Pillan and Pele below.
Pillan’s Deposit Radius:
Pele’s Deposit Radius:
With this data, we should be able to find a ratio of these two different plume deposits.
How many times bigger is the deposit radius of Pele as compared to Pillan? This can be
done by dividing the radius of Pillan into the radius of Pele’s deposit. Round your
answer to the nearest whole number.
Pele’s deposit is ____ times bigger than Pillan’s deposit.
Using the data you just listed above, look at the deposit radii and plume heights of the
three volcanoes. Using this, and the images that you used to collect this data, describe
the examples; describe the similarities and differences of the three different volcanoes
observed. Make sure to describe any trends that you believe there may be within your
data.
Answer:
Scientists have been able to narrow down the different volcanoes on Io into two distinct
categories. Do you see any way to narrow down these three cases into two categories of
volcanoes? What would the characteristics of these two classes be? Fill out the chart
below to show a way of categorizing the volcanoes of Io.
Category 1
Category 2
Characteristics:
Volcanoes:
Description:
What factors can you think of that could cause the differences in volcanic eruptions? List
any ideas that you have on this below.
Answers:
Section 3 – Analyzing Relationships with Science and Math
For this next section, we will be using two basic equations to further investigate relations
on Io as well as compare your data to scientific models. One equation that we will be
using is a simple ejection velocity equation and the other is actually a string of equivalent
energy equations.
Ejection Velocity: Vi = √2hg where Vi is the ejection velocity, h is the plume height, and
g is the gravitational acceleration (1.8m/s2 for Io, 9.8m/s2 for Earth)
Energy Relations: Combining different energy equations, we can relate how changing
different things can affect an eruption. Here are various energy equations set equal to
each other:
Speed of an object α Temperature α Maximum radius α Maximum height
(α means proportional to)
Kinetic Energy = Thermal E = Work E = Potential E
½ mvi2 = 3/2 kT = ½mgrmax = mgh
Where m = mass, Vi = velocity initial, g = acceleration due to gravity, rmax = maximum
deposit radius, and h = height. Because of this, it can be seen that ½ mvi2 = mgh which
leads to Vi = √2hg. This, though, isn’t the only relationship that can be taken out of this
set of equations.
Setting the potential and work energy expressions equal to each other, we find that the
maximum radius is twice that of the height: rmax = 2h. (There is mg on both sides, so
they cancel each other out)
If the temperature and height energy equations are set equal, 3/2 kT = mgh it can be seen
that temperature is related directly to height: T α h where α signifies a relation. If we do
the same with the temperature and work energy expressions, 3/2 kT = ½mgrmax, we find
that temperature is directly related to the maximum radius: T α rmax.
Now that we know the ejection velocity equation and some of the implications of the
energy relations, we can look at the relations of Io in quantitative way.
First, let’s find the ejection velocity for the three volcanoes using the equation Vi = √2hg,
where velocity initial (Vi) is the ejection velocity. The acceleration due to Io’s gravity is
1.8 m/s2. For h, use the heights of the plumes listed above. Show your work and results
below.
Pillan:
Prometheus:
Pele:
Now let’s use the energy expressions to relate Pillan, Prometheus, and Pele’s plume
heights to their maximum radius. Using the energy expressions we found that the radius
of the deposit should be twice the height of the plume (rmax = 2h).
Take your measured height and calculate what the radius of each deposit should be for
each Volcano. This is your “theoretical radius”. Then list the recorded radius below.
Pillan:
Prometheus:
Pele:
Theoretical Radius:
Measured Radius:
Compare this to your actual data. How do they correlate? Do any volcanoes correlate
better than the others to what the scientific equations say we should observe?
Answer:
Now let’s use the energy relations to think about possible causes of the different classes
of volcanoes and eruptions on Io. Scientists’ categories are simply small plume
producing volcanoes like Pillan and Prometheus and large plume producing volcanoes
like Pele. Using the energy relations T α rmax and T α h, how could temperature play a
role in creating different classes (or sizes) of volcanic plumes?
Answer:
We can also look at what would happen to a volcano if we changed the conditions of
eruption. Again using the relations T α rmax and T α h, what would happen if we raised
the temperature of a volcano’s eruption?
Answer:
What do your findings, and the relations of T α rmax and T α h signify about the size of
an eruption compared to its temperature?
Answer:
Section 5 – Comparisons of Io to Earth
Earlier we calculated the ejection velocity for Pillan, Prometheus, and Pele, so now we
can compare their heights to what they would be on Earth. If we say that a volcanic
eruption has the same ejection velocity, the only variable that we change is the
acceleration due to gravity. Do you think that a plume with the same ejection velocity
will be bigger on Earth or on Io?
Answer:
The equation Vi = √2hg can be used directly to estimate a plume’s height on Earth. If we
solve for the height, which has become our unknown, we get the equation: h = ½Vi2/g.
Find the height of a plume on Earth of an ejection velocity the same of the one on Io that
was just measured. (acceleration due to Earth’s gravity = 9.8m/s2)
Work:
Pillan’s Calculated Height on Earth:
Prometheus’ Calculated Height on Earth:
Pele’s Calculated Height on Earth:
Were your predictions right? Explain why the plumes are different on Earth in terms of
gravity.
Answer:
Unlike Earth, Io actually doesn’t have much of an atmosphere, due to less gravitational
force and other factors. What types of implications might this have on the shape and size
of volcanic plumes on Io compared to if Io had an atmosphere like that of Earth?
Answer:
The comparison to Geysers and Volcanoes:
On Earth, we can look at water as a driving factor in both geysers and volcanoes. Simply
put, geysers operate when water is heated up to extreme temperatures and water vapor
drives an eruption of the water above it. In a Plinian volcanic eruption, water gets mixed
in with the magma, and when it vaporizes it powers an explosive eruption, like that of
Mt. St Helens.
Plinian Eruption - Fuego (h > 17km)
(Acatenango, Guatemala)
Geyser – Old Faithful (h ≈ .050km)
(Yellowstone National Park)
What are some of the main physical differences you see between the Plinian eruption and
the Geyser? Think of the sizes and the differences in the material and ejected.
Answer:
Using the energy relations that relate temperature to size of an eruption (both height and
radius of the deposit (T α rmax and T α h), what can be said about the erupting
temperature of geysers and volcanoes (and their eruptive contents) relative to each other?
Answer:
Different volcanic eruptions on Io:
On Io, SO2 takes the role of water, and other sulfur rich compounds like S2 and SO are
the volatiles in Io’s magma.
Little Io Plume - Masubi (height ≈ 100km)
Big Io Plume - Pele (height ≈ 250km)
What are some of the main physical differences between the Big and Small Io plumes?
Answer:
Using the idea of volatiles creating bigger eruptions than pure substances, what could be
said about the amount of volatiles (remember, SO2 on Io) in the Small plumes compared
to the Big plumes? Also, using the energy relationships T α rmax and T α h, which
eruption would be hotter?
Answers:
Taking the effect of volatiles and temperature of an eruption and its material, which type
of Ionian volcano would best represent a geyser and which a Plinian eruption? Explain.
Answers:
Appendix
Deriving the Equations:
Using some physical equations, the ejection velocity (initial velocity) of the plume’s
particles can be calculated. The two basic equations that are needed to do this are as
follows:
Distance = Velocity (initial) + ½ Acceleration * Time2
d = Vit + ½at2
and
Velocity (final) = Velocity (initial) + Acceleration*Time
Vf = Vi + at
We know acceleration (Io’s gravity), the distance (our height), and we are calling final
Velocity zero (because at the top of its shot is where it stops before it starts to fall). The
only thing that we don’t need in these two equations is time. Because of this, it makes
life easy to get rid of the time variable, which we can do with some algebra. To get rid of
this, we can solve one equation for time and plug that answer into the other equation.
After you do this, solve that equation for Vi.
d = Vit + ½at2 and Vf = Vi – at
Because the acceleration is in the opposite direction as the initial velocity, the first
equation should be: d = Vit – ½at2
Using the second equation  Vf = 0, so at = Vi  t = Vi/a
Plug t = Vi/a into the first equation to get:
d = Vi(Vi/a) - ½a(Vi/a)2  d = Vi(Vi/a) - ½a(Vi2/a2)
 d = Vi2/a - ½Vi2/a
 d = ½Vi2/a 
Now we can solve this equation for Vi for ease of calculation:
 Vi2 = 2da
 Vi = √2da  The Ejection Velocity Equation
Vocabulary:
Plinian Eruption – A volcanic eruption that violently ejects gasses and ash to heights of
up to 10s of kilometers.
Plume – An upwelling of material from the interior of the Earth.
Ejecta – The ejected material from a volcano.
Elliptical Orbit – An orbit that is more shaped like an oval than a circle.
Friction – A force that opposes the relative motion of bodies in contact with each other.
Volatile Gases – Gases that are trapped within molten rock (magma).
Superheated – The state where a liquid is heated above it’s boiling point, but due to
pressure remains a liquid.
Image J Icons
Scrolling Tool – Allows you to move the image
Straight Line Tool – Allows you to make measurements and set the scale
Resources Used:
- Calculation of Plume Height from Shadow:
http://stupendous.rit.edu/classes/phys236/moon_mount/moon_mount.html