**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 H~2~0 and CO~2~. 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:

![](media/image1.png){width="2.6243055555555554in"
height="1.8680555555555556in"}
![](media/image2.png){width="1.5256944444444445in"
height="1.8645833333333333in"}
![](media/image3.jpeg){width="1.3395833333333333in"
height="1.8840277777777779in"}

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.
![](media/image4.png){width="0.22916666666666666in" height="0.21875in"}
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.

![](media/image5.png){width="2.5in" height="2.4611111111111112in"}-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**

> ![](media/image6.png){width="1.8527777777777779in"
> height="1.8395833333333333in"}

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 ![](media/image7.png){width="0.22916666666666666in"
height="0.19791666666666666in"} 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**

> ![](media/image8.png){width="3.0930555555555554in"
> height="1.9791666666666667in"}
>
> 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.
>
> ![](media/image9.png){width="3.5215277777777776in"
> height="1.6583333333333334in"}
> ![](media/image10.png){width="1.1041666666666667in"
> height="2.186111111111111in"}

**Height** equals **shadow length**/**Tangent (incidence angle**)
Brightness and Contrast

**H = L / Tan (ø)** 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 76^o^. 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**

![](media/image11.png){width="2.6569444444444446in"
height="1.8645833333333333in"}

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:**

![](media/image12.png){width="2.7708333333333335in"
height="2.7604166666666665in"}

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:** **V~i~ = √2hg** where V~i~ is the ejection
velocity, h is the plume height, and g is the gravitational acceleration
(1.8m/s^2^ for Io, 9.8m/s^2^ 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 mv~i~^2^ = 3/2 kT = ½mgr~max~ = mgh**

Where m = mass, Vi = velocity initial, g = acceleration due to gravity,
r~max~ = maximum deposit radius, and h = height. Because of this, it can
be seen that ½ mv~i~^2^ = mgh which leads to V~i~ = √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: **r~max~ =
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 = ½mgr~max~**, we find
that temperature is directly related to the maximum radius: **T α
r~max~**.

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 **V~i~ = √2hg**, where velocity initial (V~i~) is the
ejection velocity. The acceleration due to Io's gravity is 1.8 m/s^2^.
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 (**r~max~ = 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 r~max\ ~**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 r~max\ ~**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 r~max\ ~**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 **V~i~ = √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 = ½V~i~^2^/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/s^2^)

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.

![](media/image13.png){width="2.8784722222222223in"
height="4.302777777777778in"}
![](media/image14.jpeg){width="2.9541666666666666in"
height="4.302777777777778in"}

Plinian Eruption - Fuego (h \> 17km) Geyser -- Old Faithful (h ≈ .050km)

(Acatenango, Guatemala) (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 r~max\ ~**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, SO~2~ takes the role of water, and other sulfur rich compounds
like S~2~ and SO are the volatiles in Io's magma.

![](media/image15.png){width="2.803472222222222in"
height="3.6770833333333335in"}
![](media/image16.png){width="2.620138888888889in" height="3.675in"}

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 r~max\ ~**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 \* Time^2^

d = V~i~t + ½at^2^

and

Velocity (final) = Velocity (initial) + Acceleration\*Time

V~f~ = V~i~ + 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 V~i~.

d = V~i~t + ½at^2^ and V~f~ = V~i~ -- at

Because the acceleration is in the opposite direction as the initial
velocity, the first equation should be: d = V~i~t -- ½at^2^

Using the second equation  V~f~ = 0, so at = V~i~  t = V~i~/a

Plug t = V~[i]{.underline}~/a into the first equation to get:

d = V~i~(V~i~/a) - ½a(V~i~/a)^2^  d = V~i~(V~i~/a) - ½a(V~i~^2^/a^2^)

 d = V~i~^2^/a - ½V~i~^2^/a

 d = ½V~i~^2^/a 

Now we can solve this equation for V~i~ for ease of calculation:

 V~i~^2^ = 2da

 V~i~ = √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**

![](media/image17.png){width="0.22916666666666666in" height="0.21875in"}
Scrolling Tool -- Allows you to move the image

![](media/image4.png){width="0.22916666666666666in" height="0.21875in"}
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>