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AST 101 Lab 10
Overall Structure of the Solar System
Lab 10
Overall Structure of the Solar System
PURPOSE
This laboratory exercise will allow the student to explore the general characteristics of
objects in the solar system and relate them to a theory of solar system formation.
REFERENCES
●
Exploring the Planets
, Hamblin & Christiansen, 1990
BACKGROUND
How did the solar system form?
When did this happen?
Why are the objects in
the solar system arranged in the particular order we find them in?
While it is indeed difficult to interpret events billions of years in the past from the
evidence available to us today, it can be done.
A combination of careful observations of
present conditions and knowledge of physical principles allows us to reconstruct the
history of the solar system.
Observations of variables such as temperature or mass
density are crucial to our understanding of how the solar system works.
We will use these variables to build a storyline of the solar system’s formation and
evolution.
First we will examine the densities of objects and compare them to the
densities of known materials.
Then we will relate this to the temperature structure of the
solar system.
Finally, we will attempt to draw some basic conclusions about the solar
system and its history.
EQUIPMENT
●
ruler
PROCEDURE
Exercise 1: The Mass Density Profile of the Solar System
It is well established that different objects in the solar system are made from
different materials.
Is this due to random causes, or is there a reason for this?
We will
explore this issue by plotting the density of objects as a function of two different
variables.
Table 10-1 contains density data from selected objects in the solar system.
Using
this table, plot density as a function of distance from the Sun and plot density as a
function of object diameter.
AST 101 Lab 10
Overall Structure of the Solar System
Table 10-1: Density Gradient of the Solar System
Object
Distance from Sun (AU)
Density (g/cc)
Diameter (km)
Mercury
0.387
5.44
4880
Venus
0.723
5.25
12,104
Earth
1.000
5.52
12,756
Moon
1.000
3.34
3476
Mars
1.524
3.93
6787
Jupiter
5.203
1.3
143,800
Io
5.203
3.50
3640
Europa
5.203
3.03
3130
Ganymede
5.203
1.93
5280
Callisto
5.203
1.79
4840
Saturn
9.54
0.69
120,660
Mimas
9.54
1.4
392
Enceladus
9.54
1.2
500
Tethys
9.54
1.2
1060
Titan
9.54
1.88
5150
Comet Halley
18
~0.1
16 by 8
Uranus
19.18
1.28
51,120
Miranda
19.18
1.35
470
Ariel
19.18
1.66
1150
Oberon
19.18
1.58
1520
Neptune
30.07
1.64
49,560
Triton
30.07
2.01
2700
Pluto
39.44
2.06
2284
Charon
39.44
2.06
1192
Exercise #2: The Temperature Profile of the Solar System
The fact that the temperature of objects in the solar system changes with distance
from the Sun is obvious - objects closer to the Sun are hotter and objects further from the
Sun are cooler.
A more difficult question to ask is how the temperature of the original
solar nebula behaved with increasing distance from the protosun.
This is a more
fundamental question, as it addresses why different objects are made of different
materials in the solar system.
Astronomers assume that the composition of the original nebular disk was the
same as that of the present-day Sun.
The Sun consists mostly of hydrogen and helium
gas, but only the jovian planets have similar compositions.
All other objects in the solar
system are much smaller than jovian planets and are generally made up of various
combinations of solid materials.
Why are small objects not made of hydrogen and
helium?
AST 101 Lab 10
Overall Structure of the Solar System
To approach a solution, we must consider the temperature conditions of the early
solar nebula.
The central region that contained the protosun was extremely hot, as was
the rest of the nebula.
The nebula cooled from the outside-in, with objects condensing
out of the nebula.
The closer the protoplanets were to the protosun, the higher their
temperatures; the further from the protosun, the lower their temperatures.
Materials
which condense at low temperatures could not do so close to the protosun, so they tend to
be found relatively far from the Sun.
Materials which condense at high temperatures
could do so close to the protosun, so they tend to be found relatively close to the Sun.
We will plot two graphs to examine this hypothesis.
The condensation
temperatures and densities of various materials are listed in Table 10-2, along with the
distances from the protosun at which these materials could condense. First plot the
density of the materials as a function of condensation temperature and then plot the
condensation temperature as a function of distance from the Sun.
Table 10-2:
Physical Properties of Various Substances
Condensation
Condensation
Substance
Density (g/cc)
Temperature (K)
Distance (AU)*
Iron-Nickel alloy
7.9
1470
0.36
Oxide minerals
3.2
1450
0.37
Feldspars
2.8
1000
0.61
Troilite
4.6
700
0.98
Carbonates
2.9
400
2.07
Water ice
0.92
273
3.44
Carbon Dioxide ice
1.56
216
4.70
Ammonia ice
0.82
195
5.39
Methane ice
0.53
91
14.9
Nitrogen ice
0.88
63
24.3
________________________________________________________________
*
Assuming the temperatures at Mercury (r = 0.39 AU) and Jupiter (r = 5.2 AU) were 1400 K and 200 K
during the condensation phase of the solar system, respectively, other distances were estimated from a
simple power law formula.
Exercise 3: Atmospheres of Objects in the Solar System
The ability of an object to hold on to an atmosphere mostly depends on three
items: its mass, its temperature (determined by its distance from the Sun) and the
components of the atmosphere.
Because liquids require specific ranges of temperatures
and pressures to exist, atmospheres are also key to understanding the presence or absence
of various liquids on a planet’s surface.
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AST 101 Lab 10
Overall Structure of the Solar System
The average speed of a gas molecule is determined from thermodynamics:
where
k
is a quantity known as Boltzman’s constant,
T
is the temperature of the
gas and
m
is the mass of the molecule.
Any gas molecule traveling faster than a planet’s
escape velocity cannot be held by that planet.
Because individual gas molecules have a
wide range of speeds for any given temperature, a planet’s atmosphere may leak away to
space even if its escape velocity appears large enough to hold on to an average molecule.
In practice, to hold on to a specific type of molecule requires that the escape velocity be
six or more times larger than the average molecular speed.
Table 10-3 lists several planets and moons along with their surface escape
velocities and average temperatures (due to radiation from the Sun). Table 10-4 lists
various gases popular in the solar system with their average speeds at various
temperatures.
Determine from these tables which gases a planet can retain and record
those in the data section.
Table 10-3:
Average Temperatures and Escape Velocities of Objects
Solar*
Escape
Object
Temperature (K)
Velocity (km/s)
Mercury
385
4.3
0.72
Venus
285
10.4
1.73
Earth
235
11.2
1.87
Mars
190
5.0
0.83
Jupiter
100
60
10
Ganymede
100
1.9
0.32
Saturn
75
36
6
Titan
75
1.9
0.32
Uranus
55
21
3.5
Titania
55
0.54
0.09
Neptune
40
24
4
Triton
40
1.0
0.17
Pluto
35
0.07
0.012
________________________________________________________________
* Temperature is calculated from the flux of the Sun at the object’s distance from the Sun.
AST 101 Lab 10
Overall Structure of the Solar System
Table 10-4:
Average Speeds for Gases Found in the Solar System
Gas
T = 400 K
T = 300 K
T = 200 K
T = 150 K
T = 100 K
T = 50 K
H
2.2 km/s
1.9 km/s
1.6 km/s
1.4 km/s
1.1 km/s
0.79 km/s
He
1.6 km/s
1.4 km/s
1.1 km/s
0.97 km/s
0.79 km/s
0.56 km/s
CH
0.79 km/s
0.68 km/s
0.56 km/s
0.48 km/s
0.39 km/s
*
NH
0.77 km/s
0.66 km/s
0.54 km/s
*
*
*
H
O
0.74 km/s
0.64 km/s
*
*
*
*
N
0.60 km/s
0.52 km/s
0.42 km/s
0.37 km/s
0.30 km/s
*
O
0.56 km/s
0.48 km/s
0.39 km/s
0.34 km/s
0.28 km/s
*
CO
0.48 km/s
0.41 km/s
0.34 km/s
*
*
*
________________________________________________________________
* exists as liquid or solid at this temperature
AST 101 Lab 10
Overall Structure of the Solar System
LAB 10
Overall Structure of the Solar System
Data and Results
Name: _____________________
Date: ____10/17
_______
Lab Section: _____
Lab Partners:
(1) _____________________
Table Number:
__________________
(2)____________________________________
(3) ____________________________________
Exercise 1: The Mass Density Profile of the Solar System
●
Remember to attach your graphs of density vs. distance from the Sun and density
vs. object diameter.
1) Does the density of an object depend on its distance from the Sun?
If so, in what way?
Up until 10 AU, there is a direct relationship between density and distance. As distance
increases to 10 AU, density seems to fall. After 10 AU, the relationship inverses and as
distance increases, density also increases.
2) Does the density of an object depend on its size (diameter)?
If so, in what way?
Beyond 13,000 km in diameter, we don’t observe any planets above 1.7 g/mL density.
Other than that, there doesn't appear to be a relationship.
Exercise #2: The Temperature Profile of the Solar System
●
Remember to attach your graphs of density of materials vs. condensation
temperature and condensation temperature vs. distance from the Sun.
1)
Does the density of an object depend on condensation temperature? If so, in what
way?
Higher densities seem to appear more frequently at higher condensation temperatures, but
I would say more data is needed.
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AST 101 Lab 10
Overall Structure of the Solar System
2)
Does the condensation temperature depend on the distance from the Sun? If so, in
what way?
Condensation temp and distance seem to follow an almost perfect exponential curve with
higher condensation temperatures being found exclusively at smaller distances.
3)
Compare the results of the graphs from Exercise #1 to the graphs in Exercise #2.
How does this help explain the density profile of objects in the solar system?
Exercise 3: Atmospheres of Objects in the Solar System
Possible Atmospheric Constituents for:
Mercury: Nitrogen, Oxygen, & Carbon Dioxide
Venus:
Helium, Methane, Ammonia, Water, Nitrogen, Oxygen, and Carbon Dioxide
Earth:
Hydrogen, Helium, Methane, Ammonia, Nitrogen, Oxygen, and Carbon Dioxide
Mars: Methane, Ammonia, Nitrogen, Oxygen, and Carbon Dioxide
Jupiter: Hydrogen, Helium, Methane, Nitrogen, and Oxygen
Ganymede: Nitrogen and Oxygen
Saturn: Hydrogen, Helium, Methane, Nitrogen, and Oxygen
Titan: Nitrogen and Oxygen
Uranus: Hydrogen and Helium
Titania: None
Neptune: Hydrogen and Helium
Triton: None
Pluto: None
AST 101 Lab 10
Overall Structure of the Solar System
1)
Mercury has a dayside temperature of 700 K and a nightside temperature of
100 K.
How can this be reconciled with the solar temperature of 385 K at
Mercury?
The solar temperature must be an average of temperature measurements over one solar
day.
So solar temp is essentially the average temperature of a planet with respect to its solar
cycle.
2)
Venus has an escape velocity similar to the Earth's. Why doesn't Venus have
oxygen like the Earth?
There are no plants to produce it.
3)
Earth has a slightly warmer average temperature (295 K) than its solar
temperature of 235 K.
How can this be accounted for?
Earth loses some heat into space, so I guess that would be the difference.
4)
Hydrogen will leak away to space from the Earth within 1 million years.
Does
this statement tend to agree with the data from Tables 10-3 and 10-4? Why or why
not?
Yes, our hydrogen will eventually leak away, because as our planet’s temperature rises,
eventually hydrogen’s average speed will exceed Earth’s escape velocity.
5)
Why do many astronomers believe that the carbon dioxide atmosphere of Mars is
mostly still on the planet?
Because the average velocity that we have observed CO2 at is well below Mars’ escape
velocity.
6)
If Jupiter has an escape velocity to hold onto any of these gases, why is it
primarily made of hydrogen and helium?
It never had any of the other gasses, or the conditions weren’t right for hydrogen and
helium to turn into anything else.
7)
The data suggests that Triton will be unable to hold on to an atmosphere. Why
then does it have an atmosphere, and why is it primarily made of nitrogen?
Some processes must be occurring that we aren’t accounting for.