Download Activity #1: The Mass Density Profile of the Solar System

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AST 111: Lab #9
The Structure of the Solar System
Objectives
 To explore the general characteristics of the solar system
 To analyze possible relationships between object density, distance from
the Sun, diameter, and composition
 To discuss the most important physical factors that determine the scope
and composition of a planetary atmosphere
 To relate specific observations of planets and moons to their actual
atmospheres
References
 Exploring the Planets, Hamblin & Christiansen, 1990
Materials
 Ruler
 Calculator
Introduction
How did the solar system form? When did this happen? Why are objects
in the solar system arranged in the particular order we find them in?
Although it is difficult to interpret events that occurred billions of years ago,
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.
Activity #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.
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(a) Table 9-1 contains density data from selected objects (planets, moons,
& asteroids) in the solar system. Plot density as a function of distance
from the Sun on the first sheet of graph paper.
(b) Next, plot density as a function of the diameter of the object on the
second sheet of graph paper.
(c) Is there a dependence of density vs. distance from the Sun? If so, what
is it? How strong is it?
(d) Is there a dependence of density vs. object diameter? If so, what is it?
How strong is it?
Table 9-1. Density Gradient Data for the Solar System.
Name of
Object
Distance
from Sun
(AU)
Density
(g/cm3)
Diameter
(km)
Name of
Object
Distance
from Sun
(AU)
Density
(g/cm3)
Diameter
(km)
Mercury
0.387
5.44
4880
Tethys
9.54
1.2
1060
Venus
0.723
5.25
12,104
Dione
9.54
1.43
1120
Earth
1.000
5.52
12,576
Rhea
9.54
1.33
1530
Moon
1.000
3.34
3476
Titan
9.54
1.88
5150
Mars
1.524
3.93
6787
Iapetus
9.54
1.16
1460
Vesta
2.362
?
549
Uranus
19.18
1.28
51,120
Ceres
2.768
?
1020
Miranda
19.18
1.35
470
Pallas
2.773
?
538
Ariel
19.18
1.66
1150
Jupiter
5.203
1.3
143,800
Umbriel
19.18
1.51
1170
Io
5.203
3.50
3640
Titania
19.18
1.68
1580
Europa
5.203
3.03
3130
Oberon
19.18
1.58
1520
Ganymede
5.203
1.93
5280
Neptune
30.07
1.64
49,560
Callisto
5.203
1.79
4840
Triton
30.07
1.64
2700
Saturn
9.54
0.69
120,660
Nereid
30.07
?
340
Mimas
9.54
1.4
392
Pluto
39.44
2.06
2284
Enceladus
9.54
1.2
500
Charon
39.44
2.06
1192
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Activity #2: The Temperature Profile of the Solar System
That temperatures of objects change with distance from the Sun is
perhaps obvious. A more specific question to ask is how the temperature of the
original solar nebula behaved vs. distance from the forming Sun (“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 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 made up of various combinations of solid (rarely
fluid) materials. Why are small objects not made of hydrogen and helium?
In this activity we will look at the effects of temperature on composition.
Activity #3 will look at the effects of the masses of objects on their compositions.
(a) Table 9-2 contains density data from selected materials common in the
solar system. Plot density as a function of condensation temperature 1
from the Sun on the third sheet of graph paper.
(b) Next, plot condensation temperature as a function of condensation
distance2 on the fourth sheet of graph paper.
(c) Is there a dependence of density vs. condensation temperature? If so,
what is it? How strong is it?
(d) What is the dependence of condensation temperature vs.
condensation distance?
(e) Did either of the graphs from Activity #1 resemble either of these
graphs from Activity #2? If so, why?
“Condensation temperature” refers to the when a substance sifts out of gas and condenses into liquid or
solid form. These temperatures are approximations only.
2
Distances were calculated from a simple power law, assuming that the primordial temperatures at the
distance of Mercury (0.39 AU) and Jupiter (5.2 AU) were 1400 K and 200 K, respectively.
1
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Table 9-2. Physical Properties of Various Substances.
Substance
Density (g/cm3)
Condensation
Temperature (K)
Condensation
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
(f) Today, the temperature decreases rapidly as one moves further from
the Sun. What was it like during the formation of the solar system – i.e.
as one moved further from the protosun?
(g) Suppose an object made of a variety of ices moved closer to the Sun
than the Earth. What would happen to it?
(h) The original solar nebula was in the shape of a thin disk. How is it
similar today? How is it different?
(i) The Sun today is far hotter than the protosun, yet the temperatures in
the rest of the solar system are much cooler today (see Activity #3).
Why is this so?
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96
97
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Activity #3: Atmospheres of Objects in the Solar System
The ability of an object to hold on to an atmosphere depends primarily on
three characteristics: its escape velocity, as determined by its gravity; its surface
temperature, as influenced by its distance from the Sun; and the potential
components of its atmosphere. In contrast, the average speed of a gas particle
(atom or molecule) is determined from the mass of the molecule and the
temperature of the atmosphere:
v
3kT
m
where k is a quantity known as Boltzman’s constant (1.38 x 10-23 J/K), T is the
temperature of the gas, and m is the mass of the gas particle. Any gas molecule
traveling faster than an object’s escape velocity cannot be held by that object.
Because individual particles 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 to be large enough. In practice, to hold on to a specific type of
gas molecule requires that the escape velocity be about six or more times
greater than the average molecular speed.
Table 9-3 lists several solar system objects with their escape velocities
and average temperatures (due to the Sun). Table 9-4 lists various gases
popular in the solar system with their average speeds at various temperatures.
Some of the substances are liquids at low enough temperatures, so they will not
have speeds listed. Hydrogen and helium are the most common gases.
(a) Determine from these tables which gases can be retained by an object
and record those gases in Table 9-3. If an object can retain more than
three gases, list only the three lightest gases.
(b) Molecular hydrogen gas will leak away to space from the Earth within a
million years. Does this statement agree with the results in Table 9-3?
Briefly describe why or why not.
(c) Earth has a warmer average atmospheric temperature (295 K) than its
solar temperature of 235 K. Why is this so?
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Table 9-3. Average Temperatures and Escape Velocities of Various Objects.
Object
Solar Temperature
(K)
Escape Velocity
(km/s)
Mercury
385
4.3
Venus
285
10.4
Earth
235
11.2
Moon
235
2.38
Mars
190
5.0
Jupiter
100
60
Ganymede
100
1.9
Saturn
75
36
Titan
75
1.9
Uranus
55
21
Titania
55
0.54
Neptune
40
24
Triton
40
1.0
Pluto
35
0.07
Possible Atmospheric
Constituents
(d) Oxygen is actually only found on Earth in significant amounts. Why is
oxygen popular on Earth but on no other object? (Hint: could there be
other reasons besides the ones studied above?)
(e) Mercury has a daytime temperature of 700 K and a nighttime
temperature of 100 K. How can this be reconciled with its solar
temperature of 385 K? (The Moon behaves in a similar fashion)
(f) Venus has an extremely thick atmosphere and very high temperatures
(its actual temperature is 750 K, not 285 K). What is its atmosphere
made of – molecular hydrogen or carbon dioxide?
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(g) Even though the atmosphere of Mars is very thin, many astronomers
believe most of the carbon dioxide of Mars is still there. In what phase
(gas or solid) might it exist?
(h) Jupiter’s escape velocity allows it to hold on to any gas. Why then is
Jupiter primarily made of hydrogen and helium?
(i) Titan and Ganymede have the same escape velocity. Why then does
Titan have a thick atmosphere (thicker than Earth’s, by the way)
whereas Ganymede has no atmosphere?
(j) Triton has a thin atmosphere of nitrogen and Titan has a thick
atmosphere of methane. Why do these substances dominate their
respective atmospheres? Hint: Consider the various phases in which
water can be found on Earth.
(k) Finally, objects in the solar system are split into a variety of categories.
In (rough) order from the Sun, they are terrestrial planets, asteroids,
jovian planets, jovian moons, icy dwarfs and comets. Fill in Table 9-5
below. Indicate the two or three most likely popular substances to be
found in each category.
(Notes: “jovian planets” are a special case, being made primarily of
gas, so the answer is given for them. All other objects will be solid.
“Jovian moons” are simply the moons that orbit jovian planets and “icy
dwarfs” are objects like Pluto. Consult your textbook for more
information if necessary.)
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Table 9-4. Average Speeds for Gases Found in the Solar System.
(All speeds in kilometers per second)
Gas
Temperature (K)
Name
Molecular
Formula
400
350
300
250
200
150
100
75
50
Hydrogen
H2
2.2
2.1
1.9
1.8
1.6
1.4
1.1
0.97
0.79
Helium
He
1.6
1.5
1.4
1.2
1.1
0.97
0.79
0.69
0.56
Methane
CH4
0.79
0.73
0.68
0.63
0.56
0.48
0.39
*
*
Ammonia
NH3
0.77
0.71
0.66
0.60
0.54
*
*
*
*
Water
H2O
0.74
0.69
0.64
*
*
*
*
*
*
Nitrogen
N2
0.60
0.56
0.52
0.47
0.42
0.37
0.30
0.26
*
Oxygen
O2
0.56
0.52
0.48
0.44
0.39
0.34
0.28
0.24
*
Carbon
Dioxide
CO2
0.48
0.44
0.41
0.38
0.34
*
*
*
*
Notes: * = exists as liquid or solid at this temperature.
Calculations assume one Earth atmosphere of pressure.
Table 9-5. Categories of Objects in the Solar System.
Category
Likely to be made of these substances
Terrestrial Planets
Asteroids
Jovian Planets
Jovian Moons
Icy Dwarfs
Comets
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Hydrogen, helium