Download Objective

Satellite Orbital Decay
-- or --
“How to Keep a Satellite in Orbit”
Objective
Explore effects of atmosphere drag on motion of satellites that are in low enough
orbits to be affected by the Earth’s atmosphere.
This laboratory was originally developed by a team of US Air Force Academy physicists using
satellite drag to teach the concepts of energy conservation and momentum and the impacts of
space weather on the upper atmosphere. It replicates many elements of the operational software
designed to track and predict satellite motion in low earth orbit. Many of graphs you will find in
this lab originated from simulations of observations of Air Force and NASA satellites.
In this exercise you will write a program from first principles. You will learn the basic physics and
assumptions that go into writing such a program and analyze the validity of the physical models
you will use. You will then design a semi-empirical model that produces a better fit to the physical
conditions in the upper atmosphere. Following that you will analyze how the solar activity can
affect the atmosphere and cause changes in the thickness of atmospheric layers. This in turn affects
the orbit of the satellites. Finally, you will be asked to make predictions of when to boost the
satellite to keep it at an altitude that will sustain its orbit, thus preventing premature re-entry into
the dense atmosphere where it would burn and disintegrate.
H
u
b
ES J
U
S
a
R. Viereck, NOAA
Fig 1
The computer program for this exercise is provided by Delores Knipp.
Lab Activities:
• Compare and contrast ideal and model atmospheres
• Study the atmosphere’s density and temperature profile
• Develop basic physics to describe satellite motion
• Calculate boundary values for problem
• Write a program using Excel to describe satellite motion
• Plot characteristics of satellites (in near circular orbit) under the influence of drag
• Explore effects of time-varying atmosphere heating
• Collision avoidance and re-entry prediction
—1—
Introduction
The particular satellite you will be using will orbit the Earth at an altitude of ~ 350 km. This is
much higher than planes which fly at altitudes of about 30,000 feet or ~ 10 km (the latter is
roughly the same altitude as you see the high clouds in the picture below). The lower layer of
the atmosphere is called troposphere – the following atmospheric layers are called the
stratosphere, the mesosphere, the thermosphere and the exosphere. The density of the
atmosphere decreases exponentially with altitude – this is a very steep decrease in density and
basically implies that most of the mass is relatively close to the Earth’s surface and 90% of the
total mass of the atmosphere is below the height of the Mount Everest. (In the first part of the
exercise you will model the atmosphere using the exponential decrease, and in the second part
you will analyze the validity of assuming this type of decrease in density.) The diagram below
shows the atmospheric neutral layers. Embedded within the uppermost neutral layer are regions
of ionization known as the D, E and F layers of the Ionosphere.
Fig 2: Atmospheric Layers
Image taken from the University Corporation
for Atmospheric Research (UCAR) site at
http://www.ucar.edu/news/releases/2004/hirdls.shtml
This diagram shows the physical phenomena
and observing systems present at various
heights in the atmosphere. At left is the height
axis (kilometers on the left, miles on the
right). At right is the temperature at various
heights (Celsius on the left, Fahrenheit on the
right). The color of the vertical bar shows
cooling as one ascends through the
troposphere and warming in an ascent
through the stratosphere. High-flying planes
are found near the tropopause, the cold, dry
boundary region between the troposphere
and stratosphere. Ozone is most
concentrated in the lower stratosphere
(bottom left).
—2—
An Example: The Case of the Hubble Space Telescope
The Hubble Space Telescope is a cooperative program of the European Space Agency (ESA) and
the National Aeronautics and Space Administration (NASA) to operate a long-lived space-based
observatory for the benefit of the international astronomical community. Since its preliminary
inception, HST was designed to be a different type of mission for NASA -- a long term space-based
observatory. HST's current complement of science instruments include three cameras, two
spectrographs, and fine guidance sensors (primarily used for astrometric observations). Because of
HST's location above the Earth's atmosphere, these science instruments can produce high resolution
images of astronomical objects. Ground-based telescopes can seldom provide resolution better than
1.0 arc-seconds, except momentarily under the very best observing conditions. HST's resolution is
about 10 times better, or 0.1 arc-seconds.
When originally planned in 1979, the Large Space Telescope program called for return to Earth,
refurbishment, and relaunch every 5 years, with on-orbit servicing every 2.5 years. In 1985,
contamination and structural loading concerns associated with return to Earth aboard the shuttle
eliminated the concept of ground return from the program. NASA decided that on-orbit servicing
might be adequate to maintain HST for its 15- year design life. A three year cycle of on-orbit
servicing was adopted.
Due the drag in the atmosphere the orbits decay which results in a loss of altitude. The four HST
servicing missions in 1993, 1997, 1999 and 2002 were enormous successes. Without those servicing
missions and the “boosting of the orbits” the Hubble Space Telescope would have downed as illustrated
below by the blue lines. Boosting the orbits has extended HST’s lifetime.
Solar Cycle 22
Altitude (nautical miles)
Hubble altitude with
scheduled reboosts
Distance below
operational altitude
320
260
Solar Cycle
24
Solar Cycle 23
Science operations altitude
Hubble re-enters
without reboost
200
Withbroe, Director, NASA Space Physics Division
1990
1995
2000
Year
2005
2010
Credit G. Withbroe, NASA
Fig. 3
—3—
PART I
Law of Atmospheres - The Theory
Your first challenge will be to use Excel to model how the density of the atmosphere decreases in
the troposphere. Let’s first think about the meaning of density, ρ. It is the mass of air per volume
(ρ=M/Vol). In fact 1 cube meter of air at sea level weighs 1.21 Newtons. So the density at sea
level, denoted by ρo, is 1.21 kg/m3. The atmosphere in the troposphere is relatively dense, and
particles in the atmosphere collide frequently (they move with some average velocity v and have
an average temperature T). This implies that we can use the ideal gas law (remember PV=nkT?)
here. We also can assume that the density of the atmosphere declines exponentially with the
height h. Every type of exponential decline (or increase) can be described mathematically by
using the “e-to-the-power-of something” mode.
ρ = ρ 0 ⋅ e − const ⋅h
(1)
where ρo is the mass density at sea level, because:
for h=0m
ρ = ρ 0 ⋅ e0 = ρ 0
In fact the more accurate form of the law of atmospheres is:
ρ = ρ0 ⋅ e
−
mgh
kT
(2)
where m is the mass of the gas molecule, g the gravitational acceleration, and k the Boltzmann
constant.
Let’s think about this formula – the exponent is a ratio between “mgh” and “kT”. “mgh” is the
potential energy of a particle with mass m at a height h, and “kT” is the thermal energy of that
same particle. So in other words, the exponent is a balance between potential and thermal energy
of the particle – this means that the more massive the individual particles are the more the
atmosphere will be squeezed together, and the higher the temperature the more the atmosphere
will want to expand.
The “Simple Law of Atmospheres” assumes that all quantities in the exponent (the particle mass, m,
the temperature, T, and the gravitational acceleration, g) remain constant, and that the only
variable is the altitude, h. (In other words, the “Simple Law of Atmospheres” assumes equation 1
where const=mg/kT.) You will be typing this formula into the Excel spread sheet and then plot how
the density of the atmosphere, ρ, varies with altitude, h.
—4—
Instructions to use Excel
•
Double click on Satellite-Lab to open the Excel spread sheet.
•
Click on “Simple Atmosphere” at the bottom of the page. You will see a spreadsheet with
some constants highlighted in green and a formula highlighted in yellow. You will need to
calculate the purple values. Let’s start with the height. You could type in all values from 0,
1, 2, 3… to 1000, but you can also have Excel do this for you.
•
If you know how to use Excel just put those values into column [A], if not follow the
instructions in the different type font below:
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Click the cell directly underneath “h in km” [A11].
Type “0” followed by <return> for h=0 at sea level.
Now increase the altitude in steps of 1km, click on the cell underneath the “0”,
on cell [A12]
Type “=” then click on the previous cell, on [A11], at this stage Excel will insert
“A11”
Type “+1”, then click <return> to enter the formula.
Put the cursor on back on cell [A12], and left-click. Go to the bottom right of the
cell; when the cursor turns to a “thin cross”, pull down the mouse until
h=1,000km. Voila, column [A] is done.
Next let us convert km to meters and store all the values in column [B].
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Click the cell directly underneath “h in meters”, on cell [B11]
Type “=” then click on cell [A11] — at this stage Excel will insert “A11”
Type “*1000”, then click <return> to enter the formula.
Like before, put the cursor on cell [B11], and left-click; go to the bottom right of
the cell; and when the cursor turns to a “thin cross”, pull down the mouse until
h=1,000,000m.
•
You now have written your first Excel program. Calculating the density is a little more
complicated, but the general idea is the same. For every altitude, h, which is stored in
column [B], we want to calculate the corresponding value of the density and put it into
column [C]. Let’s calculate the density. Recall the formula; put in h=0 meters and solve.
We can calculate this even without a calculator since the exponent is equal to zero. So ρ at
h=0 is ρo (i.e., ρo =1.21 kg/m3).
•
Next we need to determine the density at an altitude of 1km, then at 2km. So insert 1km
(convert km to meters first – 1km=1000m) into the above formula. You’ll get:
ρ at h =1km = ρ 0 ⋅ e
⎡ mg
⎤
⎢⎣ − kT ⋅h1 km ⎥⎦
—5—
= ρ0 ⋅ e
⎡ mg
⎤
⎢⎣ − kT ⋅1000 ⎥⎦
•
What is next line for h=2km?
ρ2 =
•
Using your calculator calculate ρ1 & ρ2. ____________________________________
•
You could calculate all the values, but you can also have Excel do this for you. You
basically want to repeat the same calculation every 1000m from the sea level. Rewrite the
above formula, but substitute 1, 2, or 3 with “i” – “i” then corresponds to each ith value of
density (ρi) and altitude (hi). You’ll be solving for density iteratively, i.e. calculating a value
for density for each corresponding value of altitude.
ρi =
•
(3)
Insert this formula into Excel. If you do not know Excel, follow the instructions below:
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Click on cell “C11”
Type in “=1.21”
Click the cell to the right of “h=1” (This is cell “C12”)
Type “=1.21”, then type “*exp(-”
Click on cell “B12”, which is the altitude in meters — Excel will insert “B12”
Type “*”, then at cell “D3” click on “4.8079E-26” the value of m — Excel will
insert “m0”
Type “*”, then at cell “D4” click on “9.8” the value of g — Excel will insert
“g_surface”
Type “/”, then at cell “D5” click on “1.38E-23” the value of k — Excel will
insert “k_B”
Type “/”, then at cell “D6” click on “293” the value of T — Excel will insert “T”
Type “)”, then click <return>. Your formula is now typed into the “ρ1” cell.
Select that cell and after getting the small cross in the lower right, pull down the
mouse until h=1000km.
Scroll back to the top and check the values of ρ1 & ρ2 – they should have the
same values as what you calculated before.
—6—
Conceptually Understanding the
Law of Atmospheres
•
Now check out the graph. Put your cursor to the bottom of the Excel sheet and click on “Alt.
vs. Mass Density (simple)”. The graph should appear. It shows how density changes with
altitude. The graph is actually displayed below. Look at the green line.
•
At what altitude is the density (the green line) 50% that of the density at sea level? _____
•
Using a ruler draw that altitude into the plot.
•
At what altitude is the mass density (green line) 90% that of the density at sea level? ____
•
From the plot (the green line) read off the density at an altitude of 50km? ____________
a
b
c
Fig. 4
•
The above plot shows the altitude versus mass density for three different temperatures.
Which of a, b, c (the green, blue and red lines) has the highest temperature? Explain.
•
Put your cursor to the bottom of the Excel sheet and click on “Simple Atmosphere”. The
previous spread sheet should appear again. Scroll down to an altitude of 50km. What is
the corresponding value of the density? ___________
•
Are both of the values roughly comparable? ___________
—7—
•
Put your cursor to the bottom of the Excel sheet and click on “Alt. vs. Mass Density
(simple)”. The previous graph should re-appear. Double-click on the bottom scale of the
graph (over the number 0.5). A new window saying “Format Axis” should open. The click
on the “Scale” window. In that window place a tick mark next to “Logarithmic scale” (third
line from the bottom). Then click “ok”. The x-axis now has changed and the graph will
should like the one below.
C
b
a
Fig. 5
•
The satellite will be flying at an altitude of 350 km. Read off the value for the density_______
•
The best vacuum produced on Earth has a density of ~10-20 g/cm3 (or 10-23 kg/m3).
Compare this value to the density in which the is flying.
•
Both graphs show the same thing, the only difference is the logarithmic scale of the x-axis.
Comment on when you would prefer to use the linear plot and when you’d prefer the
logarithmic plot.
•
Also, using a logarithmic scale, the exponential decay is easily represented by a straight
line.
•
Write down the formula for exponent
•
Calculate the value for the slope (from the formula, not the graph). _____________________
•
Let’s think about the slope – what does it really represent?
_____________________
—8—
PART II
Semi-Empirical Modeling
Sometimes the theoretical model turns out not to be a good fit for the data. This is often the case if
something is missing from the theory. When this situation occurs scientists often turn to empirical
models. Empirical models are models that orginate or are based on factual information or directly
sensed information. There are four possibilities of dealing with poorly behaved theoretical models.
a)
b)
c)
d)
Rethinking the theory, i.e., the “Simple Atmosphere” from Part I
Expanding upon the theoretical model
Creating and using an empirical model from data
Tweaking the theoretical model and iteratively adding observational data,
i.e. doing semi-empirical modeling
Let’s first look at the formula for the “simple atmosphere” again and decide what it really tells us.
In the exponent we have a balance between “mgh” and “kT”. This means that more massive
particles exert a higher pressure – on the other hand the higher the temperature the more the
atmosphere will want to expand. So we actually have three more variables: m, g, and T (in
addition to the altitude h).
ρ = ρ0 ⋅ e
−
mgh
kT
In part I we assumed that all these values remain constant as we go to higher and higher altitudes.
What do you think, is this a reasonable assumption?
•
Can you assume that the gravitational acceleration is constant at higher altitudes? Explain.
•
Can you assume that the composition of individual molecules remains constant? Explain.
[Hint: What is the chemical composition of the different atmospheric layers? And what do
you think might happen if these molecules have different masses?]
—9—
•
Can you assume that the temperature remains constant? Explain.
•
If you said “no” to the above questions you were correct! The three assumptions of the “simple
law of atmospheres” are not completely correct. So how does the gravitational acceleration
change with altitude? This is something you can figure out yourself – Remember Newton’s
second law? And remember the formula for Newton’s universal Law of Gravitation? Look up
those formulae and write them into the two boxes below.
•
F=
(4)
F=
(5)
Combine them and solve for the acceleration. Recall that the radius is actually the distance to
the center of the Earth, so substitute R=Re+h, where Re is the Earth’s radius and h the altitude.
a=
•
Next we can change the simple law of atmospheres to substitute for the altitude dependence
of the gravitational acceleration. Insert the above expression for g (or actually a):
ρi = ρ 0 ⋅ e
•
(6)
−
m
⋅gi ⋅hi
kT
=
(7)
Let’s analyze how a changing gravitational acceleration affects your model. On the bottom of
the Excel sheet click on the sheet saying “Atmosphere”. Look at column [E] – it should be the
same as what you calculated in part I. Just for practice, repeat the previous exercise of typing
hi into column [B], and ρi into column [E] of this sheet.
— 10 —
•
Next, type the above formula (equation 7) into column [H], starting at cell [H11]. To
practice try it yourself. If all fails follow the instructions below.
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Click the cell [H11]; Type “=1.21”, then type “*exp(-”
Type “*”, then click on “4.8079E-26” the value of m— Excel will insert “m_o”
Type “/”, then click on “1.38E-23” the value of k — Excel will insert “kB”
Type “/”, then click on “293” the value of T — Excel will insert “T”
Type “*”, then click on “6.67E-6” the value of G — Excel will insert “G_”
Type “*”, then click on “5.97E+24” the value of Me — Excel will insert “Me”
Type “*”, then click on “h=0”, cell [B11] — Excel will insert “B11”
Type “/(”, then click on “6.37E-11” the value of Re — Excel will insert “R_e”
Type “+”, then click on “h=0”, cell [B11] — Excel will insert “B11”
Type “)^2)”, then click <return>
Click on cell [H11] and pull down formula until h=1000km.
Let’s “look” at the effect of inserting a variable acceleration. You will look at figure 2
again, but this time, compare the simple law of atmospheres to your new, more complex
version. Go to the bottom of the Excel sheet and click on “Altitude vs. Mass Density” and
look at the plot. The green line corresponds to the “simple law of Atmospheres”, the grey
one to the Law corrected for a variable gravitational acceleration. This plot is also below.
Look at the grey line and compare it to the green line. It still is a straight line – an
exponential decay, and it only differs slightly.
Fig. 6
•
So all in all, the assumption of a constant acceleration was not perfect, but what do you recon.
Was it a reasonable assumption nevertheless? _____________
— 11 —
•
And to be honest, we would not have known this unless we had really calculated and plotted
this. Okay, let’s look at the other assumptions. It turns out that the temperature of the
atmosphere is NOT constant (the temperature is much cooler at an altitude where planes fly and
increases, decreases and then increases again – see plot below). This behavior is too complex
to be described by another theoretical law. So we are going to do a trick. For every altitude,
we will insert the measured value of the temperature. Guess what – we have actually done this
for you; and even plotted it – the blue line above incorporates this temperature dependence.
We have combined a theoretical model with real data and we have now produced a semiempirical model.
Fig. 7
•
What do you think? Explain if an exponential law is a good description of the physical situation.
Comment on which region might be represented by such an exponential law.
•
Since the chemical composition (thus the mass per molecule) changes somehow (let’s not worry
about the details), we will need to insert measured values for the mass as a function of altitude.
The good news is you get a break (again) because we have done this for you! (The data are in
column [D] in the “Atmosphere” spread sheet, and the vales corrected for varying molecular
mass are in column [K].) Like in the case for temperature, this part is semi-empirical. The black
line in Figure 6 is now our “best” model – it is called the “MSIS” model (the red line incorporates
an “additional” change in temperature as you will discover in the next section). This final model,
the MSIS model is used by professional scientists at NOAA, the National Oceanic and
Atmospheric Association.
— 12 —
PART III
Theoretical Background and Orbital Drag
Because the atmosphere extends beyond 1000 km, it can interfere with the motion of near earth
satellites, for example the space satellite in near-Earth orbit. The atmosphere will cause an air
drag, which will cause the satellite’s orbit to decay and eventually down the satellite (in fact, as the
satellite re-enters, there is a good possibility of it burning up in the lower parts of the atmosphere).
A satellite in circular orbit experiences an acceleration given by (look this up)
a=
(8)
Insert the expression for the acceleration into Newton’s 2nd Law (from before, equation 4)
F2nd =
Newton’s Law of Gravitation is (from before, equation 5)
F2nd = FG =
Combine both equations and solve for the velocity
v=
(9)
By squaring both sides and then multiplying by ½ m you get the associated kinetic energy:
Ekin = ½ m v2 =
(10)
Look up the expression for potential energy:
Epot =
(11)
Why is the potential energy negative? What does that mean?
— 13 —
The total mechanical energy of the satellite is the sum of its kinetic and potential energy.
Etot = Ekin + Epot =
(12)
Remember that the altitude is the height above the Earth’s Surface + the Earth’s radius. Solving the
above equation for altitude we get:
h = r – Re =
(13)
So now we have the expressions we need – the total energy of the satellite as it flies with velocity v at
an altitude of h. We also know that as the satellite moves through the atmosphere it will experience a
drag due to the resistance of air. Basically the air drag robs the satellite of its total mechanical
energy. Will this increase or decrease the kinetic energy of the shuttle? (Do not guess, think) _______
Let’s check if your answer is correct. Look at the balance between kinetic and potential energy
(equation 12). As the satellite is exposed to orbital drag it will lose altitude. How does this affect
the balance in that equation? Does a lower altitude result in a higher or lower velocity? __________
And does this correspond to a higher or lower kinetic energy? ___________
What about the potential energy? How fast does it decrease compared to the mechanical energy?
Okay, now we need to know the expression for the drag force. This will just be given to you
without any proof (well, sometimes you get lucky!).
FD = ½ ρ A CD v2
(14)
where A is the area of the satellite and CD the drag coefficient. The work done by the drag then is
WD = FD s = ½ ρ A CD v2 s
(15)
where s is the distance traveled (for one orbit s=2πr=2π(Re+h)).
Let’s conceptually think about this formula – it depends on the front surface area of the satellite
perpendicular to the direction of motion, and on the volume V = As which the satellite displaces as
it travels the distance s. It also depends on the ambient air density ρ through which the satellite
travels, and on the square of the velocity. (Remember the kinetic energy is also dependent on the
square velocity since E = ½ mv2. Also recall that m = ρ V = ρ As.) CD is the drag coefficient and
depends on the properties of the medium, in this case the air.
Now we have all the formulae we need for the Excel spread sheet. Next you will write these
formulae into the flow chart on the next page.
— 14 —
Energy
at this
altitude
Energy
at the next
orbit
Initial
values
Next
values
Flowchart of Orbit Decay Model:
Speed
Altitude
Speed
Altitude
— 15 —
Atmospheric
density
at this
altitude
Atmospheric
density
at this
altitude
Drag Force
Drag Force
(Instructions of inserting this into Excel spread sheet are on next page)
Orbital Drag Laboratory Worksheet
Work done
by drag force
in this orbit
Work done
by drag force
in this orbit
PART IV
Satellite Orbital Decay Analysis
1. If you have not done it yet complete the worksheet on the previous page
•
Initial Values: Values at Orbit = 0. Write the formulae into the shaded boxes in the flow
chart. Shaded boxes should contain a symbolic formula and then a numerical result, while
unshaded boxes just require a number. Use your calculator to calculate the “Initial values”.
(The initial altitude is 350km, and the the drag force is zero.)
•
Next Values: The information in “next values” shows how each orbit after the first one will
be handled in the spreadsheet model. After one orbit, the satellite will have been exposed
to the drag force you just calculated and will have lost some energy.
Eorbit#1 = Eorbit#0 - WD by orbit#0
in program language
Ei = Ei-1 - WD i-1
(16); (17)
2. Go to the page entitled “Shuttle Orbit Decay.” (Open the Excel spread sheet and click on “Shuttle
Orbit Decay.”) Look at the spread sheet.
•
•
•
•
•
•
•
Column [A] contains altitude data (in km),
Column [B] contains actual temperature data (in K) for the atmosphere,
Column [C] contains the mean mass of an air molecule in unified mass units (u)
Column [D] shows atmospheric mass densities as calculated using the original (simple) form
for the Law of Atmospheres, which assumes (incorrectly) a constant value for g, a constant
temperature atmosphere, and a constant mean molecular mass.
Column [E] contains what we’ll call the true atmospheric mass density in kg/m3 – it is
calculated for you using the semi-empirical MSIS model.
Column [F] will be used later to explore the effects of increased temperatures.
Columns beyond [F] are used for various curves on the “Altitude vs. Mass Density” chart.
3. Complete the “Initial” (pink) row of the spreadsheet: Enter the “Initial” orbit (Orbit #0) information
from the top half of your worksheet flowchart. If the information is from a shaded box in the
worksheet, enter a formula in the appropriate spreadsheet cell.
•
Start with cell [D11], the Satellite’s total energy. (Note that you have typed in formulae
into the spread sheet before, so this time you will have to figure out how to do it on your
own. What you should get in that cell is something that looks like:
“=-G*Mearth*m_shuttle/(2*(hi_shuttle+Re))”.
[note hi_shuttle_km is wrong]
After hitting <return>, you should get the same number that you wrote into the flow chart.
(If that is not the case check your formula again. If all else fails consult your instructor.)
•
Next go to cell [F11] and type in the altitude in meters.
•
Next insert the formula for the velocity into cell [G11]. You should get something like
“=SQRT(G*Mearth/(Re+F11))”.
•
Insert the formula for the drag force into [H11]. You should get something like
“=C11*A_shuttle*CD_shuttle*G11^2/2”.
•
Insert the value for the initial work done before the stat of the program (i.e., “0”).
— 16 —
4. Complete the “Next” (top green) row of the spreadsheet: Enter the “Next” orbit (Orbit #1)
information from the bottom half of your worksheet flowchart. Again, be sure to enter a formula
for the satellite's total energy, altitude, and speed, as well as the drag force acting on the satellite
and the work done by drag. Start with cell [D12], then [F12], followed by [G12] and [H12]. This
time you will not get any detailed instructions. The formula you will be using are all in the
flowchart. Type them into the spread sheet. Click again on each of those cells, and pull down that
column to the 1000th orbit.
5. Search for the row in the spread sheet where a negative altitude occurs. Guess what happened!
6. Find the value for each of these quantities at the mission duration time (~240 hours or ~10 days).
These are your data, calculated using the standard temperature MSIS model. Record these values.
•
•
•
•
Velocity
Satellite Drag
Satellite Energy
Ambient Density
Initial values
_____________
_____________
_____________
_____________
after 10 days
_____________
_____________
_____________
_____________
before crashing
_____________
_____________
_____________
_____________
7. Go to the sheets named “Shuttle Vel vs. Time,” “Shuttle Drag vs. Time,” and “Shuttle Total (Mech) E
vs. Time” and observe the graphs. Get printouts. Describe in words what happens to the velocity,
ambient density, and the Satellite’s drag and energy. How do these values depend on each other?
8. Why does the satellite’s elevation drop more and more rapidly, why not linearly?
Fig. 8: This plot shows the decay of the Starshine
2 orbit. The height, averaged over one orbit, is
plotted against the date, and the gradual
decrease is caused by atmospheric drag. As can
be seen from the plot, the rate of descent is not
constant and this variation is caused by changes
in the density of the tenuous outer atmosphere
due mainly to solar activity.
Image taken from http://science.nasa.gov/headlines/y2002/25apr_starshine2.htm.
9. Compare your plots to real data (above) and comment on whether your model is realistic.
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PART V
Space Weather Effects
Space weather effects in the upper atmosphere come from many sources, however we know that
variability of the Sun is a leading cause of upper atmospheric variability. You may have heard of an
11- year solar cycle during which the number of sunspots rises and falls. Associated with the number of
sunspots is an increase the output of solar radiation at short wave lengths (X-rays and Ultra-Violet
rays). These rays are really high energy photons that can interact with and hear the earth’s upper
atmosphere. Indeed the earth’s upper atmosphere is much hotter, by several hundred degrees, during
and just after the maximum in the number of sunspots. As you already know, a hot atmosphere is an
expanded atmosphere. An expanded atmosphere has more mass at higher levels and this can
interfere with satellite orbits. The heating of the upper atmosphere due to absorption of high energy
photons is usually a gradual process that occurs over many months. Even if there is a noticeable “flare”
of radiative energy from the Sun the atmosphere will only absorb a small amount of the energy on the
sunlit side of the earth.
Recent investigations into other aspects of solar interactions with the earth’s atmosphere have revealed
that the accumulation of energy from solar photons can be augmented by a process in which mass
actually escapes from the Sun’s atmosphere and collides with the Earth’s protective magnetic field.
These solar coronal mass ejections (CMEs) create large currents and associated magnetic fields in our
upper atmosphere, and much like running a current through a curling iron, the atmosphere heats up.
Such CME-earth collisions can cause very rapid heating over short intervals. Of course there are times
when a sudden addition solar radiative input is followed by a CME event within a few hours or days.
Two such events can cause rapid expansion of the earth’s atmosphere and real trouble in tracking the
location of satellites. The diagram below shows an example of such an event that occurred in 1989
when over 1500 objects in space become “lost” to satellite tracking. It took many weeks to identify
and find all of the satellites. The subsequent figure shows the rate at which energy comes to the upper
atmosphere from several sources. The spikes in total power are from CME’s.
Fig. 9: Taken from the Air University Space Primer, Chapter 6
http://space.au.af.mil/primer/space_environment.pdf
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Let’s assume a flare occurs on the Sun and within a few minutes the energy reaches the earth. About
two days later a CME collides with the earth and also deposits energy. We can envision this with the
following diagram. There is a short spike of energy from the flare and then a longer lasting input from
the CME. Below is a diagram that represents how the satellite might respond to rapidly changing
heating rates.
1 2 3
1
2
3
Shuttle'sAltitudevs. Time
SolarActivityLevel vs. Time
400.0
4
350.0
300.0
Solar Activity Level (0, 1, 2, or 3)
3
Altitude (km)
250.0
200.0
2
150.0
100.0
1
50.0
0.0
0.00
0
0
100
200
300
400
500
600
Time(hours)
700
800
900
1000
50.00
100.00
1100
150.00
200.00
250.00
Time(hours)
Fig 10a
Fig 10b
Below is a diagram that shows the real data of when flare and CMEs actually happened.
Daily Average Power Values for Solar Cycles 21-23
3500
Jul 14
1982
Mar 13
1989
Oct 21
1989
Jun 6 Jul 13 May 10
1991 1991 1992
Jul 14
2000
Mar 31
2001
Nov 6 & 24
2001
3000
Power (GW)
2500
2000
1500
Solar
Power
Total
Power
1000
Joule
Power
500
Particle
Power
0
1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Fig 11
Year
Taken from Knipp, Tobiska, Emery at
http://lasp.colorado.edu/sorce/news/2004ScienceMeeting/SORCE%20WORKSHOP%202004/posters/knipp_3.pdf
1. What would you expect would happen to the density of the atmosphere through which the satellite
is flying? Explain. What effect might this have on the satellite’s orbit? Explain.
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Go to the spreadsheet page entitled “Atmosphere.” In the cell for "Percentage of Temperature
increase for MSIS Model (X%):" [E5] enter 10 for a 10% increase in the temperature.
2. Go to the page entitled “Altitude vs. Mass Density” and examine the curves on the graph. How are
they different from the previous graphs? Describe. Draw the new curves into the previous graphs.
Comment whether the graphs are consistent with the answer you provided to question 1.
3. Go back to the page “Shuttle Orbit Decay.” Search for the row where a negative altitude occurs.
•
•
Orbits
Hours passed
_____________
_____________
4. Go to the “Shuttle Alt vs. Time,” “Shuttle Vel vs. Time,” “Shuttle Drag vs. Time,” and “Shuttle Total
(Mech) E vs. Time” charts (or the spreadsheet data) and find the value for each of these quantities
at a time of ~100 hours. These are your data using the increased-temperature MSIS model.
•
•
•
Velocity
Satellite Drag
Satellite Energy
_____________
_____________
_____________
5. How much energy would you need to supply to the Satellite to bring it to its pre-flare and CME
state?
6. Since you desire to stay in orbit longer you will need to do something to counteract the “flare
activity”. Suggest “how” you might boost the energy of the satellite, so that you can stay in orbit.
7. When would you boost the energy of your satellite, early or late in your 10 day mission? Explain.
8. If the solar flare and CME had increased the temperature by 5%, would you have had problems?
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PART VI
“The Big Picture” Questions to think about
1. What are the assumptions which limit the utility of the (simple) Law of Atmospheres? How did we
improve on this by using the MSIS model?
2. What happens to the atmosphere as it heats up? Why is this relevant to the satellite orbit?
3. What parameters affect the duration of a satellite mission? List and explain all.
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4. What happens to the energy (comment on each: the total mechanical, kinetic, and potential energy)
of a satellite as it experiences atmospheric drag?
5. Why was an iterative technique required in this lab to calculate satellite altitude?
6. What process did you use to model the orbital decay? (Write a summary in a few sentences that
outlines the steps.)
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