PHYSICS
LABORATORY WORKSHEET
NAME ________KEY_______
SECTION___________________
Orbital Drag Laboratory Worksheet
Flowchart of Orbit Decay Model:
Altitude
Initial
values
Energy
at this
altitude
GMm
2r
 2.725x1012 J
h  350,000m
(from Atmosphere
spreadsheet)
= 4.25x10-11 kg/m3
Speed
E
v
GM

r
Atmospheric
density
at this
altitude
Drag Force
1
AC D v 2
2
 0.91N
GM
RE  h
FD 
 7697.8m/s
Work done
by drag force
in this orbit
WD   FD * ( 2r )
  FD * ( 2 [ RE  h])
 3.85x10 7 J
Altitude
E
Next
values
Energy
at the next
orbit
GMm
2r
 GMm
 r  RE  h  
2E
GMm
h
 RE
2E
 349905 m
Ethis  Elast  Wlast
Atmospheric
density
at this
altitude
(from Atmosphere
spreadsheet)
= 4.32x10-11 kg/m3
Speed
 2.725x1012 J
v
GM

r
GM
RE  h
 7697.8m/s
Drag Force
1
AC D v 2
2
 0.93 N
FD 
Work done
by drag force
in this orbit
WD   FD * (2r )
  FD * (2 [ RE  h])
 3.92 x10 7 J
PAGE 1 OF 2
PHYSICS 110
LABORATORY WORKSHEET
ANALYSIS
Values at ~101 hours mission time:
+0% Temperature
Altitude
343.3 km
Velocity
7701.6 m/s
Drag
1.04 N
Total Energy
-2.728x1012 J
+10% Temperature
62.9 km
7867.7 m/s
11,472,162 N (!)
-2.847x1012 J
“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?
 g is assumed to be constant (it actually varies with height)
 T is assumed to be constant (it actually varies with height)
 m is assumed to be constant (it actually varies with height)
The MSIS model allows each of these to vary with height, as they should. This provides much
more accurate values for the mass density as a function of altitude (as the graphs show.)
2. What happens to the atmosphere as it heats up?
It expands. At a given altitude, there will be a greater amount of atmospheric ‘stuff’ when there are higher
temperatures. (This means the shuttle runs into more atmosphere when the temperature is higher, so loses
energy more rapidly under those conditions.)
3. What parameters affect the duration of a shuttle mission?
Atmospheric temperature (which governs the amount of atmospheric ‘stuff’ at a given altitude). Also, the
initial altitude, the mass of the shuttle, and the surface area of the shuttle.
4. What happens to the energy (total mechanical, kinetic, and potential) of a satellite
as it experiences atmospheric drag?
Drag causes the satellite to LOSE energy. This means its total energy becomes more negative. Because it is
lower, it has a lower potential energy (more negative). Because it is closer to the Earth, its speed is greater,
so its kinetic energy is greater. (Recall E = U/2 = -K.)
5. Why was an iterative technique required in this lab to calculate shuttle altitude?
For each orbit, we calculated the amount of energy the shuttle would lose (because of drag) and from that,
calculated the total energy of the shuttle for the next orbit. We had to do this one orbit at a time because the
amount of atmospheric ‘stuff’ and speed of the shuttle change with each orbit.
6. What process did you use to model the orbital decay? (Write a summary in a few
sentences that outlines the steps.)
The key was finding the orbital energy for each orbit. To obtain each new orbit’s energy, we took the energy at the start
of the previous orbit and subtracted the energy lost during that orbit. The amount of energy the shuttle lost (because of
drag) was the work done by the drag force, which was just (force)(distance around one orbit). The drag force at a given
altitude depended on the atmospheric mass density (which we looked up from the Atmosphere spreadsheet) and the
speed of the shuttle at that orbit (which we calculated) and other constants. Each time we found a new orbit’s energy,
we found the corresponding altitude for that orbit, and the process continued orbit by orbit.
PAGE 2 OF 2