STK 6.0
Session 3: Newton’s Second Law
Revision 1.0 Aug 9, 2005
Preparations for the Instructor
This session contains three main tasks.
Given a pair of orbiting satellites, students determine the amount of thrust generated by a rocket engine
prepared by the instructor.
Given the Satellite Properties window, students generate one gee (9.8 m/s2) of thrust.
Given a target range of 10. km, students compute and execute maneuvers to reach and stay close to the
target range in the least time. The maximum acceleration is limited to one gee.
Task 1: Measure the force (thrust) of the provided rocket engine.
A real rocket engine expends a significant amount of mass as it generates thrust. Beginning physics
students have just learned Newton’s Second Law: F =ma. You will have to edit STK to create a custom
rocket engine that generates thrust without expending mass, allowing students to apply F = ma without
having to learn the rocket equation.
Launch STK, create a new scenario, rename it 03Newton, and save it to a new folder named 03Newton.
Under View, select Astrogator Browser. Click on the directory folder named Engine Models.
Highlight the entry named Constant Thrust and Isp (which is specific impulse – the number of seconds one
pound of rocket fuel can generate one pound of thrust). Click on the button named Duplicate.
When the Field Editor comes up, rename the engine as Newton engine #1. Under User Comment, type
“unknown thrust and zero mass loss.” When you close the Field Editor, you will see your new engine
displayed in green in the Astrogator Component Browser.
Double click on your (green) Newton engine #1 to edit its values. Double click on Isp to change its value.
The allowed upper limit is claimed to be 1.79 x 10308. This is a slight lie. Enter 1.7e307 and it will be
accepted. This large value effectively reduces the mass flow rate for the engine to zero.
Double click on the Thrust parameter. The default value is 500. N. Change it to some new value of your
choosing, such as 800. N (or 815 N). Be aware the value you enter can be found by the students if they
follow in your footsteps and launch the Astrogator browser. During the classroom session monitor the
students to ensure they do not look up the thrust value – they are to calculate it, not look it up.
Hit Okay to close out the Astrogator browser window and save the scenario. You should enter a different
thrust value on each computer your students use. Keep a table of your engines such as the one shown.
Computer ID
Engine #
Thrust (N)
_________
________
_________
_________
________
_________
_________
________
_________
_________
________
_________
End of Preparations for the Instructor
STK 6.0
Session 3: Newton’s Second Law
Revision 1.0 Aug 9, 2005
This session contains three main tasks.
Given a pair of orbiting satellites, determine the amount of thrust generated by a specified rocket engine.
Given the Satellite Properties window, generate one gee (9.80 m/s2) of thrust.
Given a target range of 10 km, compute and execute maneuvers to reach and stay close to the target in the
least time. The maximum acceleration is limited to one gee.
Task 1: Measure the force (thrust) of the provided rocket engine.
Launch STK6.0. Open the scenario named 03Newton. You should save your work often as you build
every scenario.
Insert a new satellite (either by selecting Satellite from the Insert New … menu, or by clicking on the Insert
Object icon and selecting Satellite from the pop up menu). Cancel the orbit wizard. Rename the satellite as
one of your names. (I shall arbitrarily refer to this first satellite as Alice.)
Open Alice’s properties browser window (either by quickly double clicking on the satellite’s name in the
object browser window or by right clicking on it and selecting Properties Browser from the pop up menu).
Under the Basic Properties tab change the propagator to Astrogator. An Astrogator window comes up,
with the initial state tab highlighted. Change the Element Type to Keplerian. Change the Semi-major Axis
to 1,000,000 km. Change the Eccentricity to zero (0.00). Change the Inclination to 0. Click on the
Satellite Properties … box to bring up a Spacecraft Physical Values window. Confirm the Spacecraft
Configuration Dry Mass is 500 kg, and the Fuel Tank Configuration Fuel Mass is also 500 kg. Note the
total spacecraft mass is the sum of its dry mass plus its fuel mass. Hit OK to close the Spacecraft Physical
Values window. Click on the Propagate tab. (It is probably green.) Change the Propagator listed toward
the right (not to be confused with the Astrogator Propagator listed toward the top) from Earth Full RKF to
Earth Point Mass. (This directs STK to ignore several real forces –such as drag – and treat the Earth as a
simple point mass.) Hit Apply and then OK to close the Astrogator window. Animate the scenario to
observe you have created a satellite orbiting farther from Earth than the Moon.
Click once in the Object Browser window. Click on the icon for Alice, copy it, and paste it. This creates
an identical second satellite. Rename the second satellite as Newton. Double click on Newton to open its
Basic Properties browser. Right click on the Initial State icon and select Insert After from the pop up
menu. From the Segment Selection window, select Finite Maneuver. A Finite Maneuver is inserted after
the Initial State icon, and the Finite Maneuver window is displayed. Click on the Propagator Options …
button, and change the Maneuver: Finite Trajectory Propagation Propagator (probably from Earth Full
RFK) to Earth Point Mass. Set the Trip duration to 600. seconds. Close out the Segment Properties
window. With the Finite Maneuver segment still highlighted, notice underneath the Engine Model box is
displays, “Constant thrust and Isp” with a button to the right labeled, “…” Click on the button, bringing up
the Engine Model selection window. Select Newton engine # <___> (as designated by your instructor).
Hit Okay to close the dialog windows. You have now created two satellites orbiting far from Earth.
Newton is initially identical to Alice, but immediately fires its rocket engine to accelerate ahead of Alice.
Your task is to measure the acceleration rate of Newton relative to Alice, and based on Newton’s known
mass, determine the force applied by its unknown rocket engine. The next paragraph explains the
measurement procedure.
STK 6.0
03Newton
Revision 1.0
9 Aug 2005
page 2
In the Object Browser window, click once on the icon for Alice. Now select the Access Tool (by selecting
Access from the Satellite pull down menu, or by right clicking on Alice and selecting Satellite Tools
Access, or by clicking on the Access Tool icon in the toolbar). From the Associated Objects list that comes
up, select Newton. Under Reports, select AER (short for Azimuth, Elevation, and Range). In the report
that comes up, note the Range from Alice to Newton after one minute has elapsed. Calculate the
acceleration of Newton from Alice. Based on Newton’s wet mass (dry mass plus fuel mass), calculate the
force of the rocket engine firing on Newton. Record your results. Save your scenario.
Task 2: Adjust Newton’s mass to generate 9.80 m/s2 of acceleration.
In the Object Browser window, double click on Newton to bring up its Basic Properties window. Select the
Initial State icon, then select Satellite Properties. (You’ve been here before.) Based on your measured
thrust of the rocket engine on Newton, calculate the mass of Newton necessary to cause Newton to
accelerate at 9.80 m/s2 when its engine is fired. Change the dry plus fuel mass of Newton according to
your calculations. Keep at least 1 kg of mass as fuel or your engine won’t fire. Apply your mass
adjustments to Newton, rerun the animation, and measure the resulting acceleration of Newton away from
Alice. Report the measured results.
Task 3: Stationing Newton 10. km ahead of Alice.
You are to maneuver Newton to a range of 10.0 km from Alice using your 9.80 m/s 2 thrust engine, then
hold Newton there (to within 10. m) for at least 10. minutes.
Calculate the time needed to accelerate Newton, and the time needed to apply a negative acceleration to
Newton using the mass for Newton you had entered during task 2. Open up Newton’s Basic Properties
window, select the Finite Maneuver tab, and under Selected Condition change the value to the number of
seconds Newton is to undergo a positive acceleration relative to Alice. Right click on Finite Maneuver, and
bring up its properties. Change the segment color to green and rename Finite Maneuver as Positive
Acceleration. Close the Segment Properties window. Right click on Positive Acceleration, and select
Insert After. Select Finite Maneuver. Right click to bring up its Segment Properties window. Change the
name to Negative Acceleration, change its color to red, and close that window. Change the Maneuver
Direction Attitude Control to Anti-Velocity Vector. Change the Selected Condition to the number of
seconds you calculated for this maneuver – braking Newton to rest at a final range of 10.0 km. Change the
Propagator Options Propagator to Earth Point Mass. Change the Engine Model to the Newton engine.
To quickly follow the effects of your changes, bring up the Satellite Access window (with Alice
highlighted in the Object Browser window) and choose to open a Dynamic Display. From the list of
Styles, select AER. This opens up a window that displays the range from Alice to Newton.
End of session 3.
STK 6.0 03Newton Objectives Checklist
Date: ____________
Name: ____________________
Name: ____________________
Task 1: Measure and calculate the magnitude of the force of the rocket engine on Newton
Record: Newton’s mass: ______ kg Range :_______ km Time: _____s a: _____ m/s2 F: _____ N
Task 2: Revise Newton’s mass to generate 9.80 m/ s2 of acceleration.
Record: Newton’s mass: ______ kg Range :_______ km Time: _____s a: _____ m/s2 F: _____ N
Task 3: Maneuver Newton to 10.0 km and maintain position there to within 100. m for 10. minutes.
Time for positive acceleration: ___________
Time for negative acceleration: __________
Arrival time for Newton to target destination: _____________________
Maximum range from Newton to Alice over the 10 minute interval starting at the arrival time: __________
Minimum range from Newton to Alice over the 10 minute interval starting at the arrival time: __________
STK 6.0 03Newton Instructor’s Objectives Checklist
Date: ____________________
Task 1: Measure F = _____ N for the designated rocket engine
Task 2: Adjust Newton’s mass to ________ kg total mass
Task 3: positive accel time ________ s, negative accel time is _________ s
Group #
F expected
F actual
m expected m actual
t expected
t actual
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