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Laboratory Mission 4: Orbital Rendezvous
Mission Objective
- Reinforce the Concept of Orbital Rendezvous
- Visualize Rendezvous Scenarios
Resources/Requirements
For this laboratory mission, you must have;
Successfully installed STK and borrowed a license for a period covering the class in which this
mission is to be executed (unless working in the computer lab)
Read Chapters 6.1 & 6.3 of Understanding Space
Mission Planning
REINFORCE THE CONCEPT OF ORBITAL RENDEZVOUS
SATELLITE INSPECTION: The Air Force Research Laboratory (AFRL) is building and
demonstrating a new class of low-cost satellites – referred to as “microsatellites” – weighing less
than 100 kilograms. These new satellites are being flown under the Experimental Spacecraft
System (XSS) Microsatellite Demonstration Project. In conjunction with the Air Force Space
Command (AFSPC), Air Force Space and Missiles Systems Center (SMC), the Naval Research
Laboratory (NRL), and industry, missions are underway to actively evaluate future applications of
microsatellite technologies to include: inspection; rendezvous and docking; repositioning; and
techniques for close-in proximity maneuvering around on-orbit assets.
The Air Force is conducting the Experimental Satellite System (XSS) series to demonstrate
increasing levels of microsatellite technology maturity. The XSS-10, shown in Figure 1, was the
first microsatellite in the series and was launched in 2003. It demonstrated semi-autonomous
operations and visual inspection in close proximity of an object in space—in this case a Delta II
upper stage shown in Figure 2. The success of the XSS-10 flight demonstration was the first step
in applying microsatellite technology to military space missions and paved the way for more
ambitious experiments on XSS-11 and future programs.
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Figure 1: eXperimental Spacecraft System -10 microsatellite. The XSS-10 spacecraft had a
total mass of 28 kg
Figure 2: XSS-10 view of Delta II rocket: An Air Force Research Laboratory XSS-10 microsatellite uses its on-board camera system to view the second stage of the Boeing Delta II
rocket during mission operations Jan. 30, 2003. (Photo courtesy of Boeing.)
GPS employs 24 spacecraft in circular (e=0) orbits with a semimajor axis of 26,562 km that are
inclined at 55 degrees. These spacecraft are placed in 6 orbital planes with four operational satellites
in each plane as shown in Figure 3. For XSS-12, the Air Force wants to visually inspect the four GPS
satellites in the orbital plane with Ω=0 degrees. The GPS satellites in this orbital plane are designated
GPS 11 (SSC #19802), GPS 12 (SSC #20061), GPS 13 (SSC #20185), and GPS 14 (SSC #20302).
After launch from a Delta II, the XSS-12 will be placed in a parking orbit in low Earth orbit (LEO). The
COEs of the XSS-12 parking orbit will be: a=6628 km, e=0, i=55 degrees, Ω=0 degrees, and an
argument of latitude u=20 degrees. Note that the GPS satellites and the XSS-12 microsatellite are in
the same orbital plane (co-planar).
Figure 3: GPS Block II is a production satellite first launched in 1989. Block II consists of
24 satellites in 6 orbital planes. The last one was launched in 1994.
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Using the Delta II upper stage, the XSS-12 will rendezvous with the GPS 13 satellite with an argument
of latitude, u=180 degrees. The Epoch used in this simulation will be 1 JUN 2007 12:00:00.00 UTCG
which is the projected launch timeframe for XSS-12. The epoch is defined as an instant in time that is
used as a point of reference for our orbital models. As you might imagine, the epoch used is
particularly important for rendezvous maneuvers because timing is extremely important. The COEs
for the XSS-12 and GPS 13 are located in Table 1.
Table 1: COEs for the XSS-12 and GPS 13 satellites
Orbital Element
a
e
i
Ω
ω
u
1.
XSS-12 COEs
6628 km
0.0
55.0°
0°
Undefined
20°
GPS 13 COEs
26562 km
0.0
55.0°
0°
Undefined
180°
COPLANAR RENDEZVOUS: Calculate the parameters to transfer the XSS-12 space
vehicle into the target GPS orbit.
a) Calculate the initial phase angle for the co-planar rendezvous. For the case of co-planar
circular orbits, the initial phase angle can be found by: i =(uTarget – uInterceptor). The phase angle
is sign (±) sensitive.
i =___________________________________ (rad)
Figure 4: Rendezvous figure 6-13 on pg
212 of Understanding Space
b) Calculate the angular velocities of the target (GPS) and interceptor (XSS-12) spacecraft.
ωtarget= _____________________(rad/sec) ωinterceptor= _____________________(rad/sec)
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c) Calculate the semi-major axis and time of flight for the transfer orbit.
atransfer= ______________________(km)
TOF= _______________________(sec)
d) Calculate the lead angle and final phase angle for the rendezvous.
αlead= ______________________(rad)
 f =________________________ (rad)
e) Calculate the shortest two wait times for the rendezvous.
Wait time1= __________________(sec) Wait time2= __________________(sec)
f)
Calculate the Delta V’s required for the Hohmann transfer orbit for the rendezvous.
ΔV1= ________________________(km/sec) ΔV2= ____________________(km/sec)
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CO-ORBITAL RENDEZVOUS: Once in the GPS plane, the XSS-12 must move from one
GPS satellite to another. Assuming that the GPS satellites are equally spaced throughout the
orbital plane with u=0 degrees, calculate the parameters to move from the GPS 13 satellite to the
GPS 11 satellite. The GPS 11 satellite has an argument of latitude that is 180° from the argument
of latitude of GPS 13.
a) Calculate the angle through which the target travels to reach the rendezvous location and the
time it will take to cover this angle.
travel =______________________________ (rad)
TOF=______________________________(sec)
Figure 5: Rendezvous figure 6-14 on
pg 213 of Understanding Space
b) Calculate the required size of the phasing orbit to move from one satellite to an adjacent
satellite in the same orbital plane. Although either a smaller or a larger phasing orbit
(compared to the original orbit) can be used, use the smaller orbit.
aphasing= ____________________________(km)
c) Calculate the required ΔV for the phasing orbit.
ΔV3= ________________________(km/sec) ΔV4= ____________________(km/sec)
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NOTE: The orbital speed of the XSS-12 microsatellite is faster than the speed of the transfer
orbit. Therefore, XSS-12 will have to slow down to enter the transfer orbit. This implies a thruster burn
in the direction opposite to the spacecraft’s motion, sometimes called a retro-fire or retro-burn.
Mission Execution
Now that you have calculated the wait time and Delta Vs required to maneuver the XSS-12 to the
NAVSTAR GPS satellite orbit, you must verify that your calculations are correct using STK.
CREATE A CO-PLANAR RENDEZVOUS SCENARIO
In this section, you’ll create a Scenario with four GPS Satellites in a single orbital plane at mid-Earth
Orbit (MEO) and an XSS-12 in a LEO parking orbit, co-planar with the target GPS spacecraft. Using
the results of your calculations, you will simulate an XSS-12 rendezvous with a GPS satellite.
1.
Create a new Scenario
a) Create a new Scenario and rename it “Rendezvous”
b) Open the Properties Browser for the Scenario and select the Basic/Time Period page
(Figure 6).
 change the Period Start and Epoch to 1 JUN 2007 12:00:00.00 UTCG.
 change the Period Stop to 4 JUN 2007 12:00:00.00 UTCG
Figure 6: Scenario Properties Page
c) Click OK.
2.
Add four GPS Satellites to the Scenario in a single plane
a) Add a Satellite to the Scenario but cancel the Orbit Wizard
b) Change the Satellite name to “GPS”
c) Open the Properties Browser for the Satellite. On the Basic/Orbit page, set the GPS COEs
to those in Table 2 and then click OK.
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Table 2: COEs for the GPS11 satellite
Orbital Element
a
e
i
Ω
ω
u
COEs
26562 km
0.0
55.0°
0°
Undefined (see note)
0°
NOTE: For a circular orbit (e=0), the argument of perigee and true anomaly are not defined. For
this case, STK will use the value of true anomaly as an argument of latitude. The argument of latitude
is defined as the angle to the spacecraft’s position measured from the ascending node. Leave
argument of perigee equal to zero, since STK will ignore this value.
d) Highlight the GPS icon in the Object Browser and copy the Satellite using the
the tool bar.
icon in
e) Paste three Satellites in the Object Browser using the paste (
) icon
 These will become the GPS constellation in the single orbital plane of interest.
f) Rename the Satellites “GPS11”, “GPS12”, “GPS13”, and “GPS14”
g) Enter the appropriate argument of latitude (Table 3) into the true anomaly box in each
satellite’s Basic/Orbit Properties Page.
Table 3: Argument of Latitude for GPS Constellation
Satellite
GPS12
GPS13
GPS14
Argument of Latitude (u)
90°
180°
270°
h) After changing the argument of latitude for each Satellite, click OK.
3.
Turn on reference axis and fundamental plane
a) Select the 3-D window and click on the Properties icon ( ) in the main toolbar.
b) Open the 3-D window’s Vector Property Page.
c) Turn on the Earth Inertial Axis and change the color to red (Figure 7)
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Figure 7: Add the J2000 Axis
d) Add the Earth Equator Plane by clicking Add and selecting the last item, “Equator.” Click the
blue arrow in the middle of the menu page (to move the Earth Equator Plane to the Name
List in the right menu), and click OK. (See Figure 8).
Click on the blue arrow to
move the Equator Plane to
the Name List
Figure 8: Add the Earth's Equatorial Plane
e) Highlight the Earth Equator Plane in the Name List.
f) Change the color to yellow.
g) Check the Transparent Plane box, change the Size to 5.00, and set the Transparency to 80
(see Figure 9).
h) Click OK.
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Figure 9: Set up the Fundamental Plane
4.
Open the 3-D Graphics Window, Reset and Start the current Scenario.
Are all of the GPS satellites in the same orbit?
Do they all have the same semi-major axis?
Are they at the same inclination?
Do they all have the same Right Ascension of the Ascending Node?
At the beginning of the simulation, which satellite is at the ascending node? (You may have
to zoom in on the appropriate satellite)
Which is at the descending node?
Does this make sense compared to the argument of latitude values you used for each of the
satellites?
What is the separation angle between each of the satellites?
What is the period of the GPS satellites in this orbital plane?
5.
Open the 2-D Graphics Window and watch the Satellites’ ground tracks
Estimate one of the Satellite’s orbital period based on its ground track. (Use the cursor to
determine the longitude west of the first ascending node and the longitude east of the
second ascending node.)
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6.
Create the XSS-12 Satellite in its parking orbit in LEO. In Mission 3 you were introduced to
the Astrogator engine. For this mission, you will get to work directly with Astrogator to perform
the orbital rendezvous.
a) Add a Satellite to the Scenario but cancel the Orbit Wizard.
b) Change the name of the Satellite to “XSS_12”.
c) Open the XSS_12’s Basic/Orbit Property Page.
 Change the Propagator to Astrogator.
 Change the Element Type to Keplarian
 Input the COEs given in Table 4 for the XSS-12 parking orbit.
Table 4: COEs for the XSS-12’s Parking Orbit.
Orbital Element
a
e
i
Ω
ω
u
COEs
6628 km
0.0
55.0°
0°
Undefined
20°
d) Click Apply.
7.
Build the rendezvous sequence for XSS-12 to the GPS13 satellite using Astrogator.
a) The XSS_12 Basic/Orbit Properties Page should still be open.
b) Click on the Propagate icon in the menu (Figure 10).
c) Set the value in Trip to the first wait time you calculated in step 1.e of Mission Planning.
 This is how long the XSS_12 satellite will remain in its parking orbit before initiating a Delta
V burn that will put it into the Hohmann transfer orbit to rendezvous with the GPS13
satellite.
1. Select Propagate
2. Set the Trip time to
the first value calculated
in 1.e of Mission
Planning
Figure 10: Set the Initial Propagation Time
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d) Click Apply.
e) Add a new segment by clicking on the Insert Segment button above the menu (See Figure
11). In the Segment Selection window, select Impulsive Maneuver and click OK.
NOTE: When adding a new segment to the list, make sure the last propagator segment is
highlighted so the new segment will be added below the prior segment.
2. Select Impulsive
Maneuver
1. Select Insert
Segment
Figure 11: Add a Delta V Burn
f)
g)
h)
i)
j)
Back on the Basic/Orbit page, make sure the Attitude Control block reads “Along Velocity
Vector”.
Set the Magnitude field to the ΔV1 value that you calculated in step 1.f of Mission Planning.
 This will give the XSS_12 satellite a propulsive boost into the Hohmann transfer towards
the GPS orbital plane.
Add a new segment to propagate the orbit through the Hohmann Transfer orbit by clicking on
the Insert Segment button then select Propagate and click OK.
In the Trip block, insert the Time of Flight time you calculated for the transfer orbit in Section
1.c of the Mission Planning.
Right click on this Propagate Segment and scroll down to Properties at the bottom of the
pop-up menu. Change the Color box to Red and click OK. This will change the orbit track
color to red (see Figure 12).
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Figure 12: Change the Orbit Track Color
k) Add another Impulsive Maneuver segment as you did in step 7.e above.
l) Again, make sure the Attitude Control block reads “Along Velocity Vector”.
m) Set the Magnitude field to the ΔV2 value that you calculated in step 1.f of Mission Planning.
 This segment will provide the propulsive boost the XSS_12 satellite out of the Hohmann
elliptical transfer orbit and place it in the GPS circular orbit.
n) Add a final Propagate segment as you did in step 5.h above.
o) In the Trip block, insert 12 hr. Click Apply.
 This segment will propagate the XSS_12 satellite through the GPS orbit.
8.
Run the entire rendezvous scenario.
What is the initial phase angle between the XSS_12 and GPS13 satellites at the beginning
of the scenario?
Do the XSS_12 and GPS13 satellites rendezvous?
Assuming the first possible rendezvous wait time has passed. How long will it take
(measured from the epoch) for another rendezvous opportunity (the next wait time was
calculated in Section 1.e of the Mission Planning)?
9.
Put the second wait time into the Trip box of the first Propagate segment in the XSS_12 and
click Apply.
10.
Reset and run the scenario.
CREATE A CO-ORBITAL RENDEZVOUS SCENARIO
Now that the XSS-12 satellite is in the GPS orbital plane and has rendezvoused with GPS13, we
would like to visually inspect the GPS11 satellite. This requires a co-orbital rendezvous maneuver.
11.
Add Astrogator segments to the XSS_12 satellite to make the orbital maneuver
a) In Astrogator, add a new Impulsive Maneuver segment
b) Make sure the Attitude Control block reads “Anti Velocity Vector.”
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c) Set the Magnitude field to the value of the ΔV3 value that you calculated in step 2.c of Mission
Planning.
 This segment will provide the propulsive burn (a burn opposite the velocity vector slows the
satellite down) to take the XSS_12 satellite out of the GPS circular orbit and place it into the
phasing orbit.
d) Add a new Propagate segment. Change its color to yellow as you did in step 7.j above.
e) In the Trip block, insert the Time of Flight value you calculated for the transfer orbit in step 2.a
of Mission Planning.
f) Add an Impulsive Maneuver.
g) Make sure the Attitude Control block reads “Along Velocity Vector.”
h) Set the Magnitude field to the ΔV4 value that you calculated in step 2.c of Mission Planning.
 This segment will provide the propulsive burn to take the XSS_12 satellite out of the
phasing orbit and place it back into the GPS circular orbit.
i) Add a final Propagate segment.
j) In the Trip block, insert 12 hr.
k) The final segment menu should look like Figure 123.
Figure 123: Final MCS Menu
12.
Turn on the GPS 11 satellite’s COEs in the 3-D Graphics Window
a) Double click on the GPS_11 icon in the Object Browser to bring up its Properties.
b) On the 3D Graphics / Data Display page, check the Show box for the Classical Orbital
Elements. This will show the COEs of the GPS_11 satellite in the 3-D Graphics window.
c) Click OK.
13.
Reset and Run the entire rendezvous scenario.
At what argument of latitude do the XSS_12 and GPS11 satellites rendezvous? HINT: Use
the GPS11’s Argument of Latitude (shown as the True Anamoly) displayed in the 3-D
Graphics Window.
Does the timing of the first propulsive maneuver for the co-orbital transfer matter? Explain.
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