Upload
hongraekim
View
223
Download
0
Embed Size (px)
Citation preview
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 1/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Low Energy Interplanetary Transfers
From Earth To Mars
Hong Rae Kim Aerospace Engineering
Korea Aviation Untiversity
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 2/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
To find low energy interplanetary transfer orbits from Earth
to Mars
To find Moon gravity assisted trajectory method
To find Earth gravity assisted trajectory method
To find L2 halo orbit insertion method,
Perform the L2 station-keeping operations, and
To determine halo orbit hopping method between SEM L2 halo
orbits and Mars
To design all the trajectories using STK/Astrogator
Aims and Scope
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 3/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Gravity Assisted Trajectory Method
Most famous method for sending spacecraft to distant
planets. E.g., Cassini mission to Saturn (Oct ’97- Jul ’04) Advantages: higher speeds (short transfer times).
Disadvantages: cost, constraint imposed by the fly-by
body, limitations due to impact parameter.
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 4/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Gravity Assisted Trajectory Method
B-Plane Method
The incoming and outgoing asymptotes, and , and the
focus are contained in the
trajectory plane, which is
perpendicular to the b-plane
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 5/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Gravity Assisted Trajectory Method
B-Plane Method
The b-plane is
defined to contain the focus of an idealized
two-body trajectory
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 6/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Gravity Assisted Trajectory Method
B-Plane Method
vvr
r r
ve
vr
vr n
1
||ˆ
2
)1(||
2
22
2
12
2
eab
v
r
a
r
v
a
Energy Equation
)ˆˆ(sinˆcosˆ
)1
(cos 1
eneS
e
T S R
N S
N S T
ˆˆˆ
|ˆˆ|
ˆˆ
ˆ
)ˆˆ(
ˆˆˆ
nS b B
nS B
The distance from the focus to the intersection of the incoming asymptote
and the b-plane can be shown to be equal to the semiminor axisb
The direction of the b-vector
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 7/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Gravity Assisted Trajectory Method
B-Plane Method Example “New Horizon Project”
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 8/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Calculation Results Swingby Mission
Lunar SwingbyB·R 2500km
B·T 12000km
Earth SwingbyInclination 26deg
R_Magnitutde 6700km
C3 Energy 8.8
km^2/s^2
Outgoing Declination -9 deg
Outgoing Right-ascension 353 Deg
Referance DATA : Astrogatorguilds ‘GTO Mission’
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 9/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Targeting Methods Using STK/Astrogator
The whole mission is split in steps and phases. Steps: Swingby Moon, Swingby Earth.
Phases: Impulsive maneuvers, propagation, stopping conditions.
Targeting method at every step uses the DifferentialCorrector by defining a 3-D target.
Incoming Moon and Outcoming Moon, go back Earth Incoming Earth and Outcoming Earth, go to Mars
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 10/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Targeting Methods using STK/Astrogator
StartPropagating to Moon
•Creating Calculation objects
Setting up the Targeter
Running the Targeter
Performing the Engine burn I
•Getting to Moon
•Swingby Moon
Estimating the size of the burn
Setting up the Targeter
Adjusting the Engine
burn
•Getting to Earth
•Swingby Earth
•Setting up the Targeter
Creating a Targeting
profile
•Running the Targeter
Performing the Engineburn II
•Escaping a Earth
•Creating a Targeting
Profile
Running the Targeter
Capturing the spacecraft
•Getting to Mars
•Creating a Targeting Profile
•Running the Target
1
2
3
4 5
Sequences in swingby moon and swingby earth
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 11/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Swingby Targeting methods using STK/Astrogator
Initial about 20000km, Go far from EarthSwingby Moon
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 12/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Swingby Targeting methods using STK/Astrogator
Swingby Earth Using gravity assisted
Trajectory From Earth
to Mars
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 13/37
15th AAS/AIAA Space Flight MechanicsMeeting, Copper Mountain, Colorado
Swingby Targeting methods using STK/Astrogator
Swingby moon, and Swing by Earth Caputure Mars and change altitude
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 14/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Results
1. Earth Departure: 2007/3/1
2. ~Swingby Moon
• Duration: 29 days (approx.)
• ∆V: 3.933101 km/s ( approx.)
3. ~Swingby Earth• Duration: 3 days (approx.)
• ∆V :0.642152 km/s
4. Arrive at Mars
• Duration: 150 days (approx.)
• ∆V: 0.123191km/s
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 15/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Conclusion
Saving of fuel by over 60% over Hohmann Transfer method
Saving ot time by about 30 days over Hohmann transfer
method
Considering Timing, Gravity assisted by Moon, Earthmethod is very complex
Flight Time 210 Days
Total Delta V 14.3 km/s
Flight Time 182 Days
4.7 4.68km/s
• Hohmann Transfer
• Gravity Assisted Transfer
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 16/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Solution of E.O.M. is not periodic and hence need of acontrol effort (L2).
This is called Period or Frequency control in literature.
The resulting periodic orbit is called a halo orbit.
When the spacecraft is actively controlled to follow a
periodic halo orbit, the orbit, generally does not close due
to tracking error.
The Restricted Three-body Problem
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 17/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
The Restricted Three-body Problem
21
12
,1
1
mm
a
Equation of Motion
Assume smaller mass m2
2)(2
2/1
21
3
1212
mmG
aT
)(22
2
2
2
r wwr dt
d wr
dt
d r
dt
d si si s
si si
321 zs ys xsr Position vector of the small mass
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 18/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
The Restricted Three-body Problem
3212
2
321
s z s y s xr dt
d
s z s y s xr dt
d
s
s
•
Inertial Acceleration of the small mass
3212
2
)2()2( s z s y x y s x y xdt
r d i
2/1222
1 ])[( z y xr
2/1222
2 ])1[( z y xr
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 19/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
The Restricted Three-body Problem
3
2
3
1
3
2
3
1
3
2
3
1
)1(
)1(2
)1())(1(2
r
z
r
z z
r
y
r
y y x y
r
x
r
x x y x
• Three Components in the rotating frame
• The system equations of motion are found by equating the inertial
acceleration• Assumption of zero mass for the third object theses are following a
pure Keplerian circular orbit.
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 20/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
The Lagrangian Point
• Lagrangian points are the five positions in an orbital
configuration where a small object affected only by gravity
can theoretically be stationary relative to two larger objects(such as a satellite with respect to the Earth and Moon).
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 21/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
The Lagrangian Point
3
2
3
1
3231
3
2
3
1
)1(0
)1(
)1())(1(
r
z
r
z
r
y
r
y y
r
x
r
x x
If we wish to find equilibrium points, we need to setthe rotating-frame velocity and acceleration
component to zero
0,0,0,0,0,0 z y x z y x
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 22/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
The Lagrangian Point
Explore from L2 to L5
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 23/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Halo Orbit
• A halo orbit is a Periodic, three- dimensional orbit near the
L1, L2, or L3 Lagrange points in the three-body problem oforbital mechanics.
• Halo orbits are the result of a complicated interaction
between the gravitational pull of the two planetary bodies
and the centripetal acceleration on a spacecraft.
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 24/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Halo Orbit
Explore EM L1
L1 Halo Orbit
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 25/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Calculation Results Halo Hopping Mission
SEM(L2)
Ax 80000 ~225000
Ay 50000~550000
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 26/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Calculation Results Halo Hopping Mission
SEML2C3 Target 2500km
Distance from Earth to SEM L2 1530000km
Hopping Mission
Impulsive delta V x 0.05km/s~0.1km/s
Measn Radius 11000km
C3 Energy -0.505643 km^2/s^2Rotate Mission Vy -0.4km/s (SEML2 Axis)
Rotate Mission Vx 0.244 km/s (SEML2 Axis)
Refrence DATA : Explorations of low cost connections between Lissajous
orbits from the Sun-Earth and Earth-Moon systems. AIAA 2006-6836
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 27/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Targeting Methods Using STK/Astrogator
The whole mission is split in steps and phases. Steps: Halo orbit insertion at SEL2, Halo orbit hopping sequence.
Phases: Impulsive maneuvers, propagation, stopping conditions.
Targeting method at every step uses the DifferentialCorrector by defining a 3-D target.
Perform a burn in anti-Sun line that takes the S/C in vicinity of Sun-Earth L2 Lagrangian point.
Insertion: Adjust the burn in such a way the S/C crossesSun-Planet L2 Z-X plane with Sun-Planet L2 Vx =0 Km/s.
Station keeping: After several Sun-Planet Z-X plane
crossings, perform station keeping operations.
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 28/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Targeting Methods using STK/Astrogator
StartPropagating to the Anti-Sun Line
•Creating Calculation objects
Setting up the Targeter
Running the Targeter
Performing the Engine burn I
•Getting to the vicinity of L2
Estimating the size of the burn
Setting up the Targeter
Specifying the constraints
•Cross the ZX plane with
Vx=0
Performing the Engineburn II
•Creating a Targeting
Profile
Running the Targeter
Adjusting the Engine burn
•Targeting on the 2nd ZX
plane crossing
Setting up the Targeter
Creating a Targeting profile
Running the Targeter
Completing the First Target sequence to
Orbit around L2
Performing the station keeping
Maneuver
•Setting up the Targeter
Running the Targeter
1
2
3
4
5
6
7
Sequences in halo orbit insertion & station keeping operations
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 29/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Halo Orbit Targeting methods using STK/Astrogat
Initial Earth-circular orbit and Halo orbit
insertion at Sun-Earth L2 Lagrangian point
trajectory ( as seen in VO view)
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 30/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Halo Orbit Targeting methods using STK/Astrogat
Halo orbit at Sun-Earth L2 Lagrangian pointtrajectory as seen in X-Z plane (Map View)
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 31/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Halo Orbit Targeting methods using STK/Astrogat
Halo orbit at Sun-Earth L2 Lagrangian point
in Sun-Earth rotating frame of reference as
seen in X-Y plane
Interplanetary trajectory from Sun-Earth L2
to Sun-Mars L2 in Sun-centered inertial
frame of reference as seen in X-Y plane
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 32/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Results
1. Earth Departure: 2007/8/1
2. Halo Orbit Insertion at Sun Earth L2 Lagrangian point
• Duration: 14.5 days (approx.)
•
∆V: 3.170804 km/s ( approx.)
3. Transfer from Sun Earth L2 to Mars
• Duration: 955 days (approx.)
• ∆V :1.0318345 km/s
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 33/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Result Review
Flight Time 210 Days
Total Delta V 14.3 km/s
Flight Time 182 Days
Total Delta V 4.68km/s
• Hohmann Transfer
• Gravity Assisted Transfer
• HaloHopping Transfer
Flight Time 969 Days
Total Delta V 4.2km/s
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 34/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Conculsion 1
Planets do not eclipse the spacecraft as seen in Y-Z plane Small ∆V budget for station-keeping operations for halo orbit
around Sun-Planet L2 Lagrangian point
Halo orbit hopping method is slower than gravity assisted
trajectory method (approximately 5 times slower) Saving of fuel by over 10% over gravity assisted trajectory method
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 35/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Conclusion 2
Continuous radio contact with Earth
Simultaneous mapping of the planets possible
Potential utility of placing satellites orbiting L2 and L1
Lagrangian points serving as Earth-Moon and Earth-Marscommunication relays
Method suitable for spacecrafts only, not for manned
missions
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 36/37
15th AAS/AIAA Space Flight Mechanics
Meeting, Copper Mountain, Colorado
Questions ?
7/27/2019 Hallo Hopping Term Project
http://slidepdf.com/reader/full/hallo-hopping-term-project 37/37
15th AAS/AIAA Space Flight Mechanics
Meeting Copper Mountain Colorado
Thank you !!