Hallo Hopping Term Project

7/27/2019 Hallo Hopping Term Project

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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




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




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.





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





B-Plane Method

The b-plane is

defined to contain the focus of an idealized

two-body trajectory





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





B-Plane Method Example “New Horizon Project”




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’




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




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


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


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




Swingby Targeting methods using STK/Astrogator

Initial about 20000km, Go far from EarthSwingby Moon





Swingby Earth Using gravity assisted

Trajectory From Earth

to Mars





Swingby moon, and Swing by Earth Caputure Mars and change altitude



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


• ∆V: 0.123191km/s





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


4.7 4.68km/s

• Hohmann Transfer

• Gravity Assisted Transfer





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






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






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






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.





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).

http://en.wikipedia.org/wiki/File:Lagrange_points.jpg






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






Explore from L2 to L5

http://en.wikipedia.org/wiki/File:LL2_Halo_Example_Synodic.gif





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.










Halo Orbit

Explore EM L1

L1 Halo Orbit





Calculation Results Halo Hopping Mission

SEM(L2)

Ax 80000 ~225000

Ay 50000~550000





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





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.





Targeting Methods using STK/Astrogator

StartPropagating to the Anti-Sun Line

•Creating Calculation objects



Performing the Engine burn I

•Getting to the vicinity of L2

Estimating the size of the burn


Specifying the constraints

•Cross the ZX plane with

Vx=0

Performing the Engineburn II

•Creating a Targeting

Profile


Adjusting the Engine burn

•Targeting on the 2nd ZX

plane crossing


Creating a Targeting profile


Completing the First Target sequence to

Orbit around L2

Performing the station keeping

Maneuver

•Setting up the Targeter


1

2

3

4

5

6

7

Sequences in halo orbit insertion & station keeping operations





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)






Halo orbit at Sun-Earth L2 Lagrangian pointtrajectory as seen in X-Z plane (Map View)






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





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


• ∆V :1.0318345 km/s





Result Review


Total Delta V 14.3 km/s


Total Delta V 4.68km/s

• Hohmann Transfer

• Gravity Assisted Transfer

• HaloHopping Transfer


Total Delta V 4.2km/s





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





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





Questions ?




Meeting Copper Mountain Colorado

Thank you !!

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