3. 99942Orbital characteristics
•
Aphelion.............................. 1.098505744 AU
•
Perihelion.............. .............. 0.746058621 AU
•
Semi-major axis.................0.9222821826 AU
•
Eccentricity...................... 0.1910733664
•
Orbital period......0.8857352528 yr(323.51480 d)
•
Average orbital speed............27.728 km/s
•
Mean anomaly ....................150.996453°
•
Inclination............................ 3.3312800°
•
Longitude of ascending node..........204.45743°
•
Argument of perihelion...............126.3949°
4. SPACECRAFT
SPECIFICATION
LEO altitude(km)........ 300km
Initial Spacecraft
Mass(kg)....................3100kg
Departure ΔV (km/s)...38.0522km/s
Departure Date..........March 28,2029
Mission Duration(days)....16days
Arrival Angle(deg)............12.238
Arrival Date................April 12,2029
Tolerance on Energy[ ]....... -0.1
Number of Iterations........... 2
Initial Power (KW).............7KW
Specific Impulse(sec)......3100(s)
6. INTERPLANETARY
TRAJECTORY: HOHMANN ORBIT
•
Main idea through example of
moving spacecraft from LEO
→ Asteroid
•
Average radius of Earth is
about 6,378 km
•
LEO is at 300 km above
sea level or 6,678 km from
Earth
•
To reach Asteroid.
7. HOHMANN
TRANSFER
•
We want to move spacecraft from LEO
→ Asteroid
•
Initial LEO orbit has radius R1 and
velocity VD
( )
( )
)(
2
)(
2
212
1
211
2
RRRR
R
R
V
RRRR
R
R
V
A
A
SUN
A
D
D
SUN
D
+=
=
+=
=
µ
µ
8. •
Asteroid orbit has
radius R2 and
velocity VA
R1=149282593.9km
R2=150660367.1km
LEO
Asteroid Orbit
R1
R2
VD
VA
12. Hohmann Transfer
Using GMAT
GMAT is a feature rich
system containing high
fidelity space system
models, optimization and
targeting,built in scripting
and programming
infrastructure and
compatible plots, pots and
data products, to enable
flexible analysis and
solutions, for custom and
unique applications. GMAT
can be driven from a fully
featured, interactive GUI
or from a custom script
language. HERE are some
of GMATs key features
layed out by feature group.
13. Arrival And Deflection
XY Co-
ordinates of
Earth and
Asteroid
intersection
points are
representated
in XY plane.
Red is
Asteroid's orbit
and Blue is
Earth's orbit.
-1.5 -1 -0.5 0 0.5 1 1.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
xyast vs xyear
X(AU)
Y(AU)
14. YZ Co-ordinates of Earth and Asteroid Intersection points
representated in YZ plane.
Red is Asteroid's orbit and Blue is Earth's orbit.
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
yzast vs yzear
Y(AU)
Z(AU)
15. XZ Co-
ordinates of
Earth and
Asteroid
intersection
points are
representated
in XZ plane.
Red is
Asteroid's
orbit and
Blue is
Earth's orbit. -1.5 -1 -0.5 0 0.5 1 1.5
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
xzast vs xzear
X(AU)
Z(AU)
16. A-Intersection Point
(-0.9206996046AU,-
0.3662249197 AU,-
0.158953035 AU)
SOI of Earth is 925x10^3 km
(0.0061832430AU)
B-Critical Point
(-0.9268828476AU,-
0.3600416767
AU, -0.152769792AU).
Safe distance =300000 km
(0.00200537614 AU).
C-Deflection Point
(0.93022881148AU,
0.353543398664AU,
0.15471445598504AU)
D-Earth Initial
Blue-Earth orbit
Red-Asteroid orbit
-1.5 -1 -0.5 0 0.5 1 1.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
xyast vs xyear
X(A U)
Y(AU)
A
B
C D
A
B
D
19. After Deflection
•
Direction of
sun=121.3005425deg
Thus, we can conclude by determining the
direction of the Sun and the direction of
Asteroid with respect to Sun is same where
near to each other, so the Asteroid is
deflected from the path of the Earth and
pushed into the Sun.
20. Reference
• Brophy, J. R. and Noca, M., “Electric propulsion for solar system exploration.”
Journal of Propulsion and Power.
• Casalino L. and Colasurdo G., "Missions to Asteroids Using Solar Electric
Propulsion."
• Gomes, V.M., Prado, A.F.B.A, Kuga, H.K., "Orbital maneuvers Using Low
Thrust", Recent Advances in Signal Processing.
• W lodarczyk, I., The impact orbits of the dangerous asteroid (99942) Apophis,
Contributions of the Astronomical Observatory.
• W lodarczyk, I., The potentially dangerous asteroid (99942) Apophis, Monthly
Notices of the Royal Astronomical Society.
Farnocchia, D., et al.: Yarkovsky-driven impact risk analysis for asteroid (99942) Apophis,
Icarus 224, 192 (2013).
Kro´likowska, M., Sitarski, G., So ltan, A. M.: How selection and weighting of astrometric
observations influence the impact probability. The case of asteroid (99942) Apophis, Monthly
Notices of the Royal Astronomical Society 399, 1964 (2009).
Goldberg, David: Genetic Algorithms in Search, Optimization, and Machine Learning.
AddisonWesley, First ed., 1989.
Koza, John: Genetic Programming: On the Programming of Computers by Means of
Natural Selection. Cambridge, Massachusetts: The MIT Press, First ed., 1992.
