Design and Analysis of Halo orbits around L1 Libration point for … · 2017-06-02 · Design and Analysis of Halo orbits around L1 Libration point for Sun-Earth system Pavan M S,
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International Journal of Scientific & Engineering Research, Volume 8, Issue 5, May-2017 ISSN 2229-5518
Design and Analysis of Halo orbits around L1 Libration point for Sun-Earth system
Pavan M S, Gnanesh C M
Abstract— In the last few years, the interest concerning the libration points for space applications has risen within scientific community.
This is because the libration points are the natural equilibrium solutions of the restricted three body problem. In this paper, design of halo
orbit around L1 point for the sun-earth system is done by known non-linear differential equations by their initial conditions by differential
correction and differential evolution methods.
Index Terms— (Restricted three body problem, lagrangian points, Halo orbits, Differential correction, Differential evolution)
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1 INTRODUCTION
The problem of three body systems is to determine the motion of
three bodies under the influence of their mutual gravitational forces.
If the mass of one of the bodies is a so small compared to the other
two that it cannot influence their motion, then such systems are
called restricted three body systems. This is the case of a spacecraft
moving in the gravitational fields of two massive bodies like the
Earth and the Sun or the Earth and the Moon. The problem of de-
scribing the motion of the smaller third body in such a system is
called restricted three body problem. The two larger bodies are re-
ferred to as primaries. Further if system of the two larger bodies un-
dergoes a circular orbital motion, then the problem is called circular
restricted three body problem or CRTBP in short Brief analysis of the circular restricted three-body problem (CRTBP)
model has been done here, as we used in this study. In this model,
the third body (spacecraft), assumed very small
in comparison to the two primary bodies. Around a commaon center
of mass known as barycenter, the two primaries are assumed to rotate
in circular orbits at barycenter. The origin of the coordinate frame is
fixed and rotates with the rotation of primaries. As shown in the fig1.
Fig 1: CRTBP
1.2 Lagrange points In solar system the locations where the gravitational pull from one
massive body outweighs the pull of another massive body is said to
be Lagrange points. Just as in earth and moon or sun and earth, creat-
ing points where satellite remains in orbit with less effort. As seen in
Figure 2 below there are five different points. For the Earth-Sun sys-
tem, which this report will focus on, the first two points L1 and L2
are located on the opposite sides of the Earth. L3 point lies on the
line defined by the two large masses, beyond the larger of the two.
The L4 and L5 points lie at the third corners of the two equilateral triangles in the plane of orbit whose common base is
the line between the centers of the two masses, such that the point
lies behind (L5) or ahead (L4) of the smaller mass with regard to its
orbit around the larger mass.
Fig 2: Lagrange points for sun-earth system
1.3 Halo orbits
The name Halo orbits were first used in the PhD thesis of Robert W
Farquhar in 1968. One of the most frequently studied models in the
celestial mechanics is the three-body problem. The complicated in-
teraction between the gravitational pull of the two-planetary bodies,
the cariols and centrifugal accelerations on a spacecraft results in
halo orbit. The motion resulting from particular initial conditions,
which produce periodic, three-dimensional ‘halo’ orbits. A halo orbit
is a periodic, three-dimensional orbit near the L1, L2or L3 Lagrange
points in the three-body problem of orbital mechanics. Although the
Lagrange point is just a point in empty space, its peculiar characteris-
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Pavan M S, mechanical engineer, Nitte Meenakshi Institute Of Technolo-gy, Bangalore. PH-9066247982, E-mail: [email protected] Gnanesh C M, mechanical engineer, Nitte Meenakshi Institute Of Tech-nology Bangalore, PH-9743456354. E-mail: [email protected]