THEINTERACTIVE MODELING OF A BINARY STAR SYSTEM Canberk Soytekin Çakabey Schools

2025-05-06 0 0 1.88MB 7 页 10玖币
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THE INTERACTIVE MODELING OF A BINARY STAR SYSTEM
Canberk Soytekin
Çakabey Schools
Izmir, Turkey
canberk.soytekin@cakabeyli.com
Ay¸se Pelin Dedeler
Çakabey Schools
Izmir, Turkey
ayse.pelin.dedeler@cakabeyli.com
ABSTRACT
An interactive binary star system simulation was developed to be showcased on an educational
platform. The main purpose of the project is to provide insight into the orbital mechanics of such
star systems with the help of a three-body simulation. The initial simulation script was written in
the Python programming language with the help of the VPython addition. The custom-made models
were created on Blender and exported. For the final implementation of the simulation on the Godot
game engine, the Python code was converted into GDScript and the Blender models were re-textured.
Keywords Three-Body Problem ·Binary Stars ·Interactive Learning
1 Introduction
The three-body problem was posed by Newton in Principia [
1
] , where he considered the motion of the Earth and the
Moon around the Sun. Since then, the three-body problem has been one of the most well-known problems in dynamical
astronomy [2].Extensive theoretical and numerical research has been dedicated to the study of this attractive problem;
however, for simplicity’s sake, the majority of research has focused on the circular constrained problem [
3
]. The
development of high-speed computers has increased interest in simulating the general three-body problem. Applications
of the three-body problem in astronomy are essential for determining how three stars, a star with a planet that has a
moon, or any other set of three celestial objects can maintain a stable orbit. Three-body problem based foundational
models of the gravitational influence of the Sun on Earth and the Moon were investigated while constructing significant
space missions like the James Webb Space Telescope [
4
]. The Hubble Space Telescope, the Chandra X-Ray Observatory,
the SPITZER Space Telescope, and the Kepler Space Telescope are some of the most noteworthy discovery missions
that NASA has conducted; each of these missions have used a distinct approach to the three-body problem[5].
Figure 1: The TOI-1338 Binary Star System [6]
arXiv:2210.14227v1 [physics.ed-ph] 25 Oct 2022
Orbital Explorer
Scientists are increasingly favoring active learning tools [
7
]. Simulations may not only serve to motivate students,
but also to enhance their intuitive knowledge of abstract physics problems.[
8
], To achieve our goal of turning the
three-body problem into an interactable topic for students, researchers, and enthusiasts, we have created a simulated
system consisting of two stars and one observatory satellite which are in elliptical orbits determined by a differentially
simulated application of classical mechanics principles. The initial parameters of the observatory satellite: position (x,
y, z) and velocity (x, y, z) vectors can be given by the user to initiate the simulation.
2 The Scientific Groundwork
The scientific bases of the project were obtained from Orbital Mechanics by Vladimir Chobotov [
9
], Elements of
Newtonian Mechanics by Jens M. Knudsen and Poul G. Hjorth [
10
], and the MIT 8.01SC Classical Mechanics Course.
m2
v2
0
R12
=Gm1m2
R2
12
, v2
0=Gm1
R12
, v0=rGm1
R12
;(1)
−→
p02 =0
m2·v0,X~p = 0,−→
p01 −−→
p02 (2)
Conservation of momentum and Kepler’s First Law for celestial bodies were utilized in determining the initial velocities
of the binary stars as well as satisfying the orbital prerequisites.
−−→
rH0=R12 "rx
ry
rz#,−−→
vH0= vf"vx
vy
vz#(3)
The scalar properties of the satellite are mass (m
0
) and initial speed (v
f
). The vectoral properties are its position vector
and the components of its velocity.
Figure 2: The diagram of the initial conditions.
3 Python Simulation
In the mathematical modeling of the scientific bases of the project, a differential calculation method was utilized. In the
Python simulation, the positions and the momenta of the stars and the satellite were updated approximately every 200
microseconds (dt = 200 µs).
Throughout each dt time interval, the forces on the bodies and their momenta were assumed to be constant.
The momenta were updated differentially according to the following equations:
−−→
pnew =−−→
pold +−→
∆p, −→
∆p=Zt0+∆t
t0
~
F dt (4)
lim
∆t→0
−→
∆p=~
F·∆t, ~p0
new =−−→
pold +~
F·∆t(5)
The positions were updated differentially according to the following equations:
2
摘要：

THEINTERACTIVEMODELINGOFABINARYSTARSYSTEMCanberkSoytekinÇakabeySchoolsIzmir,Turkeycanberk.soytekin@cakabeyli.comAy¸sePelinDedelerÇakabeySchoolsIzmir,Turkeyayse.pelin.dedeler@cakabeyli.comABSTRACTAninteractivebinarystarsystemsimulationwasdevelopedtobeshowcasedonaneducationalplatform.Themainpurposeoft...

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