<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, computational algorithm with the aid of Mathematica software is specifically designed for the gravitational two–body problem. Mathematical module is established to find the position and velocity vectors. Application of this module for different kind of orbits (elliptic, parabolic and hyperbolic) leads to accurate results, which proved module efficiency and to be skillful. The classical power series method is to be utilized as the methodology.</p></abstract>

In this paper, computational algorithm with the aid of Mathematica software is specifically designed for the gravitational two–body problem. Mathematical module is established to find the position and velocity vectors. Application of this module for different kind of orbits (elliptic, parabolic and hyperbolic) leads to accurate results, which proved module efficiency and to be skillful. The classical power series method is to be utilized as the methodology.

Mathematical Algorithm for Solving Two–Body Problem

Department of Mathematics, Faculty of Science

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Mathematical Algorithm for Solving Two\u2013Body Problem"}

In this paper, computational algorithm with the aid of Mathematica software is specifically designed for the gravitational two–body problem. Mathematical...

Orbit Type	r(km)	v(km/s)
Elliptic	1.19702000	0.64264300
	1.19989670	0.66492594
	0.42298299	1.87403310

Parabolic	2.1706300	0.95989400
	55.873377	0.18921011
	55.8131610	0.18930981

Hyperbolic	1.6526200	1.1352500
	226.74156	1.1219743
	213.82559	1.0585222

Orbit Type	x₀ (km)	y₀ (km)	z₀ (km)	ẋ₀ (km/s)	${\dot{y}}_{0} (k m / s)$ {\dot y_0}(km/s)	ż₀ (km/s)
Elliptic	5096.530625	3997.328251	−1767.35171	4.683016085	0.602386847	4.217758697
	0.462581670	0.063366053	0.94365569	−0.386104670	0.485499770	0.538650150
	0.467585950	0.060430695	0.94778613	−0.343550500	0.464286580	0.582594050

Parabolic	−1616.940994	7756.699643	−7712.188395	−0.6730303137	8.4349309570	0.705548375
	0.201227080	−0.449587910	−0.796666320	1.1039007000	0.4558421100	−0.841963950
	0.000786356	−0.105595880	−1.121732800	0.9715977800	0.4937057600	−0.766396930

Hyperbolic	000010000	0.0000000	0.00000000	0.00000000	0.00000000	9.20000000
	−1.61740150	−1.0018533	−0.62794583	0.56325092	0.19817751	−1.37540280
	−0.66846076	−2.0580722	−1.96420100	0.78874624	0.74895884	−0.78257152

Mathematical Algorithm for Solving Two–Body Problem

Data publikacji: 28 paź 2020

Zakres stron: 217 - 228

Otrzymano: 06 mar 2020

Przyjęty: 05 kwi 2020

DOI: https://doi.org/10.2478/amns.2020.2.00039

Słowa kluczowe
Two–body problem, Power Series Methods, Mathematica software

© 2020 M. H. Alghamdi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

The final scalar values of the position and velocity vectors

The initial values components for the position and velocity vectors

Mathematical Algorithm for Solving Two–Body Problem

Data publikacji: 28 paź 2020

Zakres stron: 217 - 228

Otrzymano: 06 mar 2020

Przyjęty: 05 kwi 2020

DOI: https://doi.org/10.2478/amns.2020.2.00039

Słowa kluczoweTwo–body problem, Power Series Methods, Mathematica software

© 2020 M. H. Alghamdi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

The final scalar values of the position and velocity vectors

The initial values components for the position and velocity vectors

Słowa kluczowe
Two–body problem, Power Series Methods, Mathematica software