Nowadays it is known about 18 thousand asteroids passing through the orbits of the Mars and the Earth (those asteroids are related to Apollo, Amor and Aten groups). Several hundreds of new objects are discovered quarterly. Among those are the asteroids closely approaching to the Earth and representing potential hazard in the case of collision.
Studying of orbit evolution of short-period comets is also necessary because they are considered to be a primary type of objects of the Solar system. Now the list of numbered short-period comets includes more than two hundred objects, new comets being regularly discovered.
In this connection it is necessary to carry out constant monitoring of evolution of all discovered objects and to control their orbits. When investigating orbit evolution of small bodies of the Solar system (asteroids and comets) it is necessary to apply modern mathematical models of celestial motion and high-precision numerical methods of differential equations solving.
Website has been developed within the project «Development of information media based on the modern mathematical models and methods for research of evolution of small bodies in the Solar system» supported by government program «Development of scientific potential of the higher school (2006–2008 years)» of the Federal Agency of Education of the Russian Federation.
Objective of the project is to develop a modern mathematical foundation and software for research of orbit evolution of small bodies of the Solar system – asteroids of Apollo, Amor and Aten groups and short-period comets.
The project was performed by associate staff, postgraduate and graduate students of Applied Mathematics and Information Science Department of Samara State Technical University.
The site was updated in July 1st, 2018.
The motion equations, based on the new principle of interaction between environment and moving bodies, were got. Solving of these equations allows to match coordinates of the Mercury and the Moon with observations without solving of additional equations, taking into account the shape of the Earth and the Moon for the time period between 1600 - 2200 years. New databank of coordinates and velocities of major planets, the Moon and the Sun for the time period between 1600 - 2200 years was created.
New differential equations with the use of databank of coordinates of major planets and the Moon were used for the numerical integration of asteroids. Performed investigations shown that obtained results are more precise in comparison with methods applied earlier for asteroids which have closest approaches with major planets.
In new calculations under investigation of asteroids orbit evolution approaches of asteroids with planets only at the distance less than 0.001 astronomical units were recorded.
The following results have been achieved during the project implementation.
- Modified mathematical model of the motion of major planets, the Moon, the Sun, short-period comets and asteroids considering gravitational, non-gravitational forces, relativistic effects, effects of planets nonsphericity has been developed.
- High-precision methods of numerical integration of the differential equations were developed on the basis of Taylor expansion method, Adams–Bashforth and Adams–Moulton methods up to order 16 inclusive and Everhart method up to order 31 inclusive.
- Software set for solving of differential equations of celestial motion with modified methods of Taylor expansion, Adams and Everhart was developed.
- By means of numerical experiment it was shown that application of the modified Everhart method is more preferable for calculation of orbits evolution of small bodies of the Solar system.
- It was found that the modified Everhart method of order 27 with integration step-size of 6 days is the most effective for calculation of orbital evolution of small bodies of the Solar system, and the step-size should be variable for the small bodies having close approaches. Stability of applied numerical method was studied and displayed.
- The new high-precision databank of coordinates and velocities of the major planets, the Moon and the Sun for the time period between 1000 and 3000 was developed.
- Calculation and analysis of orbital evolution of about 22 000 asteroids of Apollo, Amor and Aton groups for the time period between 1800 and 2206 was performed. About 2 300 objects approaching to the Earth at a distance less than 0.01 astronomical units were identified.
- High-precision databanks of coordinates and velocities of about 22 000 asteroids of Apollo, Amor and Aten groups between 1800 and 2206 with the interval of 100 days have been created.
- Calculation and analysis of orbital evolution of about 240 numbered short-period comets was performed, and high-precision databanks of coordinates and velocities of the given objects for the time period between 1800 and 2204 with the interval of 100 days have been created.
- For a number of comets the matter of influence of non-gravitational effects was studied and values of non-gravitational parameters were found.
- Electronic catalogues of orbital evolution of asteroids approaching to the Earth and short-period comets for the time period between 1800 and 2206 was developed.
- Software allowing to automate the process of research of small bodies motion of the Solar system at any time interval has been developed.
- Database containing orbit elements, coordinates and velocities of asteroids of Apollo, Amor and Aten groups between 1800 and 2206 for standard dates was developed.
The results of the site have been published in more than fifty scientific papers, the main results are the following:
- Zausaev A.F., Abramov V.V., Denisov S.S. Catalogue of orbital evolution of asteroids approaching to the Earth between 1800 and 2204. – M.: Mashinostroenie – 1, 2007. – 608 p. ISBN 978-5-94275-373-3.
- Zausaev A.F., Zausaev A.A. Catalogue of orbital evolution of short-period comets between 1800 and 2204. – M.: Mashinostroenie – 1, 2007. – 410 p. ISBN 978-5-94275-372-6.
- Zausaev A.F., Zausaev A.A. Mathematical modelling of orbital evolution of small bodies of the Solar system. – M.: Mashinostroenie, 2008. – 250 p. ISBN 978-5-94275-425-9.
- Zausaev A.F., Romanyuk M.A. Numerical methods in problems of mathematical modelling of motions of celestial bodies of the Solar system. – Samara.: SSTU, 2017. – 265 p. ISBN 978-5-7964-1988-5.