Gravitational Maneuvers Research Articles

SUBSTANTIATION OF THE ANOMALIES OF THE MEASUREMENT RESULTS FOR TRAJECTORIES OF GRAVITATIONAL MANEUVER OF SPACE VEHICLES

In astronomical research, the problem of measuring the trajectories of the gravitational maneuver of space vehi- cles in the gravitational field of large celestial bodies arises. The known measurement results differ from those predicted by classi- cal celestial mechanics. A practical solution to this anomaly is possible only based on an adequate mathematical model. For this purpose, we have adapted Newton’s law of universal gravitation to the case of moving masses in a possible range of speeds in flat space and physical time. At the same time, the finite speed of propagation of the gravitational field is taken into account. The dif- ferential equations of motion of cosmic bodies have been obtained. In the heliocentric and planetocentric coordinate systems, tran- sient processes in the cosmic three-mass system are simulated – star, planet, and man-made spacecraft (Sun-Mercury-space probe). To more deeply identify the essence of gravitational interaction, transient processes of both acceleration and deceleration of the space vehicle were simulated depending on the specified space-velocity initial conditions for the differential equations of motion. The results of the simulation of transient processes are attached.

Виртуальные гравитационные маневры при проектировании межпланетных перелётов

It is shown that the backward in time extension of the spacecraft interplanetary launch trajectory from the point of the low orbit of the departure planet generates a trajectory structurally coinciding with the virtual gravity assist trajectory near the departure planet. The pericenters of the auxiliary beam of the flying by hyperbolas and the time of their pericenter passage in this case differ slightly from the corresponding parameters of the designed departure orbit when starting from the specified point. Thus, the search for the trajectory of an interplanetary flight can be separated from the need to take into account the boundary conditions of the launch from an intermediate low pre-launch orbit. The pre-launch orbit is refined on the results of the search for the trajectory of the interplanetary flight. A structurally uniform scheme of ballistic design of spacecraft flight paths using multiple gravitational maneuvers based on the consideration of planetary ephemerides is presented.

Применение мощных энергодвигательных систем для выполнения транспортных задач в космосе

The purpose of the research was to consider the application of high power level power and propulsion systems for different space missions. The paper gives the main components of high power level nuclear power and propulsion systems as well as their architecture options and integration solutions. Within the research, we set requirements to characteristics of high power level power and propulsion systems of advanced spacecraft aimed for different transport missions in near-Earth and deep space, analyzed efficiency of nuclear power and propulsion systems applied for transport missions in comparison with conventional chemical propulsion systems. Findings of the research show that high power level power and propulsion systems have the following advantages in comparison with conventional chemical propulsion systems: increase of payload mass; possibility of direct flights (without gravitational maneuvers) to deep space objects; ensuring power supply of target equipment and communication systems at a qualitatively higher level.

Retrospective Analysis of the Orbits of Asteroids Colliding with Earth

In this paper, we consider the trajectories of real and model asteroids that lead to collisions with Earth. They highlight the close approaches to Earth that precede impact. The presence of such approaches allows us to detect a dangerous object in advance, clarify its orbit, and use the effect of a gravitational maneuver to economically prevent an asteroid from hitting Earth. In the paper we consider various families of collision trajectories: possible trajectories of real dangerous asteroids, as well as model trajectories that are not linked to a specific object. It is shown that in the first case, the approaches preceding the collision are noticeably greater.

Retrospective analysis of the orbits of asteroids colliding with the Earth

In this paper, we consider the trajectories of real and model asteroids that lead to collisions with the Earth. They highlight the close approaches to the Earth that precede the impact. The presence of such approaches allows you to detect a dangerous object in advance, clarify its orbit, and also use the effect of a gravitational maneuver to economically prevent an asteroid from hitting the Earth. The article considers various families of collision trajectories: possible trajectories of real dangerous asteroids, as well as model ones trajectories that are not linked to a specific object. It is shown that in the first case, the approaches preceding the collision are noticeably greater.

Adaptive Methods of the Flybys Constructing in the Jovian System with the Orbiter Insertion Around the Galilean Moon

We consider space expeditions with a long-term spacecraft stay near the studied celestial body (artificial satellites of small bodies of the Solar System), or expeditions with a possible spacecraft landing on the surface of the celestial body (for example, the ESA Jovian Icy Moon Explorer JUICE mission, and the Russian prospective project Laplace‑P). An effective formalism is proposed for creating adaptive search scenarios for low-cost combined spacecraft trajectories, focused on the possibility of using high-performance computing resources of the computer experimentation. Examples are given of the implementation of this formalism for searching for combinations of interlunar gravitational maneuvers in the Jovian system with the aim of entering the orbit of the Jovian moon’s artificial satellite.

Gravity Assist Maneuvers Near Venus for Exit to Non-Ecliptic Positions: Resonance Asymptotic Velocity

Venus, the closest planetary neighbor of the Earth in the Solar System, is eminently suitable for performing gravity assist maneuvers by a spacecraft for a low-cost change of its orbit inclination relative to the ecliptic. We calculate the resonance values of the spacecraft asymptotic velocity relative to the planet, such that each orbital period of the spacecraft after each gravity assist maneuver are commensurate with the few orbital period of Venus, providing a new encounter with it. This enables an increase in the orbital inclination of the spacecraft using gravity-assist maneuvers without transitions to adjacent resonances along the invariant line of the main resonance on $${{\operatorname{V} }_{\infty }}$$ -sphere, reaching a maximum inclination. A Venusian invariant has been obtained that does not vary after performing gravity assist maneuvers near Venus. An adaptive semianalytic method and its geometric interpretation for creating a sequence of sequences of gravitational maneuvers near Venus for a low-cost changes in the orbital inclination of the spacecraft have been presented.

Сближения с Землей опасных астероидов

The paper considers the asteroids approach to the Earth, for which collisions with our planet in the XXI century are possible. Close encounters on trajectories leading to collisions can often be found more than on nominal trajectories. Close encounters provide an opportunity to use the effect of a gravitational maneuver to prevent an asteroid from collisions with the Earth. As a result, the deflection of the asteroid can be carried out by the impact which is by several decimal orders less. Such an impact can be basically implemented using modern space technology. The asteroids approach to the Earth also helps to detect these asteroids, to refine their orbits from observations and to predict the characteristics of their possible collisions with the Earth in the future. In this paper, we consider the approach on the trajectories leading to collisions with the Earth for dangerous asteroids 2008 EX5, 2015 RN35, Apophis, which we have studied in detail.

An Extremal Property of Orbits in the Solar System

In this paper it is shown that the semi-major axes of the orbits of neighboring planets and of the orbits of large satellites of some planets in the Solar system are close to the orbit radii in the optimal solutions of the problem on a single-impulse transfer in a planetary system from a circular orbit to infinity with a gravitational maneuver.

On the Possibility of Deflecting an Asteroid from Collision with the Earth Using the Kinetic Method

The possibilities of deflecting an asteroid from its collision course with the Earth by changing its velocity with an impact are considered. Using the asteroid Apophis as an example, the time dependence of the positions and sizes of the keyholes leading to collision is studied. It has been found that the possibility of deflecting this asteroid usually exists, and the impact can be accomplished in principle, given the capabilities of modern space technology. A change in the velocity should be performed before the encounter of 2029 in order to use the gravitational maneuver effect. The possible accuracy of determining Apophis’ orbit and the keyholes that lead to collision and are associated with the resonance returns are considered.

Preliminary Optimization of the Complicated Interplanetary Flight Path of the Spacecraft with Electric Propulsion

The complicated interplanetary flight path of spacecraft with electric propulsion using multiple gravitational maneuvers is examined. The method developed is based on the use of solutions of the auxiliary problem for SC with chemical propulsion systems. The results of the solution of this auxiliary problem allowed rational flight paths of spacecraft with electric propulsion to be identified and the the flight paths optimized. The auxiliary problem of the analyzed particular flight path is formulated as a problem of mathematical programming. A large number of equality and inequality constraints must be satisfied in solving this problem. The complicated flight path of the spacecraft to Jupiter is discussed as a typical example. The Earth, Venus and Mars are considered as the intermediate planets where the gravitational maneuvers will be accomplished.

Ballistic design of transfer trajectories from artificial-satellite earth orbit to halo orbit in the neighborhood of the L 2 point of the Sun-Earth system

The paper considers the ballistic design of spacecraft (SC) transfer to the neighborhood of the L2 point and subsequent entry of the SC into the halo orbit. Trajectory calculations of one-impulse Earth-halo orbit transfers with and without using a lunar gravitational maneuver are presented. For the calculation of one-impulse trajectories of Earth-halo-orbit transfers, an algorithm for constructing initial approximations is applied. These approximations are constructed by calculating and analyzing the isolines as a function of two variables. This function is represented by the pericenter height of the outgoing orbit over the Earth’s surface. The arguments of the function are special parameters that characterize the halo orbit. The mentioned algorithm allows one to obtain halo orbits with specified geometrical characteristics both in the ecliptic plane, and in the plane orthogonal to it. The estimates of the characteristic velocity expenses for maintaining SC in the selected halo orbit are obtained. The described technique was used to search for working orbits of the Spectr-RG and Millimetron spacecraft. Examples of orbits obtained are presented.

Gravitational maneuvers as a way to direct small asteroids to trajectory of a rendezvous with dangerous near-Earth objects

A possibility to prevent collisions with the Earth of dangerous celestial bodies by directing at them small asteroids is considered. It is proposed to solve this problem using a gravitational maneuver near the Earth.

About one problem of trajectory optimization

The optimization problem for trajectories of spacecraft flight from the Earth to an asteroid is considered in this paper. The flight is realized in the central Newtonian gravitational field of the Sun with a possibility of gravitational maneuvers near planets. Perturbation maneuvers are taken into account using the method of point area of action with a limitation on the flyby altitude. The spacecraft is controlled by changing the value and direction of the engine thrust. The problem is solved taking into account constraints on the launch time, flight duration, and minimum distance to the Sun.

The use of the Earth’s gravitational potential for interplanetary flights

An efficient scheme of the use of the Earth’s gravity in interplanetary flights is suggested, which opens up new opportunities for exploration of the solar system. The scheme of the gravitational maneuver allows one to considerably reduce the spacecraft mass consumption for a flight and the time of flight. An algorithm of the gravitational maneuver is suggested that takes into account the restriction on the altitude of a planet flyby. Estimates are made of transport capabilities for delivery of a spacecraft to the orbits of Jupiter, Saturn, and Uranus. The spacecraft is based on a middle-class carrier launcher of the Soyuz type and includes chemical and electric plasma jet engines of the SPD-140 type, which use solar energy.

Method for optimization of trajectories including gravitational maneuvers of a spacecraft with a solar sail

A method for simulation and optimization of flight trajectories including multiple maneuvers of spacecrafts equipped with a solar sail is considered. The proposed method provides a possibility of formation of the general approach to solution of optimization problems of interplanetary missions using a solar sail. The problems of optimization of flight trajectories to Mercury and to a vicinity of the Sun on the basis of the inexpensive conversion Dnepr launch vehicle are solved using the proposed method.

Optimization of Flight Trajectories of a Spacecraft with Electric Propulsion Using the Gravitational Maneuver

Necessary conditions of optimality of the use of a gravitational maneuver during a flight are obtained, and a mathematical model for its study is proposed. With the help of the developed method of optimization of a trajectory of an interplanetary flight using a favorable gravitational maneuver, estimations of a spacecraft's transport capabilities are made for flights to Mercury and for the delivery of a solar probe into the near vicinity of the Sun.

On the fundamental possibility of using cable systems to carry out gravitational maneuvers in the vicinity of a planet

On the fundamental possibility of using cable systems to carry out gravitational maneuvers in the vicinity of a planet

Floating Common Bile Duct Stones A Cause of a False Negative Endoscopic Retrograde Cholangiogram

Endoscopic retrograde cholangiography (ERC) is the "gold standard" for the preoperative diagnosis of choledocholithiasis. Air bubbles that can cause a false positive ERC are differentiated from stones by their response to gravitational maneuvers: bubbles rise while stones sink. We report a patient with round, floating common bile duct stones that mimicked air bubbles to be the reason for a false negative ERC.