Rutherford’s extended formula and optimization of the gravity assists beam modelling in the Solar system

Rutherford’s formula for the scattering of charged α-particles in the Coulomb field can be easily generalized to the case of gravitational scattering. The extended Rutherford formula for the gravitational scattering is presented. One of the types of the gravitational scattering in the Solar system is the gravity assist maneuvers. In this paper, an effective gravitational scattering cross-section is introduced by analogy for them and the generalized Rutherford formula for gravitational scattering is presented out when performing gravity assists. Modern methods of the ballistic design of the interplanetary space flights using gravity assist maneuvers around planets [1-3] are associated with the need to calculate a lot of trajectories (i.e. of the phase beams). For their effective use it is necessary to study the structure of non-linear flyby gravitational scattering using the Rutherford’ formula and to construct the corresponding effective modelling using according regularized phase beams. It is shown that with using of such approach, it is possible to significantly increase the efficiency of the recurrent procedure for the gravity assists chains searching for ballistic scenarios of the modern interplanetary flights.

Gravity assists gravitational scattering and the perturbation rings in the Solar system

One of the types of gravitational scattering in the Solar system within the framework of the model of the restricted three-body problem (R3BP) is gravity assist maneuvers of the “particles of insignificant mass” [1] (spacecraft, asteroids, comets, etc.). For their description, a physical analogy with the beam scattering of charged α particles in a Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions for the possibility of gravity assists executing related from the restricted size of planet’s sphere of influence. At the same time, internal restrictions for the gravity assists performance estimated by the effective radii of planets are known from the literature on R3BP [2] (gravitational capture by the planet, falling into it). They depend from the particle asymptotic velocity relative the planet. For obvious reasons, their influence cuts off the possibility of effective gravity assists performance [3]. In this work the generalized estimates of the sizes of the near-planetary regions (“perturbation rings”), falling into which is a necessary condition for the implementation of gravity assists, are presented. The detailed analysis shows that Neptune and Saturn have the characteristic “perturbation rings” of the largest sizes in the Solar system, and Jupiter occupies only the fourth place in this checklist.

Use of a evolutionary algorithm to optimize interplanetary transfers

In this paper, it was studied the optimization of the cost of interplanetary missions with emphasis on reducing fuel consumption. To achieve this goal, a genetic algorithm was implemented to optimize the total impulse of orbital transfer. It was implemented a case of sending a space vehicle from Earth to a another planet using a gravity assist maneuver (swing by), in this paper it was chose sending a spacecraft from Earth to Mars with a close approach to the Venus. The method employed can be used for impulsive interplanetary missions in general, and so the solution found can become an initial solution for numerical methods of optimization of low thrust maneuvers

Venus's induced magnetosphere during active solar wind conditions at BepiColombo's Venus 1 flyby

Out of the two Venus flybys that BepiColombo uses as a gravity assist manoeuvre to finally arrive at Mercury, the first took place on 15 October 2020. After passing the bow shock, the spacecraft travelled along the induced magnetotail, crossing it mainly in the YVSO direction. In this paper, the BepiColombo Mercury Planetary Orbiter Magnetometer (MPO-MAG) data are discussed, with support from three other plasma instruments: the Planetary Ion Camera (SERENA-PICAM) of the SERENA suite, the Mercury Electron Analyser (MEA), and the BepiColombo Radiation Monitor (BERM). Behind the bow shock crossing, the magnetic field showed a draping pattern consistent with field lines connected to the interplanetary magnetic field wrapping around the planet. This flyby showed a highly active magnetotail, with e.g. strong flapping motions at a period of ∼7 min. This activity was driven by solar wind conditions. Just before this flyby, Venus's induced magnetosphere was impacted by a stealth coronal mass ejection, of which the trailing side was still interacting with it during the flyby. This flyby is a unique opportunity to study the full length and structure of the induced magnetotail of Venus, indicating that the tail was most likely still present at about 48 Venus radii.

Geostationary Orbit Transfer with Lunar Gravity Assist from Non-equatorial Launch Site

We show that it is possible to launch a satellite to Geostationary Equatorial orbit (GEO) from the non-equatorial launch site (Naro Space Center in South Korea) even though that is located in the mid-latitudes of the northern hemisphere. When launched from this site, the equatorial inclination after separation will be 80°. We use a lunar gravity assist (LGA) transfer to avoid the excessive ∆V costs of plane change maneuvers. There are eight possible paths for the LGA; there are four paths consisting of Earth departures and free-return types, and there are two nodes of the Moon’s orbit (ascending and descending). We analyze trajectories over five launch periods for each path using a high-fidelity orbit propagation model. We show that the LGA changes the orbital energy of the “cislunar” free-returns more than for the “circumlunar” free-returns, resulting in less geostationary insertion ∆V for the cislunar free-returns. We also show that the geometrical ∆V variation over the different paths is greater than the seasonal ∆V variation. Our results indicate that an ascending departure and cislunar free-return at the descending node have lower ∆V requirements than the other paths, and lower than described in several previous studies.

Solar Orbiter’s first Venus flyby: observations from the Radio andPlasma Wave instrument

<p>On December 27, 2020, Solar Orbiter completed its first gravity assist manoeuvre of Venus. While this flyby was performed to provide the spacecraft with sufficient velocity to get closer to the Sun and observe its poles from progressively higher inclinations, the Radio and Plasma Wave (RPW) consortium, along with other operational in-situ instruments, had the opportunity to perform high cadence measurements and study the plasma properties in the induced magnetosphere of Venus. In this work we present an overview of the in situ observations performed by RPW, inside the induced magnetosphere of Venus, during this first encounter of Solar Orbiter.<br />These data allowed conclusive identification of various waves at low and higher frequencies than previously observed and detailed investigation regarding the structure of the induced magnetosphere of Venus. Furthermore, noting that prior studies were mainly focused on the magnetosheath region and could only reach 10-12 Venus radii (RV) down the tail, the particular orbit geometry of Solar Orbiter’s VGAM1, allowed the first investigation of the nature of the plasma waves continuously from the bow-shock to the magnetosheath, extending to ∼ 70 R V in the far distant tail region.</p>

Venus’s induced magnetosphere during active solar wind conditionsat BepiColombo’s Venus 1 flyby

<p>Out of the two Venus flybys that BepiColombo uses as a gravity assist manoeuvre to finally arrive at Mercury, the first took place on 15 October 2020. After passing the bow shock, the spacecraft travelled along the induced magnetotail, crossing it mainly in the Y<sub>VSO</sub>-direction. We discuss the BepiColombo Mercury Planetary Orbiter Magnetometer (MPOMAG)<br />data, with support from three other plasma instruments: the Planetary Ion Camera (PICAM), the Mercury<br />Electron Analyser (MEA) and the radiation monitor (BERM). Behind the bow shock crossing, the magnetic field showed a<br />draping pattern consistent with field lines connected to the interplanetary magnetic field wrapping around the planet. This flyby showed a highly active magnetotail, with, e.g., strong flapping motions at a period of ~7 min. This activity was driven by solar wind conditions. Just before this flyby, Venus’s induced magnetosphere was impacted by a stealth coronal mass ejection, of which the trailing side was still interacting with it during the flyby. This flyby is a unique opportunity to study the full length and structure of the induced magnetotail of Venus, indicating that the tail was most likely still present at about 48 Venus radii. This presentation will take place after the second Venus flyby by Solar Orbiter and BepiColombo and Solar Orbiter on 9 and 10 August, respectively.</p>