Exploration interest has grown during the 20th century since Jupiter is the nearest and largest giant planet in our solar system. Currently, numerous engineers are engaged in efforts to deploy probes into the Jovian system, and some key technical research studies are also carried out for future Jovian system exploration missions. However, capturing into another planet’s system is a costly process, particularly for the Jovian system. The presence of 4 Galilean moons renders the gravity-assist technique a highly effective means of modifying the velocity of probes relative to Jupiter. However, if a Jovian moon is expected to be visited, the perijove of the spacecraft must be lower than the orbital radius of the moon. There are disadvantages to capturing with a low perijove. Firstly, the spacecraft is severely affected by the strong radiation of Jupiter, which is harmful to the electronic components on the spacecraft when it gets close to Jupiter. Secondly, an amount of fuel is consumed to raise the perijove to satisfy the requirements of subsequent objectives. In order to alleviate the disadvantages of low-perijove capture, one solution is to raise the perijove more efficiently by leveraging the solar gravity perturbation (SGP). In a research article recently published in Space: Science & Technology, scholars from Nanjing University of Aeronautics and Astronautics, Beijing Institute of Technology, and Shanghai Key Laboratory of Deep Space Exploration Technology together presents a multiple-moon-aided Jovian capture approach utilizing SGP, which can reduce the velocity increment substantially.
First, three dynamic models are introduced, and the datasets are computed, for the subsequent analysis of utilizing SGP. The four dynamic models include circular restricted 3-body problem (CR3BP), the simplified dynamical, the gravity-assist model, and the high-fidelity dynamical model. The CR3BP model is used to describe the motion of zero-mass spacecraft which utilizes SGP to change orbits with the gravitational dominance of Jupiter. In this model, the two primaries are the Sun to Jupiter which are fixed at the [− μ , 0, 0] T and [1− μ , 0, 0] T along the x axis of the rotating frame, respectively. In the simplified dynamical model, the 4 Jovian moons are assumed to move along a coplanar-circular orbit around Jupiter, and the real ephemeris is not considered. All of the trajectories are Kepler orbits in this model. In the gravity-assist model, the Jovian moon flyby is defined as a mutation of the velocity vector with the same position vector. The flyby altitude is limited to larger than 200 km. The high-fidelity dynamical model involves the gravitation of the Sun, Jupiter, Callisto, Ganymede, Europa, and Io. The J 2 and J 4 higher-order, spherical-harmonic expansion terms of Jupiter are also considered. Additionally, general relativity effects are included in the dynamical model. The ephemeris file are kernels in the SPICE toolkit released by NASA. Two datasets are established to investigate the mechanism of utilizing SGP. The schematic diagram of dataset computation is shown in Fig. 1. The initial position vector and velocity vector are given as the initial state of the perijove of the trajectory. The trajectory is then propagated for one revolution in the rotating coordinate system until the next perijove. Using the given parameters r , φ , and e , the initial position vector in the rotating system can be calculated by x 0 = r cos( φ ) + 1 − μ , y 0 = r sin( φ ) , z 0 = 0, and the initial velocity vector can be calculated by ẋ 0 = − v 0 sin( φ ) + r sin( φ ), ẏ 0 = v 0 cos( φ ) – r cos( φ ), ż 0 = 0, where v 0 = [ μ (1+e)/ r ]^(1/2). Two datasets adopt different ranges and intervals of parameters r , φ , and e . In this work, 4 stop conditions for classification are proposed in Table 3. According to different stopping conditions, the initial states in the dataset can be divided into 2 categories, which are usable and useless for this work. The categories and classification criteria for each initial state are shown in Table 4. Usable states are the first 2 in the table, and the last 3 are useless in this work.
Then, the influence of SGP is shown, and the mechanism of utilizing SGP is revealed. The mechanism of SGP in Jovian capture can be briefly summarized as Table 5.
First, for the perijove radius change in different quadrants, when the initial states are in the 2nd and 4th quadrants, the spacecraft is mainly accelerated by the cumulative solar gravity effect, which makes the perijoves higher. While the initial states are in the 1st and 3rd quadrants, the cumulative effect of the acceleration caused by SGP mainly slows down the motion and it will cause a lower perijove.
Second, when the eccentricity is closer to 1, this means that the magnitude of the initial velocity is higher and the trajectory has a higher apojove. The high apojove makes the flight time longer, so that the time of SGP is also longer, which enhances the cumulative effect on the motion of the spacecraft. Meanwhile, the higher apojove makes SGP more dominant relative to Jovian gravitation.
Third, the reason why the initial states in the 4th quadrant have a better peri-Jove raising (PJR) effect than those in the 2nd quadrant is that the apojoves of the former are in the 2nd quadrant, while the apojoves of the latter are in the 4th quadrant. Naturally, the apojoves in the 2nd quadrant are closer to the Sun than those in the 4th quadrant; thus, SGP is larger for the apojoves in the 2nd quadrant.
Finally, the designed trajectories using multiple-moon-aided capture and SGP are provided. The aim is to raise the perijove to higher than 17 R J and lower than the orbital radius of Callisto. An arrival excess velocity of 5.6 km/s is chosen. A 200-km flyby height is adopted. The flyby sequences are determined by the motion of the spacecraft from the outer to the inner Jovian system. The existence of the geometry of multiple-moon-aided capture trajectories is neglected in the preliminary analysis, but it is taken into account in the high-fidelity model. The period of the final orbit is set to 200 d. Before the first perijove arrival, the simplified dynamical and gravity-assist models are used to calculate the trajectory. A schematic diagram of the capture scenario is shown in Fig. 2. The JOI maneuver is operated at the first perijove. Once the state under the simplified dynamical model is determined, the initial state under the CR3BP model is determined. Then, SGP can be utilized to raise the perijove in the CR3BP model. A possible tangential maneuver PJR is operated to help raise the perijove at the apojove. The tangential maneuver to shorten the orbital period (SP) is operated to shorten the period of the elliptic orbit when the spacecraft reaches the perijove a second time. In the high-fidelity model, the trajectory is visualized in Figs. 17 to 19. The total velocity increment is similar with simulations under the simplified model. Some parameters in detail are listed in Table 7. The results indicate that the Jupiter Orbit Insertion (JOI) and PJR magnitudes are noticeably reduced using the method proposed in this paper. With the help of SGP, the PJR magnitude is usually less than 20 m/s, which could raise the perijove by more than 10 6 km.
Space: Science & Technology
31-Jul-2025