Sensitivity of the Gravity Assist to Variations of the Impact Parameter
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Sensitivity of the Gravity Assist to Variations of the Impact Parameter A. P. Yefremov* Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow 117198, Russian Federation Received February 20, 2020; revised February 20, 2020; accepted March 2, 2020
Abstract—We build a Kepler model of spacecraft gravity assist maneuver near a Venus-type planet and investigate its sensitivity to changes of the impact parameter. Analytical and numerical computations give similar results indicating a great increase of the trajectory final point shift under a small variation of the assigned spacecraft-planet distance. DOI: 10.1134/S0202289320020127
1. INTRODUCTION A planet’s gravity assist (GA) (or swing by, gravitational slingshot) is for more than 50 years a regular technique to input a controlled ballistic change of spacecraft motion. Instead of wasting chemical fuel, the rocket changes the parameters of its trajectory at the expense of the planet’s gravity. A dozen of successful space missions, from Pioneer 10 (NASA, 1973) to Cassini-Huygens (NASA, ESA, ASI, 1997) and Juno (NASA, 2011), have confirmed the effectiveness of the GA tool; the others, Parker Solar Probe (NASA, 2017) and BepiColombo (ESA, JAXA, 2018) [1] are on their way to approve the method effectiveness and precision. However, a thorough analysis of the BepiColombo trajectory [2] in the Schwarzschild gravity predicts a noticeable deviation of the spacecraft from the Kepler trajectory, with the first gravitational maneuver near the Earth serving as an amplifier for this effect. This possibility suggests a more detailed investigation of the GA process. A good overview of the GA history, math description, and problems [3] regards GA as a part of the “patched conic approximation” routine (see also [4]) elaborated to compute a spacecraft’s motion comprising slingshot maneuvers. In particular, a limiting case of the approximation is considered with the infinitesimally small radius of the sphere of planets’ gravitational influence (the Hill sphere); this makes GA an instantaneous event, which can be formulated as the method of a single instant hyperbola (SIH). In fact, any GA is just a part of the gravitational interaction involving several masses. In a simpler case, we have the three-body problem, in the absence of an exact solution offering only the Jacobi invariant. *
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This weakens the means of analytical mechanics to represent GA in the format of a prolonged assistance description (PAD), its details being possibly important for a mission draft. A comparison of the results provided by the SIH and PAD methods seems to be desirable in general. Fortunately, a fine numerical solution of the equations of the spacecraft motion subject to all involved gravitational forces is now an easily solved problem. In this paper, we suggest an analysis of a spacecraft slingshot maneuver (at a Venus-type planet) and its impact on the trajectory. In Section 2, we construct a model of GA with a subseque
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