Study on Orbital Maneuvers of Electric Sail with On-Off Thrust Control

Abstract

An electric sail is a new propulsion system uses the solar wind dynamic pressure as a thrust force. We analyzed the probability of the orbital control not changing sail plane angle but switching an electron gun connected with tethers. First, locally optimal switching laws are derived from Lagrange variational equations analytically. By theoretical calculations and numerical simulations, these switching laws are effective for changing some orbital elements. Moreover, mission applicability is studied. Assuming minimum time transfer problem between circular and coplanar orbits, optimal control laws are studied with direct approach. We conclude that the switching orbital control method is effective for exploration of other planets.

Electric sail-based displaced orbits with a refined thrust model

“…In particular, the model of Yamaguchi and Yamakawa 15 shows that, characteristic acceleration being the same, the heliostationary condition can be attained at a smaller distance if r > 1 au, see Figure 6. 70 72 74 76 78 80 82 84 86 88 90 [deg]…”

“…However, even in the most favourable case ( n ¼ n1 ), a Type II DNKO at a Sun distance of about r È , requires a characteristic acceleration greater than 6 mm/s 2 , a value well beyond the current capabilities of an E-sail. Figure 4 shows a comparison between the results of Mengali and Quarta 12 and those obtained using the thrust model of Yamaguchi and Yamakawa, 15 when n ¼ n1 . Note that for r < 1 au the thrust model of Yamaguchi and Yamakawa 15 provides a greater value of characteristic acceleration required for orbital maintenance.…”

“…Note, in passing, that the coefficients in the table emend a couple of typos found in Yamaguchi and Yamakawa. 15 The variation of the cone angle with the pitch angle n is shown in Figure 2, from which the linear law turns out to be a good approximation of equation (2) until n 4 20 (or 4 10 ). Figure 2 also shows that the maximum attainable value of the cone angle is slightly less than 20 , and is reached when the pitch angle is about 55 .…”

“…In previous studies, 12,16 the simplified model of the E-sail performance was characterized by assuming ¼ n =2, with a maximum value of the cone angle max of about 35 . Recently, Yamaguchi and Yamakawa 15 have shown that the function ¼ ð n Þ is more complex than a simple linear law, and can be accurately described by means of the following polynomial, which corresponds to a best-fit interpolation of numerical results…”

“…12,16 The analysis of Yamaguchi and Yamakawa 15 also points out that, for a given Sun-spacecraft distance r, the propulsive acceleration modulus a k k is strongly dependent on the E-sail attitude through the pitch angle n . In fact, according to the procedure described by Yamaguchi and Yamakawa, 15 if is the ratio between the modulus of the propulsive acceleration at an angle n to the maximum propulsive acceleration at a distance r from the Sun, or…”