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A fast tour design method using non-tangent v-infinity leveraging transfer

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Abstract

The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple impulsive maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent impulsive maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200-km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a Δv change of <4%. The trajectory is 2.7 years long and comprises 52 gravity assists at Titan, Rhea, Dione, Tethys, and Enceladus, and several deterministic maneuvers. Total Δv is only 445 m/s, including the Enceladus orbit insertion, almost 10 times better then the 3.9 km/s of the Enceladus orbit insertion from the Titan–Enceladus Hohmann transfer. The new method and demonstrated results enable a new class of missions that tour and ultimately orbit small mass moons. Such missions were previously considered infeasible due to flight time and Δv constraints.

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Abbreviations

α :

Pump angle between the v ∞ vector and the minor body velocity vector

δ :

Turning angle between the incoming and outgoing v ∞ vectors of a gravity assist

\({\gamma_{v\infty1}^{s}}\) :

Section of the VILT solution manifold for a given s and v ∞1

Δθ :

Spacecraft angular gain

σ i :

Element of s: if + 1 denotes a long ith arc, if − 1 denotes a short ith arc

μ M , μ P :

Gravitational parameter of the minor and major body

EI :

Element of s: if + 1 denotes exterior VILTs, if −1 denotes interior VILTs

f, E, M:

True, eccentric and mean anomaly of the spacecraft with respect to the major body

n :

Number of minor body revolutions during the VILT

m :

Number of major body revolutions during the VILT

k i :

Element of s: number of full revolutions in the ith arc

r π :

Pericenter of the gravity assist hyperbola

r a , r p , a:

Apocenter, pericenter and semi-major axis of the spacecraft with respect to the major body

r LA , r VA :

Leveraging and vacant apses of the spacecraft with respect to the major body, i.e. the furthers and closest apse to r = 1 respectively

s :

VILT parameter vector; in particular s = (σ 1, k 1, σ 2, k 2, n, EI)

v p , v a :

Velocity of the spacecraft at pericenter and at apocenter with respect to the major body

v ∞ :

Velocity of the spacecraft relative to the moon at r = 1

\({\fancyscript {V}^{\,\,s}}\) :

VILT solution manifold

1, 2:

Subscripts indicates the first or second arc

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Author notes

  1. Stefano Campagnola

    Present address: JAXA/ISAS, 3-1-1 Yoshinodai, Sagamihara, Kanagawa, 299-8510, Japan

Authors and Affiliations

  1. Aerospace and Mechanical Engineering, University of Southern California, 854 Downey Way, Los Angeles, CA, 90089-1191, USA

    Stefano Campagnola

  2. Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA

    Nathan J. Strange

  3. Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Drive, Atlanta, GA, 30332-0150, USA

    Ryan P. Russell

Authors
  1. Stefano Campagnola
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  2. Nathan J. Strange
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  3. Ryan P. Russell
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Correspondence to Stefano Campagnola.

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Campagnola, S., Strange, N.J. & Russell, R.P. A fast tour design method using non-tangent v-infinity leveraging transfer. Celest Mech Dyn Astr 108, 165–186 (2010). https://doi.org/10.1007/s10569-010-9295-1

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