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Planetary Exploration of Saturn Moons Dione and Enceladus

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Planetary Exploration of Saturn Moons Dione and Enceladus DOI: 10.13009/EUCASS2019-81 8TH EUROPEAN CONFERENCE FOR AERONAUTICS AND SPACE SCIENCES (EUCASS) Planetary Exploration of Saturn moons Dione and Enceladus Juan R. Sanmartín* and J. Peláez** * Real Academia de Ingeniería Universidad Politécnica de Madrid Pza. C. Cisneros 3, Madrid 28040, [email protected] ** Universidad Politécnica de Madrid Pza. C. Cisneros 3, Madrid 28040, [email protected] Abstract Search for habitability in Outer planets moons, requires presence of water, energy, and proper chemistry. Dissipation from tidal forces is major energy source in evolution of Icy moon systems. Saturn moons Enceladus and Dione are in 1:2 Laplace resonance. Enceladus ejects plumes of water vapor and ice particles, Dione exhibits linear virgae, hundred kilometres long, latitudinal color lines. A minor tether mission would explore this system. Following Saturn capture, repeated, free Lorentz drag at periapsis brings apoapsis to elliptical orbit at 1:1 resonance with Dione. After multiple flybys, repeated operation reaches 1:2 resonance with Enceladus, for flybys. 1. Introduction Search for habitability in moons of Outer planets, requires presence of sources of energy. Dissipation from tidal forces is a major energy source in evolution of Icy moon systems. Heating always accompanies dissipation but, in case of tidal heating, it will additionally present complex spatial distribution, reflecting on a multi-layer structure in the particular case of Icy moons. Subsurface oceans are a generic feature of large icy bodies at some point in their evolution. A standard interior model for Icy moons consists of an outer solid (ice) layer, an intermediate liquid layer, and a solid (rocky) core. As a satellite rises a tide on its planet, they exchange angular momentum, affecting satellite orbit and planet spin; the moon gains orbital energy at the expense of the planet rotational energy. A complex 3-body paradigm, Laplace resonance, involves two (or more) moons of a planet, forming by differential expansions of orbits by tidal torques. At Jupiter, moons Io, Europa, and Ganymede are in 1:2:4 resonance. Two moons of Saturn, Enceladus and Dione, are in a 1:2 resonance: Enceladus revolution and rotation periods are both 1.370 days, Dione´s periods being approximately 2.74 days. It had been recently discovered that Enceladus ejects plumes of water vapour and ice particles, evidence of a liquid water reservoir below the surface, in the South Polar Terrain. More recently, in the Spring of 2017, it was found that such plumes contain molecular hydrogen, considered sign of chemical reactions supporting microbian life [1]. Very recently, in the Fall of 2018, it was brought to light a feature observed at Dione, the 44th largest Saturn moon: it exhibits multiple color lines (linear virgae), like hundred kilometres long, parallel to the equator as latitudinal lines in a map [2]. It was suggested that such linear virgae are possibly due to impacts from dust-sized foreign material, with low mass and velocity to form streaks, while depositing onto the surface rather than forming craters. After capture by a planet, here Saturn [3], a second stage would involve apoapsis lowering, to allow frequent flyby-visits to selected moons. Tether maneuvering is particular in that closed orbits after capture could freely evolve under repeated Lorentz drag. Because drag operates near periapsis, affecting it little at capture and following tether maneuvering, as later discussed, operation is comparable to capture as regards tether performance, with cathodic-contact off during flybys. A minor tether mission could allow exploring this Laplace resonance, as it was suggested in the past to explore Jovian moons [4]. Following capture by Saturn, repeated Lorentz force around periapsis may bring the apoapsis first to an elliptical orbit at 1:1 resonance with Dione. After a number of flybys, with its Hollow Cathode off to explore Copyright 2019 by Juan R. Sanmartín & J. Peláez. Published by the EUCASS association with permission. DOI: 10.13009/EUCASS2019-81 Juan R. Sanmartín & J. Peláez Dione, (as had been suggested for a minor tether mission to moon Europa [5]) repeated tether operation might bring the apoapsis down to reach a resonance with Enceladus, for further flybys. In the present work, Sec. 2 recalls recent work on tether capture at Saturn [3], in particular showing how higher efficiency required retrograde SC orbiting, and how moon tour might, however, benefit from prograde capture. In Sec. 3 it was actually found that tangential, conveniently slow flybys of moon Enceladus, in a 1:2 resonance, are possible. Section 4 shows that Lorentz-drag peak around periapsis, greatly simplifies the analysis, and tether operation in touring Enceladus and Dione is explicitly determined. Results are discussed and conclusions summarized in Sec. 5. 2. Saturn versus Neptune Capture Review 2 Tether efficiency in spacecraft-capture (S/C-to-tether mass ratio, MSC/mt) goes down as B for weak magnetic fields: The S/C relative velocity v’ ≡ v - vpl induces in the magnetized ambient plasma co-rotating with the planetary spin Ω, a motional electric field Em ≡ v’˄ B (1) in the S/C reference frame, and B exerts Lorentz force per unit length I ˄ B (2) on tether current I driven by Em. Planetary capture is more effective the lower the incoming S/C periapsis because the planetary dipole-field B decreases as inverse cube of distance to the planet, so Lorentz drag decreases rapidly, as the inverse 6th power. Also, since Lorentz-drag will peak at periapsis of a SC orbiting a planet, it will have little effect on periapsis itself. In the 2-body general relation between specific energy ε and eccentricity e at constant periapsis rp, ε = (e – 1) µ/2rp, (3) any sequence of drag-work steps will directly relate e and ε. For a SC Hohmann-transfer between heliocentric circular orbits at Earth and planet, the arriving velocity v∞ of the hyperbolic orbit in the planetary frame provides an orbital specific energy 2 εh = ½ v∞ . Using v∞ in (3) yields 2 e−=1/ vRµ (4) h ∞ where µ is the gravitational constant and we took periapsis rp ≈ R. A Jovian gravity-assist [6] can reduce v∞ , and thus eccentricity, helping magnetic capture of a SC into elliptical orbit. Planetary capture, requiring negative Lorentz drag-work, Wd/MSC = ∆ε < 0, allows writing WWddMM = ×SC =∆×ε SC (5) mMt SC m t mt We will find Wmd / t to be a function of just ambient conditions. Greater capture efficiency in (5) thus requiring lower ∆ε , an optimum value corresponds to eccentricity after capture ec being just below unity. This allows to calculate efficiency from drag work along the parabolic orbit at periapsis. Using (3) and (4), we finally find an expression for capture efficiency, depending on Lorentz drag work and the hyperbolic velocity v∞ , Wd MSC ee h− c M SC = × 2 me− 1 m mvt ∞ /2 th t We calculate drag work W = v[ LI ∧ B] =− LI •∧( v B) (6) d t av t av 2 DOI: 10.13009/EUCASS2019-81 PLANETARY EXPLORATION OF SATURN MOONS DIONE AND ENCELADUS using length-averaged current Iav as bounded by the short-circuit value, σtEm × htwt, with σt, ht and wt being tape- tether conductivity, thickness and width, LI=×× L i whσ E u , i( L / L )1< tav t av t t m I av t * (7) t 2 1/3 L* being certain characteristic ambient-plasma length ∝ (Em/Ne ) [7], and Iav only depending on electron density through iav . With tether along the motional field Em, power in Eq.(6) becomes, using Eq.(1), m 2 ⇒W =− iσσ Lwh ×( v'' ∧ B) •∧( v B) =− it B v• v (8) d avtt t tt av ρ t From conservation of angular momentum we find 22 v• v' = v •( v −Ω ruθ ) = v −Ω rvθ = v − Ω rpp v (9) Using here, explicitly, v2 = 2μ /r from the energy equation for parabolic orbits, there immediately results Ω 22r v r •= −pp = − vv'1 v r v1 (10) 2µ rM 1/2 3/2 2 r/ r≡× 2/ ar ∝ρ / Ω M p( sp) ( pl ) (11) 2 1/3 with rM, where vv• ' changes sign, being the maximum radius presenting drag, and as = (µ / Ω ) being the 1/2 radius of an equatorial circular orbit, where velocities of SC and co-rotating plasma are equal, (µ /as) = Ωas. The last expression in (11) applies in the present analysis, where rp ≈ R. 3 3 We shall use values at as as reference values, introducing the magnetic dipole law to write B(r) = Bs as /r . Next, using (10) in Eq.(8), and the radial speed rate in parabolic orbits, we can now determine drag work r M W dr dr 2µ(rr− p ) ∫∫W dt =2,×=d1 (12a), b) ∆t d1 dt r R dr/ dt finally yielding, 1 22 2 2 5/6 2 W/ mv≡× B W B = σρ B av/2 v d1 t ∞ s 1 S t s ss t∞ (13a, b) 2 r 8/3 M dr W =2 < i >× r ∫ r− r, ( r ≡ rr /) (14) 1 rM 6 ( M ) p av 1 rr−1 where we use subscript 1 to later recall that Eq. (14) applies to value e = 1. As regards the above radial-average of the normalized length-average current iav, consider the particularly simple regime for Lt / L* > 4 1/3 2/3 LL**Ehσ 1 1 −=i ∝m × tt , < (15) av LLLN 4 ttte yielding iav > 0.75 [7]. If this regime applies at the lowest relevant Ne values, it should allow writing < iav>r ≈ 1. However small plasma density Ne might reasonably be, it may be balanced by using a long enough tether.
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