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Alfvén drag for satellites orbiting in Jupiter's plasmasphere
ICARUS 58, 182-185 (1984)
Alfven Drag for Satellites Orbiting in Jupiter's Plasmasphere* L. A N S E L M O * AND P. F A R I N E L L A ? *CNUCE, Via S. Maria 36, 1-56100, Pisa, Italy, and ~;Scuola Normale Superiore e Dipartimento di Matematica dell' Universitd di Pisa, Piazza dei Cavalieri 2, 1-56100 Pisa, Italy Received November 28, 1983; revised February 13, 1984 According to a mechanism discovered by S. D. Drell, H. M. Foley, and M. A. Ruderman ((1965). J. Geophys. Res. 70, 3131-3145), a satellite orbiting around a planet having a strong magnetic field and a dense ionospheric plasma dissipates orbital energy via radiation of Alfvrn waves. The dissipation process is effective for objects larger than a minimum size and made of material exceeding a minimum electrical conductivity. It is shown that the corresponding drag effect could have influenced in a significant way the orbital evolution of the small natural moons orbiting inside or in proximity of Jupiter's ring. In particular this mechanism could explain the absence in the ring of objects in the size range from -0.1 to - 1 0 km.
The motion of a c o n d u c t o r across a magnetic field B induces in the conductor itself an electric charge separation canceling the electric field E = (v × B)/c which is seen in the co-moving reference system (here v is the velocity of the conductor relative to the magnetic field and c is the velocity of light). If the body (e.g., a spacecraft or a natural satellite) is moving through a plasma (e.g., a planetary plasmasphere), then according to a physical mechanism described originally b y Drell et al. (1965) the charge can be conducted away via generation of Alfvrn waves. This implies that a dc current flows through the conductor and at the same time some mechanical energy is converted to that of Alfvrn radiation. In this note we intend to show that the corresponding drag effect could be relevant (and possibly measurable in the near future) for the small natural satellites orbiting in the inner plasmasphere of Jupiter. We recall that Alfvrn waves are magnetohydrodynamic disturbances of frequency oJ much less than the ion cyclotron frequency f/i = eB/Mic, i.e., < i 0 4 B ( M p / M i ) Hz,
Mp/Mi is the proton to ion mass ratio. Since a moving body of size D and velocity v radiates at frequencies of the order of v/D, the generation of Alfvrn waves is important only if D >
(2)
for B = 1 G, o -- 104 m/sec, MJMp = 1 we obtain the condition D > 1 m (except where noted, we shall use Gaussian units). Thus, in the cases of interest for us, the mechanism discovered by Drell et al. is not effective for dusty particles, but can be applied only to macroscopic objects. H o w much energy can be dissipated? If VA is the Alfv6n velocity VA = c
1+
(3)
where P is the plasma mass density (note that the usual definition VA = B/4V~o is valid only in the limit VA < C; see Clemmow and Dougherty, 1969, p. 170), then Drell et al. derived that the energy dissipation rate is B 2 V2
P = - - - - D 2. 27r VA
where B is the field strength in Gauss and
(4)
H o w e v e r , this dissipation occurs only provided three assumptions are verified: (1) we 182
00~9-1035/84 $3.00 Copyright © 1984by AcademicPress, Inc. All rightsof reproductionin any formreserved.
Mi.
BMp'
(1)
* Paper presented at the "Natural Satellites Conference," Ithaca, N.Y., July 5-9, 1983.
10 -4 U
ALFVf~N DRAG FOR JOVIAN SATELLITES are in the linear regime, implying that v VA; (2) the moving body has an internal electrical conductivity tr larger than a critical value O'cr ------cZ/2~rDUA (in the opposite case P is reduced by a factor (1 + o-cflo-)); (3) the plasma is lossless, i.e., collisionfree. Assumption (3) is not valid whenever D < L =- c/top, where tOp is the plasma frequency given by tOp = (4 7re2ne/ me) 1/2
(5)
(ne and me being the electron number density and the electron mass). When D < L, Drell "et al. (Section 4) showed that P must b e reduced by a factor approximately given b y ( L / D ) 2. The Alfvrn drag mechanism was applied by Drell et al. to explain the observed orbital decay of the Echo 1 balloon satellite. In general, it is easy to show that for large artificial structures in high Earth orbit (i.e., for sizes ~,50 m and heights ~-1000 km) the generation of Alfvrn waves can become the most important drag mechanism. A simple order-of-magnitude calculation based upon Eq. (4) yields for a height of 1000 km (B 0.1 G; p - 10 -18 g/cm 3) a semimajor axis decay of - 1 m/day (assuming an area-tomass ratio of - 10 -2 m 2 kg-l). A more exotic application of the same mechanism was proposed by Van Buren (1981), who analyzed the possible orbital evolution of asteroidal objects in the magnetosphere of a neutron star. In the following we shall discuss the case of the natural satellites whose orbit lies in the inner Jovian plasmasphere, and precisely in the zone of Jupiter's rings. Two small satellites have been discovered there by the Voyager probes, i.e., Adrastea (with semimajor axis a = 1.806gj and diameter D -~ 30 km) and Metis (a = 1.792Rj, D -~ 40 kin) (Jewitt et al., 1979; Synnott, 198I). Moreover, a number of moonlets residing in the ring (especially in the outer bright part with 1.72Rj < a < 1.81Rj) and of size D , ~ 1 km have been postulated as sources of the short-lived " d u s t y " material present in the ring (Burns et al., 1980; Griin et al., 1980).
183
Jupiter's plasmasphere at 1.8Rj is characterized by a magnetic field strength B of about 0.7 G (on the equatorial plane; see Acufia and Ness, 1976) and a plasma density p of the order of 10 -20 g cm 3 (Burns et al., 1980, and references quoted therein); the corresponding Alfvrn speed VA is about 2 x 107 m sec -1. Other relevant parameters for the generation of Alfvrn waves, with the notations introduced earlier, are O-cr= 8 x 10 -5 ~-1 m - l / D (km); top -~ 6 x 105 Hz (since ne -- 10 2 c m - 3 ) , implying L -~ 500 m; f~i - 7 x 10 3, 5 X 10 2, 2 x 10 2 Hz, respectively, for H +, O + and S + ions, implying that the minimum satellite size for which the drag mechanism is effective (see Eq. (2)) is in the range 1.2 to 40 m, depending on the involved ion types. Since the magnetic field is corotating with Jupiter's spin period of about 9.9 hr, the relative velocity v will be given b y the difference between the orbital velocity Vorb at 1.8Rj(3.13 x 104 m sec -1) and the field's corotation velocity (2.27 x 104 m sec-~); note that for orbital distances exceeding - 2 . 2 R j, the magnetic field lines would be overtaking a satellite and the drag force would cause its altitude to increase and not to decrease. Now let us restrict ourselves to the case of a conductive (o- ~> O-c~)object, and define an orbital damping time ~" = Eorb/P, where Eorb is the satellite's orbital energy; a significant orbit decay can occur in times -0.1~'. We obtain ,-B"2
U2rb UA
r =--~psD
v2 B2
= 2.8 x 108 ( ~ ) ( ~ _ ~ ) PD s
years,
where p~ is the satellite's density and the latter estimate of ~- has been derived for an orbital distance of 1.8Rj from the center of Jupiter. This lifetime applies only to satellites larger than - 1 0 m, for the reasons stated above; moreover, we have to take into account the effects of collisions in the plasma, and this means that for D < L = 500 m r must be increased by a factor of the order of (500 m/D) 2. In Fig. 1, assuming p~
184
ANSELMO AND FARINELLA
/
tivities in the range 10-8-10 -2 ~-1 m-1 (Schwerer et al., 1971 ; Dermott, 1972; Brecher et al., 1975). Therefore we cannot exclude that the lifetimes of Fig. I are real, even if conductivities lower than O'cr could slow down considerably the orbital evolution. For Adrastea and Metis, O ' c r ~'~ 3 × 10 -6 t f~-~ m -~ and z = 1.7 × 101° years, while for tI ~\ a satellite 100 km across in the same zone we would obtain o'er -~ 8 × 10 -7 f~-l m-i Jog o CA=) and z = 5.6 x 10l° years. These figures suggest that possibly orbital evolution under FIG. 1. Log-log plot of r, the orbital damping time Alfvrn drag has been important for the obfor a Jovian satellite having high conductivity, density served satellites, and in this framework a of 2 g cm -3 and orbital radius of 1.8Rj, VS the satelplausible hypothesis could envisage the lite's diameter D. For D ~> 0.5 kin, the effect of plasma common origin of Adrastea, Metis, and the collisions reverses the slope of the line, which has been dashed in the corresponding transition region. ring material (including the postulated moonlets) from the (tidal or collisional) = 2 g cm -3, we have plotted the orbital breakup of an inward-spiraled, -100-km damping times predicted for bodies of dif- size, and reasonably conductive (chondritic ferent sizes. It is interesting to note that the ?) parent body. Moreover, the Alfvrn drag shortest lifetimes are derived for satellites mechanism could explain why in the ring in the intermediate size range, centered at zone we have objects with D ~ 30 km and about D = 1 km. We shall discuss later the probably objects with D ~< 1 km, but none of intermediate size (since at intermediate possible implications of this result. Clearly the values o f z shown in Fig. 1 are sizes the orbital decay is faster). Note that lower limits, because we assumed o- >> Orcr just the lack of intermediate-size fragments, and neglected the correcting factor (1 + O'er/ which is difficult to reconcile with any reao-). Note that Orcr oc D-~, so that a limited sonable fragment mass distribution, was conductivity could increase the lifetimes used by Bums et al. (1980) as an argument preferentially for the smaller objects. Obvi- against the origin of the ring material from ously we can make no reliable estimate on the breakup of a large parent body. Finally, we point out that at present the the conductivity of the Jovian moons, whose composition is not known. We can orbital mean motions of Adrastea and Metis only try some comparison with the mea- are known to within one part in 106 (Synsured conductivities of some representative nott, 1984), and with the Galileo mission planetary or meteoritic materials, as re- probably an accuracy 100 times better will cently done in a study on asteroids by Ip be achievable over a time span of about 2 and Herbert (1983): while the metallic iron years. This opens the way to the possibility has a conductivity of ~108 ~'~-1 m-I and of measuring directly an eventual orbital various F e x S y minerals are in the range 1- decay of these satellites due to Alfvrn drag. 105 ~-~ m -~ (Parkhomenko, 1967), for silicates like olivine and fayalite the conACKNOWLEDGMENTS ductivity decreases strongly at low We thank D. P. Rubincam and an anonymous reftemperatures, being in general ~10 -8 f~-~ eree for their valuable remarks. Useful conversations m -~ at 100°K (see Dermott, 1970). The most with B. Bertotti, J. A. Bums, S. F. Dermott and V. interesting data are those of carbonaceous Zappala are also gratefully acknowledged. This work chondrites and other chondritic materials, was supported in part by the National Research Counwhich even at -100°K should have conduc- cil of Italy (CNR). l
i
ALFVt~N DRAG FOR JOVIAN SATELLITES REFERENCES ACUlqA, M. H., AND N. F. NESS (1976). Results from the GSFC fluxgate magnetometer on Pioneer 11. In Jupiter (T. Gehrels, Ed.), pp. 830-847. Univ. of Arizona Press, Tucson. BURNS, J. A., M. R. SHOWALTER,J. N. CUZZI,AND J. B. POLLACK (1980). Physical processes in Jupiter's ring: Clues to its origin by Jove! Icarus 44, 339-360. CLEMMOW, P. C., AND J. P. DOUGHERTY (1969). Electrodynamics o f Particles and Plasmas. AddisonWesley, Reading, Mass./London. DERMOTT, S. F. (1970). Modulation of Jupiter's decametric radio emission by Io. Mort. Not. Roy. Astron. Soc. 149, 35-44. DERMOTT, S. F. (1972). The electrical conductivity of Io. Icarus 17, 223-224. DRELL, S. D., H. M. FOLEY, AND M. A. RUDERMAN (1965). Drag and propulsion of large satellites in the ionosphere: An Alfv6n propulsion engine in space. J. Geophys. Res. 70, 3131-3145. GRIJN, E., G. MORFILL, G. SCHWEHM, AND T. V.
185
JOHNSON (1980). A model of the origin of the Jovian ring. Icarus 44, 326-338. IP, W.-H., AND F. HERBERT (1983). On the asteroidal conductivities as inferred from meteorites. Moon Planets 28, 43-47. JEWITT, D. C., G. E. DANIELSON, AND S. P. SYNNOTT (1979). Discovery of a new Jupiter satellite. Science 206, 951. PARKHOMENKO, E. I. (1967). Electrical Properties o f Rocks. Plenum, New York. SCHWERER, F. C., T. NAGATA, AND R. M. FISHER (1971). Electrical conductivity of lunar surface rocks and chondritic meteorites. The Moon 2, 408-422. SYNNOTT, S. P. (1981). 1979J3: Discovery of a previously unknown satellite of Jupiter. Science 212, 1392. SYNNOTT, S. P. (1984). Orbits of the small inner satellites of Jupiter. Icarus 58, 178-181. VAN BUREN, D. (1981). Gravitational scattering of asteroids onto neutron stars as a cause of y-ray bursts. Astrophys. J. 249, 297-301.
Alfven Drag for Satellites Orbiting in Jupiter's Plasmasphere* L. A N S E L M O * AND P. F A R I N E L L A ? *CNUCE, Via S. Maria 36, 1-56100, Pisa, Italy, and ~;Scuola Normale Superiore e Dipartimento di Matematica dell' Universitd di Pisa, Piazza dei Cavalieri 2, 1-56100 Pisa, Italy Received November 28, 1983; revised February 13, 1984 According to a mechanism discovered by S. D. Drell, H. M. Foley, and M. A. Ruderman ((1965). J. Geophys. Res. 70, 3131-3145), a satellite orbiting around a planet having a strong magnetic field and a dense ionospheric plasma dissipates orbital energy via radiation of Alfvrn waves. The dissipation process is effective for objects larger than a minimum size and made of material exceeding a minimum electrical conductivity. It is shown that the corresponding drag effect could have influenced in a significant way the orbital evolution of the small natural moons orbiting inside or in proximity of Jupiter's ring. In particular this mechanism could explain the absence in the ring of objects in the size range from -0.1 to - 1 0 km.
The motion of a c o n d u c t o r across a magnetic field B induces in the conductor itself an electric charge separation canceling the electric field E = (v × B)/c which is seen in the co-moving reference system (here v is the velocity of the conductor relative to the magnetic field and c is the velocity of light). If the body (e.g., a spacecraft or a natural satellite) is moving through a plasma (e.g., a planetary plasmasphere), then according to a physical mechanism described originally b y Drell et al. (1965) the charge can be conducted away via generation of Alfvrn waves. This implies that a dc current flows through the conductor and at the same time some mechanical energy is converted to that of Alfvrn radiation. In this note we intend to show that the corresponding drag effect could be relevant (and possibly measurable in the near future) for the small natural satellites orbiting in the inner plasmasphere of Jupiter. We recall that Alfvrn waves are magnetohydrodynamic disturbances of frequency oJ much less than the ion cyclotron frequency f/i = eB/Mic, i.e., < i 0 4 B ( M p / M i ) Hz,
Mp/Mi is the proton to ion mass ratio. Since a moving body of size D and velocity v radiates at frequencies of the order of v/D, the generation of Alfvrn waves is important only if D >
(2)
for B = 1 G, o -- 104 m/sec, MJMp = 1 we obtain the condition D > 1 m (except where noted, we shall use Gaussian units). Thus, in the cases of interest for us, the mechanism discovered by Drell et al. is not effective for dusty particles, but can be applied only to macroscopic objects. H o w much energy can be dissipated? If VA is the Alfv6n velocity VA = c
1+
(3)
where P is the plasma mass density (note that the usual definition VA = B/4V~o is valid only in the limit VA < C; see Clemmow and Dougherty, 1969, p. 170), then Drell et al. derived that the energy dissipation rate is B 2 V2
P = - - - - D 2. 27r VA
where B is the field strength in Gauss and
(4)
H o w e v e r , this dissipation occurs only provided three assumptions are verified: (1) we 182
00~9-1035/84 $3.00 Copyright © 1984by AcademicPress, Inc. All rightsof reproductionin any formreserved.
Mi.
BMp'
(1)
* Paper presented at the "Natural Satellites Conference," Ithaca, N.Y., July 5-9, 1983.
10 -4 U
ALFVf~N DRAG FOR JOVIAN SATELLITES are in the linear regime, implying that v VA; (2) the moving body has an internal electrical conductivity tr larger than a critical value O'cr ------cZ/2~rDUA (in the opposite case P is reduced by a factor (1 + o-cflo-)); (3) the plasma is lossless, i.e., collisionfree. Assumption (3) is not valid whenever D < L =- c/top, where tOp is the plasma frequency given by tOp = (4 7re2ne/ me) 1/2
(5)
(ne and me being the electron number density and the electron mass). When D < L, Drell "et al. (Section 4) showed that P must b e reduced by a factor approximately given b y ( L / D ) 2. The Alfvrn drag mechanism was applied by Drell et al. to explain the observed orbital decay of the Echo 1 balloon satellite. In general, it is easy to show that for large artificial structures in high Earth orbit (i.e., for sizes ~,50 m and heights ~-1000 km) the generation of Alfvrn waves can become the most important drag mechanism. A simple order-of-magnitude calculation based upon Eq. (4) yields for a height of 1000 km (B 0.1 G; p - 10 -18 g/cm 3) a semimajor axis decay of - 1 m/day (assuming an area-tomass ratio of - 10 -2 m 2 kg-l). A more exotic application of the same mechanism was proposed by Van Buren (1981), who analyzed the possible orbital evolution of asteroidal objects in the magnetosphere of a neutron star. In the following we shall discuss the case of the natural satellites whose orbit lies in the inner Jovian plasmasphere, and precisely in the zone of Jupiter's rings. Two small satellites have been discovered there by the Voyager probes, i.e., Adrastea (with semimajor axis a = 1.806gj and diameter D -~ 30 km) and Metis (a = 1.792Rj, D -~ 40 kin) (Jewitt et al., 1979; Synnott, 198I). Moreover, a number of moonlets residing in the ring (especially in the outer bright part with 1.72Rj < a < 1.81Rj) and of size D , ~ 1 km have been postulated as sources of the short-lived " d u s t y " material present in the ring (Burns et al., 1980; Griin et al., 1980).
183
Jupiter's plasmasphere at 1.8Rj is characterized by a magnetic field strength B of about 0.7 G (on the equatorial plane; see Acufia and Ness, 1976) and a plasma density p of the order of 10 -20 g cm 3 (Burns et al., 1980, and references quoted therein); the corresponding Alfvrn speed VA is about 2 x 107 m sec -1. Other relevant parameters for the generation of Alfvrn waves, with the notations introduced earlier, are O-cr= 8 x 10 -5 ~-1 m - l / D (km); top -~ 6 x 105 Hz (since ne -- 10 2 c m - 3 ) , implying L -~ 500 m; f~i - 7 x 10 3, 5 X 10 2, 2 x 10 2 Hz, respectively, for H +, O + and S + ions, implying that the minimum satellite size for which the drag mechanism is effective (see Eq. (2)) is in the range 1.2 to 40 m, depending on the involved ion types. Since the magnetic field is corotating with Jupiter's spin period of about 9.9 hr, the relative velocity v will be given b y the difference between the orbital velocity Vorb at 1.8Rj(3.13 x 104 m sec -1) and the field's corotation velocity (2.27 x 104 m sec-~); note that for orbital distances exceeding - 2 . 2 R j, the magnetic field lines would be overtaking a satellite and the drag force would cause its altitude to increase and not to decrease. Now let us restrict ourselves to the case of a conductive (o- ~> O-c~)object, and define an orbital damping time ~" = Eorb/P, where Eorb is the satellite's orbital energy; a significant orbit decay can occur in times -0.1~'. We obtain ,-B"2
U2rb UA
r =--~psD
v2 B2
= 2.8 x 108 ( ~ ) ( ~ _ ~ ) PD s
years,
where p~ is the satellite's density and the latter estimate of ~- has been derived for an orbital distance of 1.8Rj from the center of Jupiter. This lifetime applies only to satellites larger than - 1 0 m, for the reasons stated above; moreover, we have to take into account the effects of collisions in the plasma, and this means that for D < L = 500 m r must be increased by a factor of the order of (500 m/D) 2. In Fig. 1, assuming p~
184
ANSELMO AND FARINELLA
/
tivities in the range 10-8-10 -2 ~-1 m-1 (Schwerer et al., 1971 ; Dermott, 1972; Brecher et al., 1975). Therefore we cannot exclude that the lifetimes of Fig. I are real, even if conductivities lower than O'cr could slow down considerably the orbital evolution. For Adrastea and Metis, O ' c r ~'~ 3 × 10 -6 t f~-~ m -~ and z = 1.7 × 101° years, while for tI ~\ a satellite 100 km across in the same zone we would obtain o'er -~ 8 × 10 -7 f~-l m-i Jog o CA=) and z = 5.6 x 10l° years. These figures suggest that possibly orbital evolution under FIG. 1. Log-log plot of r, the orbital damping time Alfvrn drag has been important for the obfor a Jovian satellite having high conductivity, density served satellites, and in this framework a of 2 g cm -3 and orbital radius of 1.8Rj, VS the satelplausible hypothesis could envisage the lite's diameter D. For D ~> 0.5 kin, the effect of plasma common origin of Adrastea, Metis, and the collisions reverses the slope of the line, which has been dashed in the corresponding transition region. ring material (including the postulated moonlets) from the (tidal or collisional) = 2 g cm -3, we have plotted the orbital breakup of an inward-spiraled, -100-km damping times predicted for bodies of dif- size, and reasonably conductive (chondritic ferent sizes. It is interesting to note that the ?) parent body. Moreover, the Alfvrn drag shortest lifetimes are derived for satellites mechanism could explain why in the ring in the intermediate size range, centered at zone we have objects with D ~ 30 km and about D = 1 km. We shall discuss later the probably objects with D ~< 1 km, but none of intermediate size (since at intermediate possible implications of this result. Clearly the values o f z shown in Fig. 1 are sizes the orbital decay is faster). Note that lower limits, because we assumed o- >> Orcr just the lack of intermediate-size fragments, and neglected the correcting factor (1 + O'er/ which is difficult to reconcile with any reao-). Note that Orcr oc D-~, so that a limited sonable fragment mass distribution, was conductivity could increase the lifetimes used by Bums et al. (1980) as an argument preferentially for the smaller objects. Obvi- against the origin of the ring material from ously we can make no reliable estimate on the breakup of a large parent body. Finally, we point out that at present the the conductivity of the Jovian moons, whose composition is not known. We can orbital mean motions of Adrastea and Metis only try some comparison with the mea- are known to within one part in 106 (Synsured conductivities of some representative nott, 1984), and with the Galileo mission planetary or meteoritic materials, as re- probably an accuracy 100 times better will cently done in a study on asteroids by Ip be achievable over a time span of about 2 and Herbert (1983): while the metallic iron years. This opens the way to the possibility has a conductivity of ~108 ~'~-1 m-I and of measuring directly an eventual orbital various F e x S y minerals are in the range 1- decay of these satellites due to Alfvrn drag. 105 ~-~ m -~ (Parkhomenko, 1967), for silicates like olivine and fayalite the conACKNOWLEDGMENTS ductivity decreases strongly at low We thank D. P. Rubincam and an anonymous reftemperatures, being in general ~10 -8 f~-~ eree for their valuable remarks. Useful conversations m -~ at 100°K (see Dermott, 1970). The most with B. Bertotti, J. A. Bums, S. F. Dermott and V. interesting data are those of carbonaceous Zappala are also gratefully acknowledged. This work chondrites and other chondritic materials, was supported in part by the National Research Counwhich even at -100°K should have conduc- cil of Italy (CNR). l
i
ALFVt~N DRAG FOR JOVIAN SATELLITES REFERENCES ACUlqA, M. H., AND N. F. NESS (1976). Results from the GSFC fluxgate magnetometer on Pioneer 11. In Jupiter (T. Gehrels, Ed.), pp. 830-847. Univ. of Arizona Press, Tucson. BURNS, J. A., M. R. SHOWALTER,J. N. CUZZI,AND J. B. POLLACK (1980). Physical processes in Jupiter's ring: Clues to its origin by Jove! Icarus 44, 339-360. CLEMMOW, P. C., AND J. P. DOUGHERTY (1969). Electrodynamics o f Particles and Plasmas. AddisonWesley, Reading, Mass./London. DERMOTT, S. F. (1970). Modulation of Jupiter's decametric radio emission by Io. Mort. Not. Roy. Astron. Soc. 149, 35-44. DERMOTT, S. F. (1972). The electrical conductivity of Io. Icarus 17, 223-224. DRELL, S. D., H. M. FOLEY, AND M. A. RUDERMAN (1965). Drag and propulsion of large satellites in the ionosphere: An Alfv6n propulsion engine in space. J. Geophys. Res. 70, 3131-3145. GRIJN, E., G. MORFILL, G. SCHWEHM, AND T. V.
185
JOHNSON (1980). A model of the origin of the Jovian ring. Icarus 44, 326-338. IP, W.-H., AND F. HERBERT (1983). On the asteroidal conductivities as inferred from meteorites. Moon Planets 28, 43-47. JEWITT, D. C., G. E. DANIELSON, AND S. P. SYNNOTT (1979). Discovery of a new Jupiter satellite. Science 206, 951. PARKHOMENKO, E. I. (1967). Electrical Properties o f Rocks. Plenum, New York. SCHWERER, F. C., T. NAGATA, AND R. M. FISHER (1971). Electrical conductivity of lunar surface rocks and chondritic meteorites. The Moon 2, 408-422. SYNNOTT, S. P. (1981). 1979J3: Discovery of a previously unknown satellite of Jupiter. Science 212, 1392. SYNNOTT, S. P. (1984). Orbits of the small inner satellites of Jupiter. Icarus 58, 178-181. VAN BUREN, D. (1981). Gravitational scattering of asteroids onto neutron stars as a cause of y-ray bursts. Astrophys. J. 249, 297-301.