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75 Chapter 6 GRAVITATIONAL AND CELESTIAL DYNAMICS This chapter includes both a discussion of earth-based obser- vations that do not require the presence of a spacecraft and consideration of experiments in which a spacecraft is an essential component of the system. EARTH-BASED OBSERVATIONS Radar systems now in existence and expected to undergo improve- ment within the next five years, and proposed new radar sys- tems, will be able to range on the principal satellites of Jupiter and Saturn. The high accuracy of such measurements will add to the precision of the ephemerides of at least the four large Galilean satellites of Jupiter and the two largest satellites of Saturn. Interesting questions related to the apparent existence of secular terms in the mean motions of the satellites have arisen, and there is also great interest in the commensura- bility relationships that exist between the mean motions of pairs and triples of satellites. An improvement in the ephemerides may allow new deductions to be made concerning the mechanisms responsible for these effects. One of the forces suspected to be of importance in this respect is the tidal interaction with the planet. The time scale for the evolution of satellite orbits may have been dominated by tidal friction, and new information is thus of considerable value in cosmogonical discussions. Radar reflectivity can provide useful information on the dielectric constants of the surfaces of the satellites, espe- cially if measured at two or more wavelengths. The scatter- ing law for different angles of incidence indicates the sur- face roughness. Satellite rotation rates can be observed through Doppler broadening of the returned signal or through periodic variations in reflected power. Any departure from synchronism between spin rate and orbital motion about the planet would be of great interest, especially in view of the
76 recent knowledge, also obtained by radar, of the resonant but nonsynchronous rotation rates of Venus and Mercury. Occultations of the Gallilean satellites by Jupiter occur fre- quently, and in each case the detailed manner of decay or rise of the reflected radar signal can be detected. From measure- ments of changes in amplitude and phase, information can be obtained concerning the density and structure of the iono- sphere of Jupiter, the existence of an ionosphere on Saturn, and the scale heights of the upper neutral atmospheres of the two planets. This radar information becomes clearer and less ambiguous when results at more than one frequency are avail- able, owing to the different frequency dependence of the refraction produced by the ionosphere and the neutral atmos- phere. A parallel effect is the retardation of the radar signal as it passes out and back through the strong gravitational field of a planet. This effect of general relativity is independent of frequency and is largest when the signal grazes the planet; it then causes an apparent increase in round-trip path length of the signal of ~60 m for Jupiter and ~18 m for Saturn. This retardation is of interest both as a further test of general relativity theory and as a correction that must be taken into account in determining ionospheric and atmospheric refraction. SPACECRAFT EXPERIMENTS Many of the observations described above can be performed more precisely from a spacecraft, either flyby or orbiter, than from the earth. The principal advantages of the space- craft from this point of view are shorter range and variable line of sight with respect to the sun-target line. It is, however, apparent that the spacecraft must be tracked very accurately from the earth, in order that spacecraft-based observations may be properly interpreted. Further, the bi- static mode (reception of both direct and scattered earth radar signals by the spacecraft) should provide useful infor- mation. In addition to improved radar observations of the principal satellites of Jupiter and Saturn, there is the possibility of direct measurement of the motion of the innermost satellite of Jupiter from a nearby spacecraft. Jupiter V, or Amalthea,
77 would make a particularly interesting radar target. It is only l.6 Jovian radii above the surface of the planet, so that its orbit will be especially sensitive both to departures of Jupiter's gravitational field from spherical symmetry and to tidal interaction. Since the orbit of Amalthea is slightly inclined to the equatorial plane of Jupiter, it may be possible to detect a lack of symmetry between the northern and southern hemispheres of Jupiter. Such a "pear shape" of the earth has been discovered from observations of artificial satellites in inclined orbits. Secular changes in the orbit of Amalthea would give valuable information concerning tidal elasticity and friction of Jupiter. It is even possible that extremely precise Doppler radar observations of Amalthea could detect a gravitational anomaly arising from the Great Red Spot of Jupiter. For example, if we assume that the Red Spot is an island of density 0.0l g cm~-' floating on a substrate of zero shear strength and twice this density, it is equivalent to a somewhat localized dipole source of gravitational field, with positive mass on top and negative underneath. With an assumed thickness of 20,000 km, it would then give Amalthea a downward velocity component of roughly 4 cm sec~l each time it crosses the longitude of the Red Spot. This assumed gravitational anomaly of the Red Spot would also affect the spacecraft trajectory. Since the spacecraft speed is comparable with that of Amalthea, its travel time near the Red Spot will also be comparable and the change in vertical velocity component will be roughly the same as that of Amalthea for the same altitude. For other altitudes, the effect is approximately inversely proportional to the cube of the altitude. If the spacecraft trajectory is chosen so that it is oc- culted by the planet, all the effects mentioned earlier â of refraction by the ionosphere and the neutral atmosphere and of general relativistic retardation -- can be measured. There is also a very much smaller general relativistic effect which arises from the rotation of the planet. This is a "dragging" of the inertial frame by the rotating massive planet, in the neighborhood of the planet. It is proportional to the planet's angular momentum and, hence, could, in prin- ciple, provide a measure of the moment of inertia if rigid- body rotation is assumed. The effect consists of a slight
78 speeding up of the radar signal that passes on one side of the planet in the equatorial plane and an equal retardation on the other side. Unfortunately, the pathlength change is extremely small, only l0~^ cm for Jupiter and less for Saturn -- far too small to be of observational interest. Because of the duration of a spacecraft mission to the out- er planets and the motion of the earth, the spacecraft will be on the opposite side of the sun from the earth several times while en route. These opportunities can be used to measure the solar corona plasma and the general relativistic effects of the sun's gravitational field, in much the same way as just described for occultation of the spacecraft by Jupiter or Saturn. All these effects are much larger in the case of the sun; the apparent round-trip pathlength is increased approximately 60 km because of the gravitational field, the inertial frame dragging effect caused by solar rotation amounts to a change in pathlength on the order of l cm. Finally, it is worth mentioning a new kind of test of the equivalence principle that may be possible from a precise measurement of the orbital parameters of Jupiter. The EStvb's - Dicke experiments show that the ratio of gravita- tional to inertial mass is the same for a wide variety of materials, with a precision of one part in l0 . Since these materials differ in chemical composition, their impor- tant difference is in nuclear binding energy. Thus, existing experiments show that the decrease in mass of atomic nuclei in comparison with their component protons and neutrons â the mass defect -- affects equally the inertial mass of the material and the gravitational force exerted on it by the earth and the sun. The question remains whether the mass defect of a massive object caused by the gravitational attraction of its parts will affect the object's inertial and gravitational masses differently. Such a departure from the equivalence principle is best looked for in an object of large gravitational self- energy, and Jupiter is the most likely candidate. A lower limit for the ratio of the mass defect to the total mass is obtained if Jupiter is assumed to be a homogeneous sphere, in which case this ratio is l.2 x l0~8. If the entire mass defect were effective in contributing to Jupiter's inertia and none to the force of gravity exerted on it by the sun, or vice versa, the relation between orbital radius and period
79 would be slightly different from that predicted by Kepler's third law in conjunction with the orbital parameters of the other planets. For example, for given known period, the fractional change in mean distance from the sun would be one third the above ratio, or 0.4 x l0~ . This would result in a discrepancy in the radius of Jupiter's orbit of 3.l km, if the lower limit for the mass defect obtained above is entirely effective as a contributor to either the gravitational or inertial mass of Jupiter but not to both. Such an effect might be detected in detailed studies of the scale of the solar system based on radio tracking of spacecraft and radar and optical observations of the planets. RECOMMENDATIONS l. Existing earth-based radars should be improved so that precise observations of the principal satellites of Jupiter and Saturn can be carried out with the objectives of improving their ephemerides, determining their radar reflec- tivities, and observing their occultations. 2. Spacecraft to Jupiter and the outer planets should be tracked with the greatest possible precision, in order to improve the ephemerides of the satellites of Jupiter and Saturn and also of Jupiter itself. 3. Spacecraft should be used to study the motion of Amalthea, the innermost satellite of Jupiter. 4. At least one spacecraft trajectory should be planned to be occulted by Jupiter. 5. Advantage should be taken of the occultations of the spacecraft by the sun during the mission.
