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where Re and Rp are the equatorial and polar radii, respectively. The other difference between the planetocentric and planetographic systems is that while planetocentric longitudes run eastwards, planetographic longitudes run in the direction opposite to the rotation. Hence, for planets which have prograde spins, the longitudes run westwards, while for planets with retrograde spins, such as Venus and Uranus, they run eastwards.

Measurements of the J-coefficients of the giant planets, by observing the gravitational perturbations acting on satellites, rings, and passing spacecraft, can be used to determine the distribution of mass in the interior. In addition to the J-coefficients themselves, we can tell even more about the interior of the planets if we can measure, or estimate, the polar moment of inertia C. To directly measure C requires that we observe the precession of the rotation axis, which is not possible for

Figure 2.8. Definition of the planetographic and planetocentric latitude systems. Here 0 is the planetocentric latitude, and is the planetographic latitude.

the giant planets. However, C may be calculated if we can measure the mass M of the planet, its equatorial radius Re, its sidereal rotation period T, and the /2-coefficient. This calculation assumes that the interior of the planet is in hydrostatic equilibrium (i.e., that the interior has no shear strength and responds to tidal forces essentially as a liquid). The moment of inertia ratio C/MR2 is particularly useful since it indicates the degree of mass concentration towards the center. For a hollow sphere (Jones, 2007) the ratio is 2/3, while for a sphere with uniform density it is 0.4, and for a sphere where all the mass is at the center it is 0. The gravitational constants of the giant planets are listed in Table 2.5.

Table 2.5. Gravitational and magnetic properties of Earth and giant planets.

(km)

J2 (x10-2)

J4 (x 10-4)

J6 (X10-4)

C/MR2

Magnetic dipole moment (Am2)

Earth

6,378

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