The inclination of orbit, equatorial radius, and escape velocity are subject to the t location-scale distribution, which contains the scale parameter [sigma], the location parameter [mu], and the shape parameter v.
From our discussion on the t location-scale distribution in Carme group, it is easy to understand the distribution inference of semi-major axis, mean orbit velocity, equatorial radius, surface gravity, and escape velocity in the Ananke group (see Table 3).
Now, we try to predict the equatorial radius of the Erinome.
For a spheroidal drop [r.sub.0] = 0 corresponds to the axis of rotation and [r.sub.1] is the equatorial radius, with a vanishing slope [f.sub.r] = df/dr at r = 0 and a tangent angle [psi], defined by tan [psi] = [f.sub.r], of [psi] = -[pi]/2 at r = [r.sub.1] where f ([r.sub.1]) = 0.
The equatorial radius [r.sub.E] decreases monotonically and the polar radius [z.sub.P] increases monotonically with increasing rotation rate, consistent with the imposed constraint of equal volumes for the family.
The equatorial radius is [r.sub.E] [approximately equal to] 0.5[R.sub.0], and the prolate solution is elongated enough that near its midsection (r [approximately equal to] [r.sub.E]) the eigenmode is approximately sinusoidal with a computed wavelength of 2[pi]/k = 0.6124[R.sub.0].
On Saturn, solid diamond should exist from about 6,000 to 36,000 km below the cloud tops, reaching more than halfway down into the planet (Saturn's equatorial radius
is 60,000 km).
On page 223 of the Supplement, the semi-duration of the total or annular phase is given as [L.sub.2]/n, where [L.sub.2] is the radius of the umbra (which term applies to both total and annular eclipses) at a height Z above the fundamental plane, and n is the speed of the shadow (my emphasis), both reckoned in units of the Earth's equatorial radius. (Time = distance/speed).
Multiplication by 6378, being the equatorial radius of the Earth in km, followed (if hourly variations are used for the derivatives) by division by 3600, the number of seconds in one hour, gives the result in km per second.
The equatorial radius
(r) for the bodies is divided by the Schwarzschild's radius ([r.sub.schw]) to obtain the reduction ratio.
The centre of the lunar umbra in the fundamental plane has the coordinates (x,y) in units of the equatorial radius of the Earth.
All points on the Earth's surface satisfy the geodetic equation [X.sup.2] + [Y.sup.2]/[p.sup.2] + [Z.sup.2] = 1, where p is the geocentric distance of the poles in units of the equatorial radius of the Earth.