On that date Mercury's

solar phase angle was 87[degrees] and its distance from the Sun was 0.45 au according to the website https://ssd.jpl.nasa.gov/horizons.cgi.

Both the

solar phase angle of Saturn, [alpha] and the tilt of the ring plane, B, were changing during the time period covered in Table 1.

In both equations, Rm is the measured R filter brightness; a, b, c and d are coefficients to be determined and a is the

solar phase angle. In equation 4, k is the fraction of the Moon's disk which is illuminated as seen from Macon, Georgia and r and [nth root of (term)]] are defined previously.

(I have defined b as the square root of the absolute value of the product of the Saturnicentric latitude of the Earth and of the Sun; b is a latitude that is always within about 27[degrees] of Saturn's equator.) The selected

solar phase angle coefficient, in units of magnitudes per degree are [c.sub.B] = 0.029 [+ or -] 0.009, [c.sub.V] = 0.025 [+ or -] 0.005, [c.sub.R] = 0.024 [+ or -] 0.005 and [c.sub.I] = 0.018 [+ or -] 0.006.

The selected

solar phase angle coefficients (in magnitudes/degree) are: 0.041 [+ or -] 0.006, 0.034 [+ or -] 0.005, 0.022 [+ or -] 0.007 and 0.027 [+ or -] 0.007 respectively.

11, 2007 (

solar phase angle = 0.15[degrees]) were 0.19 and 0.06 magnitudes for the B and V filters respectively.

The

solar phase angle and the measured magnitude values are listed in the fourth and fifth columns.

The normalized magnitudes of Saturn for a ring tilt angle of 22[degrees] are: B(1,0) = -8.55 [+ or -] 0.01, V(1,0) = -9.60 [+ or -] 0.01, B(1,0) = -10.27 [+ or -] 0.01 and I (1,0) = -10.47 [+ or -] 0.01; the corresponding

solar phase angle coefficients are: [c.sub.B] = 0.027 [+ or -] 0.006, [c.sub.V] = 0.021 [+ or -] 0.005, [c.sub.B] = 0.020 [+ or -] 0.005 and [c.sub.B] = 0.022 [+ or -] 0.005.

The normalized magnitudes, at a ring tilt angle of B = 26.5[degrees], were: B(1,0) = -8.75[+ or -]0.02, V(1,0) = -9.77[+ or -]0.01, R(1,0) = -10.43[+ or -]0.01 and I(1,0) = -10.65[+ or -]0.01 while the corresponding

solar phase angle coefficients were: [c.sub.B] = 0.045[+ or -]0.007, [c.sub.V] = 0.035[+ or -]0.005, [c.sub.R] - 0.031[+ or -]0.002 and [c.sub.I] = 0.027[+ or -]0.005.

As in previous studies, the normalized magnitude of Saturn at

solar phase angle [alpha], X(1, [alpha]), was evaluated as in Schmude and Hallsworth [9] except that the "0.743" in equation [2] of that paper has been replaced by 0.851 which corresponds to a ring tilt of 24[degrees] instead of 20[degrees].

The measured normalized magnitudes of Saturn, extrapolated to a

solar phase angle of 0[degrees], are: -8.53[+ or -]0.02, -9.57[+ or -]0.03, -10.26[+ or -]0.02 and -10.46[+ or -]0.04 in the B, V, R and I filters respectively.

The selected normalized magnitudes for Saturn are: B(1,0) = -8.45[+ or -]0.02, V(1,0) = -9.44[+ or -]0.01, R(1,0) = -10.10[+ or -]0.02 and 1(1,0) = -10.35[+ or -]0.02 while the selected

solar phase angle coefficients for the B, V, R and I filters are: 0.047[+ or -]0.008 0.035[+ or -]0.002, 0.038[+ or -]0.009 and 0.040[+ or -]0.009 respectively.