NATIONAL AERONAUTICS AND SPACE ADMINISTRATION eport 1132-17'523 Compute Photometric Magnitudes of the Planets and Their Satellites G. Pace JET P N LABORATORY CA1~~~RN~AINSTITUTE OF TECHNOLOGY PASA D E MA, C A 18 FOR N IA February 15,1971 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION G. Pace February 15,1971 Prepared Under Contract No. NAS 7-100 National Aeronautics and Space Administration The work described in this report was performed by the Guidance and Control Division of the Jet Propulsion Laboratory. ...111 Thanks go to Janis Beltz for coding and checking out the subroutine. ......................... 1 ................ 1 ......................... 2 1W . ~rogra~Usage en Logie .................... 2 Referenees ........................... 5 ppendix Subroutine UBV Flow Diagram and Listing ............ 6 1 . Planet and satellite body numbers and photometry data ........ 3 2 . Values for Am = -2.5 log rP, (4) ................3 Figures 1 . Observational geometry .................... 2 2 . Variation of magnitude with phase angle for the planets and their moons ...4 ct This computer subroutine computes the visual, blue and ultraviolet photometric magnitudes of the planets, their natural satellites, and the sun at varying observa- tion distances and phase angles. Currently available observational magnitude and phase function data are stored in the program and used in the computation. wte Photometric Ma lanets and Their . lntroduction in AU, r, is the observer-body distance in AU, and a, is the visual phase function dependent on the phase angle $J Design and performance evaluation of optical sensors where 0 5 + 5 180 deg. The phase angle is the sun- and instruments for planetary missions requires the body-observer angle. All logs are to the base 10. Figure 1 knowledge of planet and moon brightness. A computer illustrates the observational geometry. subroutine has been written to calculate the Johnson and Morgan (Ref. 1) visual (V), blue (B), and ultraviolet (U) photometric magnitudes of the planets, all their known For the sun the visual magnitude is given by: natural satellites, and the sun. V = V, f 5 log ro (2) isual where V(1,O) is replaced by V, the visual magnitude of the sun at one AU and r, is the sun-observer distance The visual magnitude of a planet or satellite is given in AU. by: 1 V = V( 1,O) + 5 log rsro - 2.5 log % (+) (1) The above equations are valid only for large planet- observer distances, typically greater than twenty planet where V( 1,O) is the visual magnitude at one astronomical radii. For distances closer than this, the phase angle unit (1 AU = 149, 597, 893 km) from the sun and ob- varies over the surface of the planet and an integration server and 0 deg phase angle, r8 is the sun-body distance technique is required. I is done. Although the indexes do vary with phase, there 'n' are only limited data available, and thus it is not mod- eled in the program at this time. Where no color infor- mation was available, a reasonable value has been stored in the program. These assumed values are noted by parentheses in Table 1. Uncertainties in the color indexes are due to the same factors that affect V(1,O). Table 2 indicates how the visual magnitude varies with phase angle. The quantity -2.5 log aW (+) is also given by Am, and it is this quantity that is stored in the program. The phase function data have been determined empirically from observational data or from theoretical Fig. 1. Observational geometry considerations. For planets and moons outside the earth's orbit, observations can only be made over a limited range in phase angle. Mars can only be observed from 111. Stored Data the earth up to about 48 deg phase angle, and the value Data stored in the program are listed in Tables 1and 2. of Am must be extrapolated as indicated by the paren- The data were obtained from various references and theses in Table 2. Since the phase angle of the outer these are indicated by the numbers in parentheses in planets and their moons never exceed more than a few Table 1 and in the column headings of Table 2. degrees as seen from the earth, a theoretical phase func- tion must be assumed. The same phase function has been assumed (Ref. 2) for the larger planets with optically Table 1 lists the object, its body number as assigned thick atmospheres; Jupiter, Saturn, Uranus and Neptune. in the program, V(1, 0), the B-V and U-B color indexes, Since the size of Pluto is closer to the size of Mars, the and QW the visual phase function assumed as identified Mars phase function has been assumed for Pluto. Since by Table 2. The values for V(1,O) are average values the phase function of the earth's moon is the only one since actual magnitude can vary with the variation in that has been accurately observed over all phase angles, the sun's magnitude or with changing features due to it has been assumed as the phase function for all the planet or moon rotation, seasonal variations, atmospheric moons at this time. conditions, or other surface changes. This variation can be as large as two magnitudes as is the case with Iapetus (Ref. 2). The value for Saturn is for "no-rings'' as the Extrapolated values of Am at 180 deg phase, in Table 2, actual magnitude varies with the changing aspect of are given to allow interpolation in the program. The the rings. An empirical formula (Ref. 2) for the change actual magnitude of a planet or moon at 180 deg phase in magnitude due to the rings is would be a function of the observer-body distance, the sun-body distance, the planet or moon radius and the atmospheric properties of the planet or moon. These AV = -2.60 sin B + 1.25 sin2,B(0" 5 < 27") (3) factors would determine if a halo were visible or not. Thus, care should be used when interpreting the pro- where B is the saturnicentric latitude of the observer. gram output when the phase angle is within a few de- grees of 180 deg. Additional variations in the values for V( 1,O) are pos- sible due to observational uncertainties. Since not all the planets can be observed at exactly 0 deg phase angle, As a matter of interest Am is plotted for all the planets some uncertainty is possible when extrapolating to 0 deg. and moons in Fig. 2. Some of the dimmer moons have only been observed photographically, and errors may be introduced when converting to photometric magnitudes. e Note that constant values of the color indexes B-V and The subroutine is coded in Fortran V for use on U-B are stored in the program and that no computation the JPL Scientific Computing Facility Univac 1108 Visual Color indexes Body I Visual Color indexes Objecl magnitude Body number Object magnitude V(1,O) 8-V number W1,O) B-v U-8 111. Titania - 7.03 4- 1.30 (2) 0.62 0. Sun 0.00 -26.74 (6)& 0.63 0.14 (2) IV. Oberon - 7.04 + 1.49 (2) 0.65 1. Mercury - 1.oo - 0.42 (3) 0.97 (0.4) (3) 1 V. Miranda -7.05 + 3.8 (2) (0.8) 2. Venus -2.00 - 4.41 (3) 0.82 0.50 (2) 2 8. Neptune -8.00 - 6.87(2) 0.41 0.21 (2) 1. Triton -8.01 - 1.16(2) 0.77 0.40 (2) 3. Earth - 3.00 - 3.87 (2) 0.2 (0.0) (4) 3 11. Nereid - 8.02 + 4.0 (2) (0.8) (0.4) 1. Moon -3.01 + 0.21 (2) 0.92 0.46 (2) 6 9. Pluto - 9.00 - 1.01 (2) 0.80 4. Mars -4.00 - 1.73 (5) 1.33 0.63 (3) 4 1. Phobos - 4.0 1 +12.1 (2) 0.6 (0.3) (2) 6 11. Deimos -4.02 4-13.3 (2) 0.6 (0.3) (2) 6 5. Jupiter -5.00 - 9.25(2) 0.83 0.48 (2) 5 Table 2. Values for am = -2.5 log (41) 1. lo -5.01 - 1.90 (2) 1.17 1.30 (2) 6 - 11. Europa -5.02 - 1.53 (2) 0.87 0.52 (2) 6 Phase functions& 111. Ganymede -5.03 - 2.16(2) 0.83 0.50 (2) 6 Phose tingle, IV. Callisto -5.04 1.20 (2) 0.86 0.55 (2) 6 1 2 3 4 5 6 - des! (Ref. 3) (Ref. 3) (Ref. 3) (Ref. 5) (Ref. 2) (Ref. 3) V. Almalthea -5.05 4- 6.3 (2) (0.8) (0.4) 6 0 0.000 0.000 0.000 0.000 VI. Hestia -5.06 + 7.0 (2) (0.8) (0.4) 6 0.000 0.000 10 .355 .139 .133 VII. Hera -5.07 + 9.3 (2) (0.8) (0.4) 6 .340 (.016) .280 20 .667 .291 VIII. Poseidon -5.08 +12.1 (2) (0.8) (0.4) 6 .271 .510 (.056) .564 30 .950 .451 IX. Hades -5.09 +11.6 (2) (0.8) (0.4) 6 .420 .659 (.127) 345 40 1.210 .630 X. Demeter -5.10 +11.9 .(2) (0.8) (0.4) 6 .580 311 (.215) 1.131 50 1.471 1.406 XI. Pan -5.1 1 4-11.4 (2) (0.8) (0.4) 6 320 559 (1.000) (.327) 60 XII. Andrastea -5.12 +12.1 (2) (0.8) (0.4) 6 1.726 1.031 .952 (1.200) (.468) 1.690 70 2.010 1.251 1.165 (1.410) (.649) 2.003 6.