Recent measurements of planetary dimension

Reese, E. J.

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NEW MEXICO STATE UNIVERSITY
	 7
LAS CRUCES, NEW .MEXICO 88001
AREA 505 646-2614
Observatory
MEASUREMENTS OF PLANETARY DIMENSIONS
E. J. REESE
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(CATEGORY)
The Observatory'"
New Mexico State University
Las Cruces, New Mexico 88001
14 15 707
-June 1969
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Supported in part by NASA Grants NGL 32-003-001 and NGL.32-003-027.
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MEASUREMENTS OF PLANETARY DIMENSIONS
E. J. Reese
The Observatory
New Mexico State University
Las Cruces, New Mexico 88001
INTRODUCTION
Some recent measurements of planetary dimensions are summarized in this
note. The results are based on measurements of good quality photograph-. with
a Mann measuring machine. The techniques used were essentially the same as
those used by W. H. Wright (1925) and others; however, a few variables which
were of concern to Wright have been eliminated. A good background to the
problems involved in measuring planetary images can be found in an article
and its accompanying references by R. A. Wells (1965).
The photographic plates used in this program were exposed at the f:75
Cassegranian focus of the NMSU 61-cm reflector. The all-mirror optical
system of this instrument provides a plate scale which is the same for
light of all wavelengths. The plate scale has 'been determined by photog.-
raphing several pairs of stars in the Pleiades cluster whose separations
are known with great accuracy. The photographic plates were Eastman
spectroscopic plates, and were developed in a low-contrast, fine-grain
developer: UFG for Jupiter and HC 110 for the other planets. The vari.-
ous spectral regions were isolated with the aid of Schott filters. Planets
2.
having bright 1j1bs were given normal exposures which produced images
having an optical density of about 0.60 above the plate background.
Jupiter, which has pronounced limb darkening in most wavelengths, was
given one and one-half times its normal exposure to obtain images having
an optical density of about 0.90. Photographs of the outer planets used
in this work were taken only within a very few days of opposition to
avoid real and photographic ph.
-se effects.
The interpret, , tion of the position of the true limb of the planet on
its photographic image is, of course, the crux of the problem. The writer's
technique has been to bring the micrometer web in until it appears solidly
tangent to the limb of the planet. A measurer seems to acquire a :sub-
conscious ability to counteract the small effects of irradiation (turbidity)
on images exposed in the normal to twice normal range by setting the micro-
meter web a little "harder" against the edge of a dense image than a less
dense image. In all cases the tendency is to set the web at the point of
maximum contrast. Irradiation from the limb of blue and ultraviolet images
of the outer planets causes the point of maximum contrast to be halfway
between the outermost edge of the image and the point inside the limb where
maximum intensity is attained. On red and infrared images, however, limb
darkening counteracts irradiation and the point of maximum contrast lies
much nearer the extreme outer edge of the image. This technique should
prevent the loss of limb in red light, and suppress the effects of ir-
radiation in blue and ultraviolet light. Using this method of measuring,
the diameter of Mars in blue light is a little less than 3% larger than it is
in red light; however, when the micrometer web is set on the extreme outer
x
3.
edge of both the blue and red images, the diameter in blue light is nearly
7% larger.
When converting diameters in seconds of arc at unit distance to diameters
in kilometers, the unit distance is taken as 149,600,000 kilometers.
Since unknown systematic errors may be larger than the accidental
measuring errors, the standard deviations given herein may not be a reliabl..
indication of the accuracy of the measurements.
PLATES AND FILTERS
Plate Filter 'Wavelength Planet
II- 0 UG - 2 3700 Jupiter, Saturn
III-0 UG-2 3700 Venus
III-0 N . F. 4300 A Jupiter, Saturn
III-0 GG-13 4400
O
A Mars, Venus
III-G GG-14 5500 A Jupiter, Saturn
III-G OG - 5 5500
O
A Venus
III-F OG-2 6200 A Jupiter, Saturn
IV-E OG - 2 6400
O
A Mercury, Mars, Venus
I-N RG-5 7900
O
A Jupiter, Saturn
MERCURY
Date	 Wavelength	 Diameter at unit distance	 Diameter and S.D.
O
1968, May 25
	 6400 A ( red)	 6:1723	 42876 ± 25 km
O
1968, Oct 19
	 6400 A (red)
	 6.690	 4,852 + 11
m^'
4.
The measured diarr.3ter of Mercury was the diameter joining the cusps. For
comparison, the diameter adopted by the American Ephemeris is 4,845 km. The
diameter obtained by radar measurements (O'Handley, 1969) is 4,878.2 + 1.0 km.
VENUS
The diameter of Venus was measured under two different conditions of
illumination: 1. Near dichotomy in February 1969 when the phase angle was
near 90°. These photographs were given normal exposure. 2. Near the inferior
conjunctions of 1967 (Fig. 1) and 1969 (Fig. 2) between phase angles 151 0 and
170° when the thin crescent subtended considerably more than a semicircle.
These photographs were exposed to give the sky background an optical density
of about 0.6 so that the faint extensions of the horns would be recorded to
best advantage. Since the illuminated crescent must have been extremely
thin along the measured diameter connecting the horns, it was assumed to
have no thickness at all, and the micrometer web was set to bisect the thin
rim of light at each limb. Thus, these measurements should be free from any 	 -
i
effects of irradiation (Smith, 1964).
VENUS, NEAR DICHOTOMY (FEBRUARY, 1969)
Wavelength
	
Diameter at unit distance
	
Diameter and S. D.
0
6400 A (red)
	
16'.'860
	
12,228 ± 8 km
0
4400 A (blue)
	
16.890
	
12,250 ± 18
0
3700 A (UV)
	
16.924
	
12, 275 ± 15
VENUS, NEAR INFERIOR CONJUNCTION (1967)
Wavelength
0
7900 A (infrared)
6400 A (red)
5500 A (green)
Mean
Diameter at unit distance
16':911
16.893
16.918
16':904
Diameter an4 S. D.
12 0 265 ± 13 km
12,252 ± 11
12,270 + 17
12 0 260 t 8 km
VENUS NEAR INFERIOR CONJUNCTION (1969)
5.
Wavelength
0
7900 A (infrared)
0
6400 A (red)
0
5500 A (green)
0
3700 A (ultraviolet)
Mean
Diameter at unit distance
161.1901
16.901
16.900
16.913
16'.'902
Diameter and S. D.
12 0 258 t 8 km
12,258 ± 6
12,257 ± 8
12 2 267t 8
12 1 259 + 4 km
The measured diameter of the scattering layer in the atmosphere of Venus
near inferior conjunction is about 30 kilometers greater than the diameter of
the reflecting layer in red light near dichotomy. This suggests that the
middle of the scattering layer is about 15 kilometers above the opaque :loud
deck. The diameter of the solid surface of the planet obtained from radar
measurements (Melbourne, 1968), is 12,111.6 km. The top of the opaque cloud
deck at dichotomy would be 58 kilometers above the solid surface.
MARS (15 APRIL 1967)
Wavelength	 Diameter at unit distance
	
Diameter and S. D.
0
6400 A (red)	 91:336
	
6,771 + 4 km
0
4400 A (blue)
	 9.603
	
6,965 ± 19
The measured diameter was inclined about 25° to the planet's equator
to avoid very bright cloud-like areas on the equatorial limb in photographs
taken in blue light. Figure 3 illustrates the difference in size between
the blue and red images of Mars. The writer feels rather confident that
the difference in size is too great to be explained in its entirety by
irradiation and turbidity on photographs taken in blue light. Loss of the
77:1
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6.
true limb due to limb darkening in red lio . !it seems more probable. Opposed
to this, however, is the fact that the measurad diameter of Mars on photo-
graphs taken in red light is very near the generally accepted value. The
measurements make the radius of the blue images 97 ± 10 km greater than the
radius of the red images.
in order to test the effects of irridation and turbidity on the photographic
emulsions used in taking the photographs of Mars in red and blue light, Thomas
Kirby and Susan Dean made a number of photographs of the full moon with various
exposures using the same or similar photographic plates and filters that were
used for Mars. The photographs of the moon were taken at the primary focus
of a 5-inch reflector of 20.3 inches focal length and gave images of the moon
that were comparable in size to images of the planets taken with the 61-cm
reflector. Measurements of the images of the moon photographed in red and
blue 1.i-ht revealed no difference in diameter whatsoever, and this is rather
convincingly illustrated in Figure 4. Also, there was no appreciable increase
in diameter of the images of the moon in either red or blue light as the optical
density of the images increased from 0.44 to 0.84. These results strongly
indicate that turbidity and scattering in the blue emulsion were not responsible
for the larger images of Mars in blue light.
The diameter of Mars adopted by the American Ephemeris is 6,790 km. The
diameter obtained by radar measurements (Melbourne, 1968), is 6,750.6 km.
JUPITER (OPPOSITION, 1969)
Equatorial diameter 	 Polar diameter
I
Wavelength
O
7900 A (infrared)
O
6200 A (orange)
O
2500 A (green)
O
4300 A (blue)
O
3700 A (ultraviolet)
Unit distance Kilometers
	
Unit distance Kilometers Oblateness
196':203 142,302+62 183:'490 1332082+81 0.0648
195.843 142,041±87 182.888 132,645+63 0.0662
195.964 142,129+94 182.656 132,477+132 0.0679
197.486 143,233±38 183.959 133,422+86 0.0685
197.518 143,256+58 183.887 133,370+76 0.0690
7.
The equatorial diameter of Jupiter measures about 1% larger in blue light
than in orange light. Photographs taken in rapid succession in red and blue light.
when the satellites Io and Europa are being occulted by the limb of Jupiter, indicate
that at least part of this apparent difference in diameter is caused by a loss of
limb in red light. The measured oblateness of the planet remains greater in blue
light than in red light by a nearly constant ratio even when the optical densities of
the images are increased two or three times.
The diameters of Jupiter adopted by the American Ephemeris are 142,837 km
for the equatorial diameter, and 133,322 km for the polar diameter. These
ephemeris diameters give the planet an oblateness of 0.0667.
SATURN (OPPOSITION, 1965)
Wavelength
O
7900 A (infrared)
O
b. ) A (orange)
O
5500 A (green)
O
4300 A (blue)
Equatorial diameter Polar diameter
Unit distance Kilometers Unit distance	 Kilometers Oblateness
166 1.759 1202947 --- --- ---
166.658 1200874+123 147':285 106,823+162 0.1132
166.834 1210002+151 148.752 107,887+210 0.1084
167.106 1210199+119 149.856 108,688+212 0.1032
Unlike Jupiter, the oblateness of Saturn appears to increase with increasing
wavelength.
The diameters of Saturn adopted by the American Ephemeris are 120,875 km
for the equatorial diameter, and 108,168 km for the polar diameter. The
ephemeris diameters give Saturn an oblateness of 0.1051.
8.
SATURN'S RINGS (OPPOSITION,	 1968)
Diameter at Diameter Ratio Ratio
Object unit distance in kilometers	 (A (outer) : 1) (Cassini a 1)
Ring A, outer edge 376 1;756 2739254 + 80 110000 1.1421
Ring A, inner edge 335.480 243,317 ± 134 0.8904 1.0170
Cassini';, Division 329.869 2390248 + 110 0.8755 1.0000
Ring B, outer edge 324.259 235,179 ± 117 0.8606 0.9829
Ring B, inner edge 252.883 183,411 t 160 0.6712 0.7666
Ring C, inner edge 208.172 150,983 t 328 0.5525 0.6310
Since the dimensions of Saturn's rings revealed no appreciable dependence
on wavelength, the measurements made in infrared, orange, green, and blue light
were avcrapcd together. Measurements of Ring C, however, were made only in blue
and green li f "ht since that ring appeared to be considerably brighter at the
shorter wavelengths. From these measurements, the width of Cassini's Division
is 4069 km. Ring C was measured only on photographs that were given twice the
normal exposure, while the other rings were measured on photographs given a
normal exposure.
JUPITER'S GREAT RED SPOT
Although somewhat out of context, this note will be concluded with a brief
summary of the changing dimensions of Jupiter's Red Spot since it became a
prominent object in 1878. Most references to the length of the Red Spot in
astronomical publications give such values as 30,000 miles and 40,000 kilometers.
Such values were occasionally applicable to the Red Spot prior to 1930; however,
during the last 40 years the mean length has been 29,800 kilometers (18,500
miles) and the mean width about 13,000 kilometers (8,000 miles).
I low
^y
^: L
i
Q	 3	
x.:3
F 	 ,=3*
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DIMENSIONS OF JUPITER'S RED SPOT
9.
Interval	 s" Length Width Source
1879-82	 -24°3 33 0.7 38,670 km 11 0.6	 13,020 km 1
1887-88	 -24.0 33.3 38,300 13.0	 14,580 2
1890-92	 -23.9 33.0 37,980 12.2
	
13,680 3
1893-97	 -23.9 31.6 36,370 ---	 ---- 3
1914	 -22.3 27.5 31 9 980 11.0	 12,280 4
1918-20	 -20.6 31.5 37 9 01C ---	 --- 5
1925-28	 -23.3 29.0 33,510 ---	 ---- 5
_325-30	 -24.0 31.9 36,690 13.0	 14,580 3
1930-39
	 -21.8 26.2 30,550 ---	 ---- 5
1930-39	 -21.9 28.3 32,400 11.2
	
12,490 4
1940-49	 -23.7 25.5 29,400 ---	 ---- 5,6
1950-59	 -23.0 25.7 29,750 ---	 ---- 5,6
1960-66	 -22.5 24.1 28,000 ---	 ---- 6
1960-69	 -22.5 24.2 28,100 12.2	 13,630 7
*Zenographic latitude of the center of the Red Spot.
The lengths and widths of the Red Spot tabulated above were obtained from
the following sources:
1.	 Peek,	 B.	 M.	 (1958). "The Planet Jupiter." Chapter 15. Macmillan, New York.
2.	 Williams,	 A.	 S. (1909). "Zenographical Fragments, Volume II." Taylor and
Francis, London.
3.	 Measurements of L.ck Observatory photopi-aphs by H. G. Solberg and E. J.
Reese.
4.	 Measurements of- various photographs by H. G. Solberg and E. J. Reese.
10.
S.
	 Memoirs of the British A3tronomical Association.
6. Journal of the Association of Lunar and Planetary Observers.
7. Measurements of New Mexico State University Observatory photographs by
H. G. Solberg and E. J. Reese.
RECENT MEASUREMENTS OF JUPITER'S RED SPOT MADE BY
H. G. SOLBERG AND E. J. REcSF: AT NEW, MEXICO STATE UNIVERSITY OBSERVATORY
Apparition s" *	 Length Width
1961-62 -220.6 24°6 28,560 km 12°9 14,410 km
1962-63 -22.7 24.2 28 0 070 13.0 14,530
1963-64 -22.5 23.7 27 0 530 12.5 13,960
1964-65 -22.1 23.4 27,240 12.0 13,390
1965--66 -22.3 23.3 27 0 100 11.5 12,840
1967-68 -22.9 24.8 28,720 12.1 13,530
* Zer_ographic latitude; of the center of the Red Spot.
NOTE: Measurements made from 1 February 1966 to 25 January 1968 were excluded
be;;ause the true outline of the Red Spot apparently was concealed during this
interval. All measurements of the length of the Red Spot made at the New
Mexico State University Observatory pertain to the elliptical outline of
the dark Red Spot as photographed in blue light. The extended tips or
belt-like appendages sometimes visible at the preceding and following ends
of the Red Spot were not lr,eluded in the measured lengths.
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	 .-	 ...» ^	 . ^, v^m^..w.A	 ^	 W^.a...a.— .^^.ie.¢ ^+t^.,_..z...e..—s ^c.
11.
REFERENCES
Melbourne, W. G., end O'Handley, D. A. (1968). Recent development ephemerides.
Space Programs Su-mmary 37-53, Vol. III, p.l.
O'Handley, D.A. (1969). Private communication to B. A. Smith.
Smith, B. A. (1964). A photographic optical semidiameter of Venus. Astronomical
Journal 69, No. 2, 201-204.
Wells, R. A. (1965). A re-evaluation of W. H. Wright's plates of the 1924 and
1926 oppositions of Mars. Planetary Space Science 13, 261-263.
Wright, W. H. (1925). Photographs of Mars made with light of different colors.
Lick Observatory Bulletin XII, No. 366, 48-61.
rFig. 1. Venus on 3 September 1967, 1533 U'[', phase angle 163 0.9. This
photograph, which was taken in infrared light with an exposure of
0.08 second, shows the illuminated crescent subtending an arc of 191°.
The greater twilight extension recorded in Fig. 2 was due to a lon,-er
exposure on a darker sky. The arrow indicates celestial north.
Photograph taken by T. Pope with the 61-cm reflector at the MIS11
Observatory.
Fig. 2. Venus on 28 March 1969, )125 UT, phases angle 152 0.7. This
5 second exposure in red light shows the illuminated crescent subtending
an arc of 203°. The arrow indicates celestial north. Photogra ph taken
by C. F. Knuckles with the 61-cm reflector at the WSU Observatory.
-°-W::- wFae s r. 	 4
Fig. 3. Comparison photographs of 'Mars taken in red and blue light
on 15 April 196' at 0840 UT. The upper half of each s=liced image was
taken in red light using a IV-I: plate with an OG-' filter. The lower
half of each image was taken in blue light using a III-0 plate with a
GG-13 filter.
MT
w
'ix..
'irk;
Fig. 4. Comparison photographs of the Moon taken in red and blue light.
Two photogra phs of the same hemisphere of the moon spliced together.
The upper halt was taken in red light using a III-F Kodak spectroscopic
plate with a Schott OG-3 filter. The lower half was taku,i 14 minutes
later in blue light using a III-O plate with a Schott GG-13 filter.
The photographs were taken at the primary focus of a 5-inch reflector
of 20.3 inches focal length. Photographs by Thomas B. Kirby and Susan
A. Jean.
l


Measurements of planetary dimensions

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