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A photographic investigation of the gegenschein and the Earth-Moon libration point L5
mARus 9, 499-439
WW
A Photographic
Investigation
and the Earth-Moon
ROBERT Department
of Astronomy,
Libration
Point Lg
G.ROOSEN
University
Received
Communicated
of the Gegenschein
March
of Tezas, Austin,
Tezas 78718
6, 1968
by G. de Vaucouleurs
A photographic study of the gegenschein and a search for the suspected “cloud satellites” at the L, Earth-Moon libration point was conducted at the McDonald Observatory from March, 1966 to March, 1967. The gegenschein appears to have a welldefined peak in intensity located at the antisolar pomt, with no measurable geocentric parallax. Neither a net displacement in longitude nor a latitude variation were observed for this peak. The effects of extmction and airglow on the gegenschein’s outer isophotes are considered. No evidence was found for the reported “cloud satellites” at the L, point, to a level of detection more than 30 times fainter than the brightness rrported by Kordylewski and Simpson. It is concluded that the so-called “Kordylewski clouds,” if real, are not associated with the Earth-Moon hbration pomts
The gegenschein has been studied visually, photographically, and photoelectrically for over 109 years, yet its position, size, shape, brightness, and cause remain in dispute. The four most popular theories of the nature of the gegenschein are that it is due to (1) an Earth’s gas tail, (2) an Earth’s dust tail, (3) an accumulation of particles near the collinear libration point L, in the Earth-Sun system, or (4) a circumsolar dust cloud. General descriptions of and observational tests for these models have been given by Brandt (1962)) and more extensively by Tanabe (1965). Thus further observations of the gegenschein are of interest. A physically separate but observationally similar problem concerns the recent assertions of accumulations of dust in the form of visible clouds at or near the quasistable equiliateral libration points L, and I~, in the Earth-Moon system (Kordylemski, 1961; Simpson, 1967). These clouds were reported to have, at opposition, surface brightness slightly less than that of
the gegenschein, and diameters on the order of 1 to 5 degrees. Although photoelectric and satellite techniques are now being brought to bear on such problems, the results of the present paper indicate that ground-based photographic studies made from good dark sites still have much to contribute. METHODS
The observing program included (1) a photographic search for L, clouds when the gegenschein was necessarily at relatively large eastern hour angles and (2) photography of the gegenschein alone at smaller hour angles (Fig. 1). Since the light of the night sky is known to be highly variable, repeatability of results is the most important single criterion of any successful program dealing with diffuse objects of limiting surface brightness such as the gegenschein and libration points. To this end, on any given night a few strategic areas were repeatedly photographed. For a site such as the McDonald Observatory which is totally free of interference
430
ROBERT
from artificial hghts, the hght of the night sky is composed of diffuse galactic light, integrated starlight (direct and scattered), zodiacal light, and airglow (Roach, 1964). For the purposes of this investigation we need consider only the contributions due to the zodiacal light and airglow, since the others are essentially constant. Through the technique of duplication and multiple observations, I have attempted to eliminate the errors arising from variable airglow, undetected haze or clouds, and enmlsion irregularities (de Vaucouleurs, 1948). As described previously {Roosen, 1966), the observations used for this analy~-is were made with a 35-ram Nikon camera mounted on a sidereal drive, with an ]/1.4, 50-mm focal length lens stopped down to ]/2.8, Nikon 1,39 UV cutoff filter (similar to Wratten 2B). Kodak 103a-0 film and 20- to 40-rain. exl)o~ure times. Photographs were taken on 24 separate nights from 12 March, 1966 to 12 March, 1967.
(;,
ItOOSEX
Initial attempts to interpret the photographs by means of composite printing techniques (Roosen, ~966) proved to be both highly time-consuming and somewhat misleading as a consequence of differential vignetting. Therefore. a more complete analysis of each individual frame was made with a Technical Operations Isodensitracer at the Goddard Space Flight Center in the summer of 1967. The operahon of this instrument has been described by Miller et al. (1964). Of the 128 photographs taken, many were exposed on nights known or suspected to have thin clouds during part of a night (as entered in the observing log). Most of these showed disagreement between sequential photographs and accordingly were judged unsuitable. Thus it is seen that good nights are hard to find and the criterion of repeatability is indeed a necessary one. Tracings of 32 photographs were used for
431
GEGENSCHE1N AND LIBRATION CLOUI)S
study of the L5 point and 33 for the gegensehein.
displacement in longitude of the photometric peak from the ant]solar point:
T H E ~EGENSCHEIN
AX = X(gcgenst'hein) - [X(Sun) + 180°1. (l)
The best gegenscheln photographs were taken on the mghts of April 9 and December 2, 1966 and March l, 2, 3, 4, 7. 10, and 12, 1967 UT. 51ic~ophotometer scans were made alo,g the ecl.ptlc on ten of the photographs taken in March, 1967, on which the gegenschein was nearly centered. The result was essentmlly the same on all scans-a gradual increase in brightness toward the antisolar l)oint, ~uperlmposed on the vignetting function (Appendix I), with a definite peak near the antisolar point. If the gegenschein is relatively near the Earth, its apparent position with respect to the antisolar point should in principle be a function of local hour angle (H) of the antisolar point. To test this question of diurnal parallax, let /xX be the observed
Figure 2a shows the relation between A)~ and sin H for the photometric peaks found on the ten photographs scanned. A leastStlUares fit in the form ~X = AXe + B(sm H)
(2)
was made to the points in Fig. 2a; the coefficients are collected in Table I. The geoceutric parallax re. can be defined in terms of the slope as ~. = - B/(('os 30°)(('os 23°),
(3)
where the terms in the denominator are, respectively, factors allowing for the latitude of the observatory and the inclination of the ecliptic to the celestial equator. The mean parallax 7to = +0.°03 ± 0 ? 1 (m. e.) is essentially zero, in direct contradiction
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F=c,. 2. Effect of gege.schem raze on apparent geocentric parallax, shown by the relatmn between and sin H for (a) the gegenschein peak brightness, (b) the 4* gegenschem, and (c) the 15 ° gegenschein.
,.~X
432
ROBERT
G. R O O S E N
TABLE I APPARENT PARAIA,AX OF GEGENSCHEIN DeRn~tlon
of gegenschem
AX0•
re,~*
Ba
Peak brightness Small (4°)
0 02 +_ 0 04 - 0 0"2 :t: 0 03
--() 12 4: (} I)5
0 02 + (} 09
- 0 03 4- 0 11 +0 14 -1- 0 06
L a r g e ( 1 5 °)
-0
-2
+2
2 8 _+ O 0 7
3 2 -4 (I 14
91 -t- 0 18
In degrees. The error.~ gwea are standard deviations. to the values close to 3.5 degrees reported by Rozhkovskii (1950) and Astapovich (1950). Scans in latitude on three of the photographs yielded a mean latitude ~ -----0°.08 ± 0.°26 (m. e.). Hence, the gegenschein has a well-defined peak in intensity centered on the antisolar point within the small errors of the data. The absence of an observed net displacement in longitude is in agreement with the results of D u m o n t (1965) and T a n a b e (1965), but in strong disagreement with the 3 ° net westward displacement reported by Astapovich (1950). For a diffuse cloud of dust parUcles, peaking in the back-scattering intensity
at the antisolar point m a y well outweigh any small variations in particle density. Hence the absence of parallax and displacement for the brightness peak m a y be less an indicator of the distance than of the nature of the gegenschein. A different method of measuring the distance of the particles producing the gegenschein is therefore needed. A possible alternative method m a y be based on the relation between elongation and phase angle. The intensity distribution for a typical scan in longitude is shown in Fig. 3. Here the relative intensity is given as a funchon of elongation ~ from the Sun. For a reflecting particle, the relation between phase angle a and elongation ~ is sin a = sin
200
~/R,
(4)
where R is the distance of the particle from the Sun in astronomical units (Fig. 4). 195
>.
-~ 190
/ ~85
R
I A.U. i 185"
I 180 Q
/
I 17~ °
ELONGATION
Fro. 3 Relative intensity (arbitrary units)
of the
gegenschein along the ecliptic for a 20-rain expomxre taken on March 10, 1967. No correction has been made for the effects of airglow and vignettiug.
FIG. 4. Geometry for reflection of sunlight by a particle at distance R from the Sun.
GEGENSCHEIN
433
AND L I B R A T I O N C L O U D S
3•
2°
I*
0o
_1B
-2°
-3 • I
Z
l
300*
360*
60*
I
J
120*
180"
I
I
240*
300"
X
Fro. 5. Observedechptic latitude of the center of the 4° gegenscheinand longitude of the 8Jltisolar point. The curve is the projection of the invariant angular momentum plane. Thus the observed back-scattering peak near E = 180 ° must be broader than the peak of the phase function by a factor R. It follows that if the phase function of the particles producing the gegenschein were known, a distance for the gegenschein could be determined directly by comparison of the relative slopes of the elongation curve and the phase curve. While this method may someday be useful in practice, there are complications in that the nature of the particles producing the gegenschein is not well-known, and the particles probably have considerable depth in R. A lower limit for the distance of these paffticles can be set from the observation that the gegenschein exhibits a peak in brightness at the antisolar point. If the particles were closer to the Earth than 150 Earth radii, those within ¼° of the antisolar point would be inside the Earth's umbra, producing a dark spot in the center of the gegenschein. Since such a spot was not found, the particles producing the gegenschein are at least 150 Earth radii from the Earth. While the results so far mentioned have dealt with the central peak, it is of course possible that the observed or inferred posi-
tion of the gegenschein, seen as a whole, depends on the way the boundary is defined (the observed size and shape of the gegenschein would then depend on the resolution used and the contrast detection threshold). To investigate such effects both a "small" (4 ° diameter) and a "large" (15 ° diameter) gegenschein were defined by means of the isophotes. After correction for vignetting {Appendix I), the observed displacements in longitude for both the 4 ° and 15 ° gegcnscheins were plotted against sin H (Figs. 2b, c). The coefficients of the least-squares solutions by Eq. (2) are given in Table I. The positive geocentric parallaxes are explained by the tendency for the centroid of the gegenschein to be depressed toward the horizon, due to the influence of the increased airglow brightness near the horizon. For typical conditions at McDonald Observatory this effect outweighs that of extinction, which tends to act in the opposite direction. As expected, the distortions are much greater for the large gegenschein than for the small. This may account for the large parallax reported by Astapovich (19,50) for visual observations. Rozhkovskii (1950) showed photographic results for three nights, during
434
ROBERT (;. ROOSEN
20 @
15 °
z I0°
0
Z 1
50
w
0o
12 h
II h
I0 h
RIGHT ASCENSION
15 @
I0 °
}... Z 0 @
--J l.l
-5 °
I 12 h
~
i
I ii h
a RIGHT ASCENSION
i
I i0 h
FIG 6. Two photographs of the same area of sky taken (a) March I and (b) March 3, 1967. The .solid hne indicates the ecliptic ( ~ marks the antlsolar point for each night), and the dotted hne indicates the .Moon's orbit (X marks the position of the L~ point on March l). Note that ~he small bright spot just northeast of the L~ p(~int m (a) is stdl present two :lights later in (b). Thereft,re the spot cannot be a libration cloud
GEGENSCHEIN
AND
L I B R A T I O N
435
C L O U D S
in longitude nor a latitude variation has been observed in this work. The outer lsophotes of the gegenschein are displaced by airglow and atmospheric absorption; the larger and fainter the isophotes the larger the errors. All of these results are con.-lstent w i t h an interpretation of tile gegenschein as hght reflected from a circum~-olar dust cloud (e.g., H o f f m e l s t e r , 1940).
of which the gegenschein exhibited negative parallax. His reported parallax of 3°5 is therefore considered to be highly questionable. The latitude measurements for the 4 ° gcgenschein are plotted in Fig. 5 again.~t t h e longitude of Lhe antisolar point at the time of observation. The apparent latlt~ude of the 4 ° gegenschem does not appear to be related to the invariant plane. This is in agreement with the results of D u m o n t (1965), but contrary to those of Hoffme]ster (1940), Astapovich (1950), Roach and Rees (1956), and Tanabe (1965). However, it should again be noted that the absence of observed latitude variation could still be consistent with theories wherein material producing the gegenschein is concentrated toward the invariant plane, since peaking of the scattering function 180 ° may strongly outweigh the ncar ~ concentration effects. In conclusion, the brightest part of the gegenschein has been found to lie at the antisolar point, with negligible time geocentric parallax. Neither a net displacement
one
THE LIBRATION POINT L5 The best photographs of tile predicted L~ point (for the three-body problem in the Earth-Moon system) were taken on the nights of March II and 12, April 9, and December 2, 1966 and March l, 2, and 3, 1967 UT. Bright patches 2 degrees or less in diameter located within a few degrees of the libration point were recorded on several occasions; a p'trtlcularly good example is from the mght of March l, 1967 (Fig. 6a). These patches were invariably due to one of two effects: (l) faint nebulae or st.ars--the~-e appeared consi,-tently m photographs of ttle area taken on
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I"m. 7. lsodensitracmg of a photograph of a umformly illuminated surface, showing the vJgnett)ng of the camera lens u,,~d.
436
ROBERT I
O. R O O S E N
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dlstonce
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of vlgnettin 9
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F r o . 8. T h e r e l a t i o n b e t w e e n A X a n d l o n g i t u d i n a l d i s t a n c e of t h e a n t i s o l a r p o i n t f r o m t h e c e n t e r o f t h e v i g n e t t i n g p a t t e r n f o r (a) 4 ° g e g e ~ c h e i n a n d (b) 15 ° g ~ , ~ c h e i n .
other nights (Fig. 6b); or (2) emulsion irregularities or possibly very small airglow cells as evidenced by the fact that a patch appearing on one photograph did not appear on any others taken the same night. The photographs were also examined for evidence of larger clouds (from 2 ° to l0 ° across) associated with the libration points. No evidence of any extraterrestrial clouds was found in this size range. The observations for the night of 12 March, 1966 must
be considered anomalous in that the central peak of the gegensehein was much broader than on other nights, and all of the isophotes were shifted 3 ° to 4 ° eastward along the ecliptic. Possible explanations for this phenomenon are mentioned by Roosen et al. (1967). In short, no real cloud of the Kordylewski type was found on any of the seven nights. A numerical upper limit on the brightness of any clouds at or near the L5 point
GEGENSCHEIN
AND
can be set from the isodensitometric tracings. While the slope of the characteristic curve varies slightly for each series of photographs, the contour interval in Fig. 6 is very close to a 2% change in intensity. Since a density change in the general background of one and one-half intervals is easily detectable, the threshold of detection is slightly less than 3% of the background level of approximately 22 mag/arcsec 2. Therefore any cloud must have been fainter than about 26 mag (photographic/ arcsecL This is in sharp contrast to the report of Kordylcwski (1961) that, "The surface intensity of the libration clouds is a little less in their opposition than that of the gegenschein." Such a brightness would correspond to about 22 mag/arcsec 2, about 30 times brighter than the detection threshold set here. Although numerical data are not given, Simpson (1967) reported libration clouds of the same order of brightness as Kordy2"
LIBltATION
437
CLOUDS
lewski's. In view of the anomalous result found on the same night (March 12, 1966) as Simpson reported two clouds, his observation was presumably of something other than libration clouds. One may wonder whether the libration clouds, if real, undergo slow changes in content and brightness. In particular, Steg and De Vries (1966) have suggested that the brightness of the libration clouds may be increased due to the addition of particles knocked off the Moon by meteor showers. However, the negative results reported here for observations made December 2, 1966, 15 days after the great Leonid meteor shower of November 17, 1966, indicate that this effect is also not detectable. It has been suggested ((3pik, 1967; Simpson, 1967) that if the libration points are observed when they are near opposition, the gegenschein might be a source of interference. If, however, as it appears from this work and others (Hoffmeister, 1940;
,
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0 •
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Slope of f i t , O 0 1 : l : O 0 1 ( m e ) Intercept : - O e 0 8 ± O ° O 8 { m
-2"
I
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I
I
40
6o
5o
i0 •
e )
I~ltudJnal distance of anti-solar point from center of vignettlfl~ pattern
FIQ, 9. The relation between B and vignetting pattern.
the latitudinal distance of the antisolar point from the center of the
438
ROBERT G. ROOSEN
Tanabe, 1965), the gegenschein is due to light reflected from a circumsolar dust cloud, the contrast between any libration point cloud and the zodiacal cloud would be essentially independent of elongation. In this case there is an advantage in observing the libration points near their opposition, since the phase effect would increase the brightness of any extraterrestrml cloud, thus enhancing the contrast relative to the airglow. During these observations the L.~ point was from about 5 ° to 20 ° from the antisolar point. Thus no evidence for the existence of hbration clouds was found in this work, to a detection limit of 3% of the background level--more than 30 times fainter than their previously reported brightness. I therefore conclude that the so-called "Kordylewski clouds," if real, are not associated with the EarthMoon libration points. The negative findings reported here and previously (Roosen, 1966, are in agreement with those of Wolff et al (1967) and .Morris et al. (1964), and with the theoretical negative expectation arising from the effect of solar perturbations (of. Roosen et al., 1967). Other recent theoretical studies of the problem include those of Schutz (1966) and Schechter (1967); more general discussions have been made by Steg and Dc Vries (1966), and by (Spik (1967). ACKNOWLEDGMENTS The author acknowledges with thanks the helpful advice and guidance received from Professors H. J. Smith and G. de Vaucouleurs, and from Dr. C. Wolff. The ephemerides for the Ls point were calculated by Dr. R. S. H a y rmgton This work was supported in part through an NDEA Fellowship at the University of Texas and a summer research assistantship at the University of Ma .ryland
APPENDIX I Because vignetting can seriously affect photographic observations of extended sources, a special study was made of these effects in the camera used for this investigation. Photographs of a uniformly illuminated surface were taken; a typical result for f/2.8 is shown in Fig. 7. Since the
asymmetry observed was found to be the same for a second lens of the same model, it presumably arises from the design. The intensity d(,erease approximately follows a cos' O law, where 0 is the off-axis angle. Vigncttmg .~ystematically shifts the center of an isophote toward the center ot the vigncttmg pattern. The effect in longitude fox" tile 4 ° and 15 ° gegenscheins is shown in Fig. 8. The regression lines shown were determined by the method of least squares and were used to correct the measured ~xAs. It should be noted that this correction masks any net displacement in longitude which may exist in the isophotes. The shift in latitude for the 4 ° gegenschein (Fig. 9~ is much smaller than that. in longitude, presumably because the intensity gradient is greater m latitude than in longitude. Since the net shift in latitude is no larger than the errors in the leastsquares fit, no correctmn was made to the latitude measurements. REFERENCE~ Asr~.POVlCll, I S. (1950). l':idwmende:, of the count~,rglow (m Russmn). Aslron. Ts~rk, No. 103-10~1, 19-23
Ba~NDr, J C (1962) The problem of the gegen~'heln .4,t~.,I ,_Nor l'(~c~fic Leaflet .Vo 391, DuMoxr, R (1965) Soparatmn of the atmospheric, m(erplan~,ta~v, and stellar components of the mght -k~ at 5000.~ Apphcatmn to the zodmcaI hght and the g[,genschem (m Fren(.h) Ann Astrophy.q 28, 265-320 Hov~r.mTrn, C (1940). The axt~ of the zodmcal hght and the constants of it~ plane of symmetry (m German) Aslron. Nach," 271, 49-67. KOaDYL~:WSKL K (1961). Photographic investigations of the hbratlon point L~ m the earthmoon system (m German) Acla Astron I I , 165-169. Air Force Camhrldge Research Laboratorws. Research Translation E-T-G-64-35. MILLER, C S., PARSONS, ];'. G , ~ND KOI.'SKY, I. S (1964) Slmphfied t~o-dlmensional mwroden.~itometry Nature 202, 1196-1200 Meatus, E C, RIxG, J, ~ND SrzPH~.','s. H G (I,°£)4) Photographic and photoelectric mvestlg~ttlons of the earth-moon hbration regmns L, and I., from Mt Chacaltaya. Bohvia In "Astrogeologic Studies," Annual Progress Report, Part D, August 25, 1962 to July 1. 1963, pp 71-74. U. S Geological Survey C)PIK, E. J (1967). Cloud Satellites of the moon? Irzsh A~t~on .I 8, 110-112
GEGENSCHEIN
AND
ROACH, F E. (1964). The hght of the ntght sky: astronomical, interplanetary and geophysical. Space Scz. Rev 3, 512~540. ROACH, F E , ANt) REES, M. H (1956). The a))solute t)hotometry of the gegcnschem. In "The Airglow and the Aurorae" (E. B. Armstrong, ed), pp 142-155. Pergamon Press, London and New York. ROOSEN, R. G. (1966). A photographic mvestlgatmn of the IJs point in the earth-moon system. Sky and Telescope 32, 139 ROOSEN, R. G., H~RRINGTON, R. S, AND JEFFESYS, W. H (1967) Doubt about libratlon clouds. Phys. Today 20, 9-11. ROZ~KOVSKII, D A. (1950). Photographic isophotes of the gegenschein from observations m 1948 and 1949 (in Russian), Astroa Zh. 27, 34-40. SCHZCHrZa, H. B. (1967). "Three-Dimensional Nonlinear Stablhty Analyms of the Sun-Perturb:,d Earth-Moon Eqmlnteral Points " Ph D.
LIBRATION
CI,OUDS
439
,hssertatlon, Stanford Umverslty, Stanford, Cahforma ScHuTz, B. E. (1966). "Motion of a Spacecraft near a Triangular Llbratlon Point of the EarthMoon System. Technical Reprint No. 1002, Univer.~lty of Texas Engineering Meehaniea Research I,aboratory, Austin, Texas. SIMPSON, J. W. (1967). Dust cloud moons of the earth. Phys. Today 20, 39~t6. STEG, I,., ^ND Ds VXtES, J. P. (1966). Earth-moon hbratlon point,s: theory, existence and applicauons. Space Sci. Rev. 2, 210-233. T^NABE, H. (1065). Photoelectric observations of the gegensehein. Publ. Astron. Soc. Japan 17, 339-366 VAUCOULEURS, G. DE (1948). Origin and correction of local errors m photographic photometry (in French). Rev. Opt. 27, 541-546. WOLFF', C., D U N K E L M A N , L, AND HAUOHNEY, L. C. (1967). Photography of the earth's cloud sallellites from an aircraft. Science 157, 427-429.
WW
A Photographic
Investigation
and the Earth-Moon
ROBERT Department
of Astronomy,
Libration
Point Lg
G.ROOSEN
University
Received
Communicated
of the Gegenschein
March
of Tezas, Austin,
Tezas 78718
6, 1968
by G. de Vaucouleurs
A photographic study of the gegenschein and a search for the suspected “cloud satellites” at the L, Earth-Moon libration point was conducted at the McDonald Observatory from March, 1966 to March, 1967. The gegenschein appears to have a welldefined peak in intensity located at the antisolar pomt, with no measurable geocentric parallax. Neither a net displacement in longitude nor a latitude variation were observed for this peak. The effects of extmction and airglow on the gegenschein’s outer isophotes are considered. No evidence was found for the reported “cloud satellites” at the L, point, to a level of detection more than 30 times fainter than the brightness rrported by Kordylewski and Simpson. It is concluded that the so-called “Kordylewski clouds,” if real, are not associated with the Earth-Moon hbration pomts
The gegenschein has been studied visually, photographically, and photoelectrically for over 109 years, yet its position, size, shape, brightness, and cause remain in dispute. The four most popular theories of the nature of the gegenschein are that it is due to (1) an Earth’s gas tail, (2) an Earth’s dust tail, (3) an accumulation of particles near the collinear libration point L, in the Earth-Sun system, or (4) a circumsolar dust cloud. General descriptions of and observational tests for these models have been given by Brandt (1962)) and more extensively by Tanabe (1965). Thus further observations of the gegenschein are of interest. A physically separate but observationally similar problem concerns the recent assertions of accumulations of dust in the form of visible clouds at or near the quasistable equiliateral libration points L, and I~, in the Earth-Moon system (Kordylemski, 1961; Simpson, 1967). These clouds were reported to have, at opposition, surface brightness slightly less than that of
the gegenschein, and diameters on the order of 1 to 5 degrees. Although photoelectric and satellite techniques are now being brought to bear on such problems, the results of the present paper indicate that ground-based photographic studies made from good dark sites still have much to contribute. METHODS
The observing program included (1) a photographic search for L, clouds when the gegenschein was necessarily at relatively large eastern hour angles and (2) photography of the gegenschein alone at smaller hour angles (Fig. 1). Since the light of the night sky is known to be highly variable, repeatability of results is the most important single criterion of any successful program dealing with diffuse objects of limiting surface brightness such as the gegenschein and libration points. To this end, on any given night a few strategic areas were repeatedly photographed. For a site such as the McDonald Observatory which is totally free of interference
430
ROBERT
from artificial hghts, the hght of the night sky is composed of diffuse galactic light, integrated starlight (direct and scattered), zodiacal light, and airglow (Roach, 1964). For the purposes of this investigation we need consider only the contributions due to the zodiacal light and airglow, since the others are essentially constant. Through the technique of duplication and multiple observations, I have attempted to eliminate the errors arising from variable airglow, undetected haze or clouds, and enmlsion irregularities (de Vaucouleurs, 1948). As described previously {Roosen, 1966), the observations used for this analy~-is were made with a 35-ram Nikon camera mounted on a sidereal drive, with an ]/1.4, 50-mm focal length lens stopped down to ]/2.8, Nikon 1,39 UV cutoff filter (similar to Wratten 2B). Kodak 103a-0 film and 20- to 40-rain. exl)o~ure times. Photographs were taken on 24 separate nights from 12 March, 1966 to 12 March, 1967.
(;,
ItOOSEX
Initial attempts to interpret the photographs by means of composite printing techniques (Roosen, ~966) proved to be both highly time-consuming and somewhat misleading as a consequence of differential vignetting. Therefore. a more complete analysis of each individual frame was made with a Technical Operations Isodensitracer at the Goddard Space Flight Center in the summer of 1967. The operahon of this instrument has been described by Miller et al. (1964). Of the 128 photographs taken, many were exposed on nights known or suspected to have thin clouds during part of a night (as entered in the observing log). Most of these showed disagreement between sequential photographs and accordingly were judged unsuitable. Thus it is seen that good nights are hard to find and the criterion of repeatability is indeed a necessary one. Tracings of 32 photographs were used for
431
GEGENSCHE1N AND LIBRATION CLOUI)S
study of the L5 point and 33 for the gegensehein.
displacement in longitude of the photometric peak from the ant]solar point:
T H E ~EGENSCHEIN
AX = X(gcgenst'hein) - [X(Sun) + 180°1. (l)
The best gegenscheln photographs were taken on the mghts of April 9 and December 2, 1966 and March l, 2, 3, 4, 7. 10, and 12, 1967 UT. 51ic~ophotometer scans were made alo,g the ecl.ptlc on ten of the photographs taken in March, 1967, on which the gegenschein was nearly centered. The result was essentmlly the same on all scans-a gradual increase in brightness toward the antisolar l)oint, ~uperlmposed on the vignetting function (Appendix I), with a definite peak near the antisolar point. If the gegenschein is relatively near the Earth, its apparent position with respect to the antisolar point should in principle be a function of local hour angle (H) of the antisolar point. To test this question of diurnal parallax, let /xX be the observed
Figure 2a shows the relation between A)~ and sin H for the photometric peaks found on the ten photographs scanned. A leastStlUares fit in the form ~X = AXe + B(sm H)
(2)
was made to the points in Fig. 2a; the coefficients are collected in Table I. The geoceutric parallax re. can be defined in terms of the slope as ~. = - B/(('os 30°)(('os 23°),
(3)
where the terms in the denominator are, respectively, factors allowing for the latitude of the observatory and the inclination of the ecliptic to the celestial equator. The mean parallax 7to = +0.°03 ± 0 ? 1 (m. e.) is essentially zero, in direct contradiction
Io
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F=c,. 2. Effect of gege.schem raze on apparent geocentric parallax, shown by the relatmn between and sin H for (a) the gegenschein peak brightness, (b) the 4* gegenschem, and (c) the 15 ° gegenschein.
,.~X
432
ROBERT
G. R O O S E N
TABLE I APPARENT PARAIA,AX OF GEGENSCHEIN DeRn~tlon
of gegenschem
AX0•
re,~*
Ba
Peak brightness Small (4°)
0 02 +_ 0 04 - 0 0"2 :t: 0 03
--() 12 4: (} I)5
0 02 + (} 09
- 0 03 4- 0 11 +0 14 -1- 0 06
L a r g e ( 1 5 °)
-0
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+2
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3 2 -4 (I 14
91 -t- 0 18
In degrees. The error.~ gwea are standard deviations. to the values close to 3.5 degrees reported by Rozhkovskii (1950) and Astapovich (1950). Scans in latitude on three of the photographs yielded a mean latitude ~ -----0°.08 ± 0.°26 (m. e.). Hence, the gegenschein has a well-defined peak in intensity centered on the antisolar point within the small errors of the data. The absence of an observed net displacement in longitude is in agreement with the results of D u m o n t (1965) and T a n a b e (1965), but in strong disagreement with the 3 ° net westward displacement reported by Astapovich (1950). For a diffuse cloud of dust parUcles, peaking in the back-scattering intensity
at the antisolar point m a y well outweigh any small variations in particle density. Hence the absence of parallax and displacement for the brightness peak m a y be less an indicator of the distance than of the nature of the gegenschein. A different method of measuring the distance of the particles producing the gegenschein is therefore needed. A possible alternative method m a y be based on the relation between elongation and phase angle. The intensity distribution for a typical scan in longitude is shown in Fig. 3. Here the relative intensity is given as a funchon of elongation ~ from the Sun. For a reflecting particle, the relation between phase angle a and elongation ~ is sin a = sin
200
~/R,
(4)
where R is the distance of the particle from the Sun in astronomical units (Fig. 4). 195
>.
-~ 190
/ ~85
R
I A.U. i 185"
I 180 Q
/
I 17~ °
ELONGATION
Fro. 3 Relative intensity (arbitrary units)
of the
gegenschein along the ecliptic for a 20-rain expomxre taken on March 10, 1967. No correction has been made for the effects of airglow and vignettiug.
FIG. 4. Geometry for reflection of sunlight by a particle at distance R from the Sun.
GEGENSCHEIN
433
AND L I B R A T I O N C L O U D S
3•
2°
I*
0o
_1B
-2°
-3 • I
Z
l
300*
360*
60*
I
J
120*
180"
I
I
240*
300"
X
Fro. 5. Observedechptic latitude of the center of the 4° gegenscheinand longitude of the 8Jltisolar point. The curve is the projection of the invariant angular momentum plane. Thus the observed back-scattering peak near E = 180 ° must be broader than the peak of the phase function by a factor R. It follows that if the phase function of the particles producing the gegenschein were known, a distance for the gegenschein could be determined directly by comparison of the relative slopes of the elongation curve and the phase curve. While this method may someday be useful in practice, there are complications in that the nature of the particles producing the gegenschein is not well-known, and the particles probably have considerable depth in R. A lower limit for the distance of these paffticles can be set from the observation that the gegenschein exhibits a peak in brightness at the antisolar point. If the particles were closer to the Earth than 150 Earth radii, those within ¼° of the antisolar point would be inside the Earth's umbra, producing a dark spot in the center of the gegenschein. Since such a spot was not found, the particles producing the gegenschein are at least 150 Earth radii from the Earth. While the results so far mentioned have dealt with the central peak, it is of course possible that the observed or inferred posi-
tion of the gegenschein, seen as a whole, depends on the way the boundary is defined (the observed size and shape of the gegenschein would then depend on the resolution used and the contrast detection threshold). To investigate such effects both a "small" (4 ° diameter) and a "large" (15 ° diameter) gegenschein were defined by means of the isophotes. After correction for vignetting {Appendix I), the observed displacements in longitude for both the 4 ° and 15 ° gegcnscheins were plotted against sin H (Figs. 2b, c). The coefficients of the least-squares solutions by Eq. (2) are given in Table I. The positive geocentric parallaxes are explained by the tendency for the centroid of the gegenschein to be depressed toward the horizon, due to the influence of the increased airglow brightness near the horizon. For typical conditions at McDonald Observatory this effect outweighs that of extinction, which tends to act in the opposite direction. As expected, the distortions are much greater for the large gegenschein than for the small. This may account for the large parallax reported by Astapovich (19,50) for visual observations. Rozhkovskii (1950) showed photographic results for three nights, during
434
ROBERT (;. ROOSEN
20 @
15 °
z I0°
0
Z 1
50
w
0o
12 h
II h
I0 h
RIGHT ASCENSION
15 @
I0 °
}... Z 0 @
--J l.l
-5 °
I 12 h
~
i
I ii h
a RIGHT ASCENSION
i
I i0 h
FIG 6. Two photographs of the same area of sky taken (a) March I and (b) March 3, 1967. The .solid hne indicates the ecliptic ( ~ marks the antlsolar point for each night), and the dotted hne indicates the .Moon's orbit (X marks the position of the L~ point on March l). Note that ~he small bright spot just northeast of the L~ p(~int m (a) is stdl present two :lights later in (b). Thereft,re the spot cannot be a libration cloud
GEGENSCHEIN
AND
L I B R A T I O N
435
C L O U D S
in longitude nor a latitude variation has been observed in this work. The outer lsophotes of the gegenschein are displaced by airglow and atmospheric absorption; the larger and fainter the isophotes the larger the errors. All of these results are con.-lstent w i t h an interpretation of tile gegenschein as hght reflected from a circum~-olar dust cloud (e.g., H o f f m e l s t e r , 1940).
of which the gegenschein exhibited negative parallax. His reported parallax of 3°5 is therefore considered to be highly questionable. The latitude measurements for the 4 ° gcgenschein are plotted in Fig. 5 again.~t t h e longitude of Lhe antisolar point at the time of observation. The apparent latlt~ude of the 4 ° gegenschem does not appear to be related to the invariant plane. This is in agreement with the results of D u m o n t (1965), but contrary to those of Hoffme]ster (1940), Astapovich (1950), Roach and Rees (1956), and Tanabe (1965). However, it should again be noted that the absence of observed latitude variation could still be consistent with theories wherein material producing the gegenschein is concentrated toward the invariant plane, since peaking of the scattering function 180 ° may strongly outweigh the ncar ~ concentration effects. In conclusion, the brightest part of the gegenschein has been found to lie at the antisolar point, with negligible time geocentric parallax. Neither a net displacement
one
THE LIBRATION POINT L5 The best photographs of tile predicted L~ point (for the three-body problem in the Earth-Moon system) were taken on the nights of March II and 12, April 9, and December 2, 1966 and March l, 2, and 3, 1967 UT. Bright patches 2 degrees or less in diameter located within a few degrees of the libration point were recorded on several occasions; a p'trtlcularly good example is from the mght of March l, 1967 (Fig. 6a). These patches were invariably due to one of two effects: (l) faint nebulae or st.ars--the~-e appeared consi,-tently m photographs of ttle area taken on
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436
ROBERT I
O. R O O S E N
I
1
I
I°
0 o
--I o Slope o f f=t • 0 0 8 +- 0 0 I ( m e ) Intercept : - 0 = 3 5 - - - O = ' 0 3 ( m e )
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Intercept
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dlstonce
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point from
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0 2 ( m e.)
• 0 = 4 6 .t- O = 0 9 ( m e )
of vlgnettin 9
i
i0 o pattern
F r o . 8. T h e r e l a t i o n b e t w e e n A X a n d l o n g i t u d i n a l d i s t a n c e of t h e a n t i s o l a r p o i n t f r o m t h e c e n t e r o f t h e v i g n e t t i n g p a t t e r n f o r (a) 4 ° g e g e ~ c h e i n a n d (b) 15 ° g ~ , ~ c h e i n .
other nights (Fig. 6b); or (2) emulsion irregularities or possibly very small airglow cells as evidenced by the fact that a patch appearing on one photograph did not appear on any others taken the same night. The photographs were also examined for evidence of larger clouds (from 2 ° to l0 ° across) associated with the libration points. No evidence of any extraterrestrial clouds was found in this size range. The observations for the night of 12 March, 1966 must
be considered anomalous in that the central peak of the gegensehein was much broader than on other nights, and all of the isophotes were shifted 3 ° to 4 ° eastward along the ecliptic. Possible explanations for this phenomenon are mentioned by Roosen et al. (1967). In short, no real cloud of the Kordylewski type was found on any of the seven nights. A numerical upper limit on the brightness of any clouds at or near the L5 point
GEGENSCHEIN
AND
can be set from the isodensitometric tracings. While the slope of the characteristic curve varies slightly for each series of photographs, the contour interval in Fig. 6 is very close to a 2% change in intensity. Since a density change in the general background of one and one-half intervals is easily detectable, the threshold of detection is slightly less than 3% of the background level of approximately 22 mag/arcsec 2. Therefore any cloud must have been fainter than about 26 mag (photographic/ arcsecL This is in sharp contrast to the report of Kordylcwski (1961) that, "The surface intensity of the libration clouds is a little less in their opposition than that of the gegenschein." Such a brightness would correspond to about 22 mag/arcsec 2, about 30 times brighter than the detection threshold set here. Although numerical data are not given, Simpson (1967) reported libration clouds of the same order of brightness as Kordy2"
LIBltATION
437
CLOUDS
lewski's. In view of the anomalous result found on the same night (March 12, 1966) as Simpson reported two clouds, his observation was presumably of something other than libration clouds. One may wonder whether the libration clouds, if real, undergo slow changes in content and brightness. In particular, Steg and De Vries (1966) have suggested that the brightness of the libration clouds may be increased due to the addition of particles knocked off the Moon by meteor showers. However, the negative results reported here for observations made December 2, 1966, 15 days after the great Leonid meteor shower of November 17, 1966, indicate that this effect is also not detectable. It has been suggested ((3pik, 1967; Simpson, 1967) that if the libration points are observed when they are near opposition, the gegenschein might be a source of interference. If, however, as it appears from this work and others (Hoffmeister, 1940;
,
I•
0 •
-
|
•
$
Slope of f i t , O 0 1 : l : O 0 1 ( m e ) Intercept : - O e 0 8 ± O ° O 8 { m
-2"
I
I
I
I
40
6o
5o
i0 •
e )
I~ltudJnal distance of anti-solar point from center of vignettlfl~ pattern
FIQ, 9. The relation between B and vignetting pattern.
the latitudinal distance of the antisolar point from the center of the
438
ROBERT G. ROOSEN
Tanabe, 1965), the gegenschein is due to light reflected from a circumsolar dust cloud, the contrast between any libration point cloud and the zodiacal cloud would be essentially independent of elongation. In this case there is an advantage in observing the libration points near their opposition, since the phase effect would increase the brightness of any extraterrestrml cloud, thus enhancing the contrast relative to the airglow. During these observations the L.~ point was from about 5 ° to 20 ° from the antisolar point. Thus no evidence for the existence of hbration clouds was found in this work, to a detection limit of 3% of the background level--more than 30 times fainter than their previously reported brightness. I therefore conclude that the so-called "Kordylewski clouds," if real, are not associated with the EarthMoon libration points. The negative findings reported here and previously (Roosen, 1966, are in agreement with those of Wolff et al (1967) and .Morris et al. (1964), and with the theoretical negative expectation arising from the effect of solar perturbations (of. Roosen et al., 1967). Other recent theoretical studies of the problem include those of Schutz (1966) and Schechter (1967); more general discussions have been made by Steg and Dc Vries (1966), and by (Spik (1967). ACKNOWLEDGMENTS The author acknowledges with thanks the helpful advice and guidance received from Professors H. J. Smith and G. de Vaucouleurs, and from Dr. C. Wolff. The ephemerides for the Ls point were calculated by Dr. R. S. H a y rmgton This work was supported in part through an NDEA Fellowship at the University of Texas and a summer research assistantship at the University of Ma .ryland
APPENDIX I Because vignetting can seriously affect photographic observations of extended sources, a special study was made of these effects in the camera used for this investigation. Photographs of a uniformly illuminated surface were taken; a typical result for f/2.8 is shown in Fig. 7. Since the
asymmetry observed was found to be the same for a second lens of the same model, it presumably arises from the design. The intensity d(,erease approximately follows a cos' O law, where 0 is the off-axis angle. Vigncttmg .~ystematically shifts the center of an isophote toward the center ot the vigncttmg pattern. The effect in longitude fox" tile 4 ° and 15 ° gegenscheins is shown in Fig. 8. The regression lines shown were determined by the method of least squares and were used to correct the measured ~xAs. It should be noted that this correction masks any net displacement in longitude which may exist in the isophotes. The shift in latitude for the 4 ° gegenschein (Fig. 9~ is much smaller than that. in longitude, presumably because the intensity gradient is greater m latitude than in longitude. Since the net shift in latitude is no larger than the errors in the leastsquares fit, no correctmn was made to the latitude measurements. REFERENCE~ Asr~.POVlCll, I S. (1950). l':idwmende:, of the count~,rglow (m Russmn). Aslron. Ts~rk, No. 103-10~1, 19-23
Ba~NDr, J C (1962) The problem of the gegen~'heln .4,t~.,I ,_Nor l'(~c~fic Leaflet .Vo 391, DuMoxr, R (1965) Soparatmn of the atmospheric, m(erplan~,ta~v, and stellar components of the mght -k~ at 5000.~ Apphcatmn to the zodmcaI hght and the g[,genschem (m Fren(.h) Ann Astrophy.q 28, 265-320 Hov~r.mTrn, C (1940). The axt~ of the zodmcal hght and the constants of it~ plane of symmetry (m German) Aslron. Nach," 271, 49-67. KOaDYL~:WSKL K (1961). Photographic investigations of the hbratlon point L~ m the earthmoon system (m German) Acla Astron I I , 165-169. Air Force Camhrldge Research Laboratorws. Research Translation E-T-G-64-35. MILLER, C S., PARSONS, ];'. G , ~ND KOI.'SKY, I. S (1964) Slmphfied t~o-dlmensional mwroden.~itometry Nature 202, 1196-1200 Meatus, E C, RIxG, J, ~ND SrzPH~.','s. H G (I,°£)4) Photographic and photoelectric mvestlg~ttlons of the earth-moon hbration regmns L, and I., from Mt Chacaltaya. Bohvia In "Astrogeologic Studies," Annual Progress Report, Part D, August 25, 1962 to July 1. 1963, pp 71-74. U. S Geological Survey C)PIK, E. J (1967). Cloud Satellites of the moon? Irzsh A~t~on .I 8, 110-112
GEGENSCHEIN
AND
ROACH, F E. (1964). The hght of the ntght sky: astronomical, interplanetary and geophysical. Space Scz. Rev 3, 512~540. ROACH, F E , ANt) REES, M. H (1956). The a))solute t)hotometry of the gegcnschem. In "The Airglow and the Aurorae" (E. B. Armstrong, ed), pp 142-155. Pergamon Press, London and New York. ROOSEN, R. G. (1966). A photographic mvestlgatmn of the IJs point in the earth-moon system. Sky and Telescope 32, 139 ROOSEN, R. G., H~RRINGTON, R. S, AND JEFFESYS, W. H (1967) Doubt about libratlon clouds. Phys. Today 20, 9-11. ROZ~KOVSKII, D A. (1950). Photographic isophotes of the gegenschein from observations m 1948 and 1949 (in Russian), Astroa Zh. 27, 34-40. SCHZCHrZa, H. B. (1967). "Three-Dimensional Nonlinear Stablhty Analyms of the Sun-Perturb:,d Earth-Moon Eqmlnteral Points " Ph D.
LIBRATION
CI,OUDS
439
,hssertatlon, Stanford Umverslty, Stanford, Cahforma ScHuTz, B. E. (1966). "Motion of a Spacecraft near a Triangular Llbratlon Point of the EarthMoon System. Technical Reprint No. 1002, Univer.~lty of Texas Engineering Meehaniea Research I,aboratory, Austin, Texas. SIMPSON, J. W. (1967). Dust cloud moons of the earth. Phys. Today 20, 39~t6. STEG, I,., ^ND Ds VXtES, J. P. (1966). Earth-moon hbratlon point,s: theory, existence and applicauons. Space Sci. Rev. 2, 210-233. T^NABE, H. (1065). Photoelectric observations of the gegensehein. Publ. Astron. Soc. Japan 17, 339-366 VAUCOULEURS, G. DE (1948). Origin and correction of local errors m photographic photometry (in French). Rev. Opt. 27, 541-546. WOLFF', C., D U N K E L M A N , L, AND HAUOHNEY, L. C. (1967). Photography of the earth's cloud sallellites from an aircraft. Science 157, 427-429.