New optical measurements of planetary diameters V. Planet Mercury

Telescopic measurements using the double-image technique, during transits of Mercury across the solar disk, give 2429 ± 18 km for the mean radius of Mercury along the two meridians centered at longitudes 90° and 270°, respectively (IAU system).     

The motion of major planets from observations 1769–1988 and some astronomical constants

Modern planetary theories may be considered as a realisation of a four-dimensional dynamical reference frame. The existence of secular trends between the dynamical system and the adopted system of the Fundamental Catalogue (as well as between time scales involved) has been studied by discussing planetary observations of different types and by comparison with a numerical theory constructed for the time span 1769–1988. Parameters of the theory were fitted to radar ranging data for 1961–1988 for inner planets and to meridian observations of 18^th–20^th centuries for outer planets. Then a set of the inner planet optical observations, which includes USNO meridian observations, transits through the solar disk and occultations of fundamental stars are discussed. The main results are the following:

1. Radar data were used to estimate the time derivative? of the gravitational constantG (in another interpretation, the secular trend between the atomic and dynamic time scales): $$\dot G/G = (0.37 \pm 0.45) \times 10^{ - 11} /y.$$ This estimation, being statistically insignificant, gives some physically meaningful restriction to?.
2. From the same data a new estimation of relativistic effects in the motion of Mercury was obtained, which has confirmed the Einstein value of the perihelion advance with the error 0″.06/cy. So in the frame of Einstein's theory the value of solar dynamic oblateness cannot be larger than 2×10^?6.
3. The analysis of time behavior of residuals in the inner planet longitudes shows secular trends. It is demonstrated that these trends may be explained by combined action of a linear trenddT of Brouwer's time scale (which is adopted as a standard for reduction of observations before 1959) and the error in Newcomb's value of the constant of precession. From USNO meridian observations fordT the following estimate was obtained:dT=?14.5±2.1 sec/cy with the corresponding correction,dp, to Newcomb's precessiondp=0″.46±0″.13/cy. The estimate ofdT is in good agreement with the value ofdT determined from transits of Mercury and Venus through the solar diskdT=?12.9±1.3 sec/cy which does not depend on any precession error.
4. As a by-product, new accurate ephemerides of the outer planets are obtained over the time interval 1769–1988, the average residuals being presented.

     

A comment on the insolation at Mercury

E. Van Hemelrijck and J. Vercheval [Icarus48, 167–179 (1981)] presented calculations of the insolation at Mercury and Venus which neglect the finite angular size of the Sun. To determine the temperature structure in the subsurface a more accurate calculation is needed, especially at longitudes ±90° on Mercury, where the Sun takes 18 days to rise or set. These calculations are presented here.     

On the variations in the insolation at Mercury resulting from oscillations of the orbital eccentricity

This paper describes variations in the insolation on Mercury resulting from fluctuations of the orbital eccentricity (0.11≤e≤0.24) of the planet. Equations for the instantaneous and the daily insolation are briefly discussed and several numerical examples are given illustrating the sensitivity of the solar radiation to changes ine. Special attention is paid to the behavior of the solar radiation distribution curves near sunrise and sunset which at the warm pole of Mercury (longitudes ±90°) occur as the planet goes through perihelion. It has been found that for eccentricities larger than about 0.194 there exists two permanent thermal bulges on opposite sides of the Mercurian surface that alternately point to the Sun at every perihelion passage. The critical value ofe past which the Sun shortly sets after perihelion is near 0.213.     

Observations of 1970 May 9 Mercury transit

During the 1970 May 9 Mercury transit on the solar disk, the Rome Astronomical Observatory performed various direct and spectroscopic observations of the apparent diameter of the planet, the instant of its third contact, the position angles of egress, and the least distance from the sundisk center. Independent methods were used for diameter determination: photometry, isodensitometry, dark calibrated disks, and photometric observations through a diaphragm closing on the planet's image. The maximum deviation among the different determinations is not larger than 0.37″ of arc; the mean weighted value gives a Mercury diameter at 1 a.u. of 6.74″ with an uncertainty of 3.8%. Also observed was a deformation phenomenon on the solar limb near the third contact: its value is estimated as 2.2″ but is not definitive.     

Observations of the sodium tail of Mercury

Cross-sections of the sodium emission tail of Mercury were measured at various distances down the tail when Mercury was moving away from the Sun (true anomaly angles <180°), and again when Mercury was moving towards the Sun (true anomaly angles >180°). As predicted in early modeling studies, significant differences were expected between these two cases, as the result of Doppler shifts to higher solar intensity in the former case, and to lower solar intensity for the latter case. For observations with Mercury moving away from the Sun, the sodium tail was observed out to about 40,000 kilometers (16 Mercury radii, RM) downstream, expanding, on average, at a rate of 1.9±0.3 km/s. The source rates for sodium generation from Mercury into the tail were found to be in the range 2-5×¹⁰²³ atoms/s, corresponding to between 1 and 10% of the estimated total sodium production rate on the planet. The limiting value of radiation acceleration required to produce an observable sodium tail was estimated to be 112±24 cm/s². For observations where Mercury was moving towards the Sun, the emission intensity in the sodium tail decreased very rapidly with distance downstream, disappearing entirely beyond 12,000 (6 RM) kilometers for radiation accelerations of 128.7 and 135.4 cm/s². For smaller radiation accelerations, the sodium tail was not detectable at all, yielding a limiting value for tail generation of about 122±2 cm/s². Interpretation of the limiting radiation acceleration values suggests that the process that generates the sodium tail yields atoms with energies greater than 3 eV. Particle sputtering is the most reasonable source process.     

New fission-track age determinations on impact glasses

Abstract— Four samples from Libyan Desert glass, one sample from Muong-Nong-type tektite, labelled Guang-Dong, and one sample from Czech Moldavite were analysed using the fission-track dating method. The Moldavite was unaffected by partial thermal track annealing, whereas the ages of Libyan Desert glass and Guang-Dong tektite appear to have been thermally lowered. Fission-track ages of the latter impact glasses were corrected using the plateau method. Apparent ages of Libyan Desert glass (between 26.0 ± 1.8 Ma and 29.0 ± 1.8 Ma) and Guang-Dong tektite (0.61 ± 0.05 Ma), as well as plateau ages (weighted mean: 28.5 ± 0.8 Ma for Libyan Desert glass and 0.77 ± 0.08 Ma for Guang-Dong) resulted in close agreement with previous determinations published in the late 1970s by Storzer and Wagner (1977). The age of the Moldavite (15.2 ± 0.08 Ma) also resulted in agreement with previous fission track and K-Ar determinations.     

An analysis of Martian satellite photographic observations of 1967

Photographic observations of the Martian satellites were made at the opposition of 1967 with the Naval Observatory's 61-inch astrometric reflector. A small partially transparent metallic film filter was used to diminish the light from Mars in order that a measurable image for the planetary disk as well as for the satellites could be obtained. The plates were reduced by the method of plate constants using positions for the faint background stars determined from astrographic field plates. The random mean error of these observations was estimated to be not greater than ±0″.10.The main result of the orbital adjustment is a +2° correction to the zero of mean longitude for Phobos. This confirms the findings of Wilkins (1970) and is compatible with the results of the Mariner 9 observations. The scale of the orbits of both satellites gave accordant values for the mass of Mars and the combined value of 30 99 500 ± 2800 (m.e.) is in good agreement with modern determinations.The mean error for Deimos derived from the residuals after solution is ±0″.11, which agrees well with the observational error and indicates no large systematic error in either the theory or the observations. For Phobos, however, the residual error, ±0″.19, is twice the expected observational error. The implications of this discrepancy are discussed.     

Vertical distribution and kinematics of planetary nebulae in the milky way

Based on published data, we have produced a sample of planetary nebulae (PNe) that is complete within 2 kpc of the Sun. We have estimated the total number of PNe in the Galaxy from this sample to be 17 000±3000 and determined the vertical scale height of the thin disk based on an exponential density distribution to be 197 ± 10 pc. The next sample includes PNe from the Stanghellini–Haywood catalog with minor additions. For this purpose, we have used ~200 PNe with Peimbert’s types I, II, and III. In this case, we have obtained a considerably higher value of the vertical scale height that increases noticeably with sample radius. We have experimentally found that it is necessary to reduce the distance scale of this catalog approximately by 20%. Then, for example, for PNe with heliocentric distances less than 4 kpc the vertical scale height is 256 ± 12 kpc. A kinematic analysis has confirmed the necessity of such a reduction of the distance scale.     

Testing the Distance Scale of the Gaia TGAS Catalogue by the Kinematic Method

We have studied the simultaneous and separate solutions of the basic kinematic equations obtained using the stellar velocities calculated on the basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values of Ω'₀ found by separately analyzing only the line-of-sight velocities of stars and only their proper motions, we have determined the distance scale correction factor p to be close to unity, 0.97 ± 0.04. Based on the proper motions of stars from the Gaia TGAS catalogue with relative trigonometric parallax errors less than 10% (they are at a mean distance of 226 pc), we have found the components of the group velocity vector for the sample stars relative to the Sun (U, V,W)_⊙ = (9.28, 20.35, 7.36) ± (0.05, 0.07, 0.05) km s^?1, the angular velocity of Galactic rotation Ω⁰ = 27.24 ± 0.30 km s?1 kpc?1, and its first derivative Ω'₀ = ?3.77 ± 0.06 km s^?1 kpc^?2; here, the circular rotation velocity of the Sun around the Galactic center is V₀ = 218 ± 6 km s^?1 kpc (for the adopted distance R₀ = 8.0 ± 0.2 kpc), while the Oort constants are A = 15.07 ± 0.25 km s^?1 kpc^?1 and B = ?12.17 ± 0.39 km s^?1 kpc^?1, p = 0.98 ± 0.08. The kinematics of Gaia TGAS stars with parallax errors more than 10% has been studied by invoking the distances from a paper by Astraatmadja and Bailer-Jones that were corrected for the Lutz–Kelker bias. We show that the second derivative of the angular velocity of Galactic rotation Ω'₀ = 0.864 ± 0.021 km s^?1 kpc^?3 is well determined from stars at a mean distance of 537 pc. On the whole, we have found that the distances of stars from the Gaia TGAS catalogue calculated using their trigonometric parallaxes do not require any additional correction factor.     

The Absolute Magnitude of RR Lyraes: from Hipparcos Parallaxes and Proper Motions

We have used HIPPARCOS proper motions and the method of Statistical Parallax to estimate the absolute magnitude of RR Lyrae stars. In addition, we have used the HIPPARCOS parallax of RR Lyr itself to determine its absolute magnitude. These two results are in excellent agreement with each other and give a zero-point for the RR Lyrae M_v,[Fe/H] relation of 0.77 ± 0.15 at [Fe/H]= -1.53. This zero-point is in good agreement with that obtained recently by several groups using Baade-Wesselink methods which, averaged over the results from the different groups, gives M_v = 0.73 ± 0.14 at [Fe/H] = -1.53. Taking the HIPPARCOS based zero-point and assuming a value of 0.18 ± 0.03 for the slope we find the distance modulus of the LMC is 18.26 ± 0.15. This value is compared with recent estimates based on other methods. Potential problems that may affect the results are outlined. This revised version was published online in July 2006 with corrections to the Cover Date.     

Forty years of measurements of the mean magnetic field of the Sun: View from today

During the last 40 years, the Crimean Astrophysical Observatory and five other observatories around the world have carried out more than 18 500 (daily) measurements of the mean magnetic field (MMF) of the Sun as a star. The main MMF periodicity is due to the equatorial rotation of the Sun with a synodic period of 26.92 ± 0.02 day (it was stable for decades, but “bifurcated” in the 23rd cycle). It is shown that (a) the average sidereal period of the equator, 25.122 ± 0.010 day, is in close resonant relations with orbital and axial rotations of Mercury (5: 2 and 5: 3, respectively); (b) the most powerful long period, 1.036 ± 0.007 years, is suspiciously close to the orbital period of the Earth and (c) coincides with the average synodic period of revolution of giant planets 1.036 ± 0.020 years; and (d) MMF reveals a significant period of 1.58 ± 0.02 years, which agrees, within errors, with the synodic period of Venus (1.60 years), and (e) a significant periodicity of 19.8 ± 2.5 years probably related to the 22-year magnetic cycle of the Sun. The nature of all these periodicities is mysterious.The assumption is made that the resonances originated at the early stages of formation of the Solar System, and their existence in the modern epoch is due to the specific features of the structure and dynamics of the central core of our star. It is found that the MMF level averaged over 40 years is practically zero, ?0.018 ± 0.015 G. The anomalous behavior of the 23rd cycle is pointed out; this is expressed in (1) violation of the Gnevyshev-Ohl rule for the pair of cycles 22–23, (2) accelerated rotation of the solar equator by 1.2%, and (3) considerable increase in the cycle duration (not smaller than 11.5 years), as compared to the average cycle duration in the 20th century (11.5 years). The problem of the so called magnetic “monopole” of the Sun is briefly discussed.     

Analysis of the orbit of 1970-97b (cosmos 378 rocket)

Cosmos 378 rocket, 1970-97B, entered orbit on 17 November 1970, with orbital inclination 74.0°, period 105 min and perigee height 230 km, and decayed on 30 September 1972 after 683 days in orbit. The RAE computer program PROP was used, with more than 1900 observations from 64 stations, to determine the orbit at 39 epochs between February 1971 and September 1972.The main aim of the analysis was to determine the atmospheric rotation rate from the decrease in orbital inclination, which was determined with a mean standard deviation of 0.0010° and a best standard deviation of 0.0003°. After removal of relevant perturbations, analysis of the variation in inclination between July 1971 and April 1972 yields the surprisingly low average atmospheric rotation rate of 0.75 ± 0.05 rev/day, at a mean height of 250 km. The local time at perigee is however strongly biassed towards daytime values (07–16 hr), so the results lend support to the picture of east-to-west winds by day and west-to-east winds by night.Values of scale height are obtained by analysis of the change in perigee height.     

Cosmic-ray tracks and cobalt-60 in near-surface samples of the Jilin chondrite

Abstract— Cosmic-ray track densities (CRTDs) have been measured on several spot samples from two Jilin specimens from the strewn field (VI-21-057 and VI-42-04), along with ⁶⁰Co activity in three and four sections, respectively, of the same specimens. The observed CRTD gradient agrees remarkably well with that predicted by Bhattacharya et al.'s calculations (1973) of CRTD variation as a function of shielding depth, which indicates a negligible contribution from the first 2π-irradiation stage. The shortest distance of each specimen to the preatmospheric surface is 3.6 cm and 6.8 cm, respectively. The distance scale deduced from these measurements allows the determination of the variation of ⁶⁰Co activity with shielding depth, at low depth values, which is found to be much less steep than model predictions. Two slightly different ⁶⁰Co profiles are proposed that correspond to the two specimens studied. The mean preatmospheric radius of the Jilin chondrite is 85 ± 8 cm, the uncertainty reflecting in part the meteoroid surface roughness.     

The mean coronal magnetic field determined from HELIOS Faraday rotation measurements

Coronal Faraday rotation of the linearly polarized carrier signals of the HELIOS spacecraft was recorded during the regularly occurring solar occultations over almost a complete solar cycle from 1975 to 1984. These measurements are used to determine the average strength and radial variation of the coronal magnetic field at solar minimum at solar distances from 3–10 solar radii, i.e., the range over which the complex fields at the coronal base are transformed into the interplanetary spiral. The mean coronal magnetic field in 1975–1976 was found to decrease with radial distance according to r ^?α, where α = 2.7 ± 0.2. The mean field magnitude was 1.0 ± 0.5 × 10 ^?5 tesla at a nominal solar distance of 5 solar radii. Possibly higher magnetic field strengths were indicated at solar maximum, but a lack of data prevented a statistical determination of the mean coronal field during this epoch.     

Analysis of the orbit of 1970-114F in its last 20 days

The satellite 1970-114F, the final-stage rocket of the Molniya 1S communications satellite, decayed in the atmosphere on 3 March 1973. During the last 20 days of its life the orbit suffered exceptionally rapid decay, with the apogee height decreasing from 7000 to 1000 km while the perigee height remained near 110 km. About 650 observations, made by visual observers in Britain and by U.S. Navy sensors, have been used with the PROP6 orbit refinement program to determine orbits at 14 epochs. Although the decay rate was more than ten times greater than in any previous orbit determination with PROP, good orbits were obtained, the standard deviation in inclination being less than 0.002° on eight orbits.The combination of high drag and good accuracy allows three techniques in orbital analysis to be successfully applied for the first time. Since zonal winds have little effect on the orbit, the changes in inclination are analysed to determine meridional winds near perigee, at heights of 110–120 km, latitudes of 63–65°S, and 6–12 hr LT. The changes in right ascension of the node are also successfully analysed for the same purpose. The two methods agree in indicating a south-to-north wind of 40 ± 30 m/sec from 11 to 21 February, a geomagnetically quiet period, and a south-to-north wind averaging 150 ± 30 m/sec from 22 February to 3 March, a geomagnetically disturbed period. Thirdly, the changes in the argument of perigee are analysed to determine atmospheric oblateness, which is found to be equal to the Earth's oblateness, to within ±20%. Lastly, the drag coefficient in transition flow is evaluated and found to be 0.85 ± 0.20.     

The radial brightness distribution of the Sun at 3.2 mm as determined from the June 30, 1973 total solar eclipse and a reanalysis of the March 7, 1970 total solar eclipse

The radial brightness distribution of the Sun at 3.2 mm is recalculated for the 7 March, 1970 total solar eclipse by an improved method. The results from the first contact of the 30 June, 1973 total eclipse are also analyzed. Limb brightening is apparent for the 1970 eclipse when all four contacts are averaged. The 1973 eclipse indicates strong limb brightening, although the detailed shape differs from the 1970 eclipse.     

Mass distribution of lyrid meteoroids

Long-term visual observations of the Lyrid meteoroid shower have been analyzed to determine the mass distribution of Lyrid meteoroids. The value of the parameter S has been confirmed to be less than 1.8, which is normally assumed for meteoroid streams. The inclination of the descending and ascending branches of the S curve, depending on the longitude of the Sun, does not seem to exceed 3°. Observations carried out from 1987 until 2007 reveal that the minimum value of S corresponding to the longitude of the Sun 32.19 ± 0.04° is equal to 1.54 ± 0.02 (2000.0). The analysis of the S parameter derived from visual observations did not discover any particularities in the mass distribution of the meteoroids in the stream connected with the assumed 12-year enhancement period in the activity of the Lyrids.     

The mass,gravity field,and ephemeris of Mercury

This paper represents a final report on the gravity analysis of radio Doppler and range data generated by the Deep Space Network (DSN) with Mariner 10 during two of its encounters with Mercury in March 1974 and March 1975. A combined least-squares fit to Doppler data from both encounters has resulted in a determination of two second degree gravity harmonics, J₂ = (6.0 ± 2.0) × 10⁻⁵ and C₂₂ = (1.0 ± 0.5) × 10⁻⁵, referred to an equatorial radius of 2439 km, plus an indication of a gravity anomaly in the region of closest approach of Mariner 10 to Mercury in March 1975 amounting to a mass deficiency of about GM = −0.1 km³sec⁻². An analysis is included that defends the integrity of previously published values for the mass of Mercury (H. T. Howard et al. 1974, Science 185, 179–180; P. B. Esposito, J. D. Anderson, and A. T. Y. Ng 1978, COSPAR: Space Res. 17, 639–644). This is in response to a published suggestion by R. A. Lyttleton (1980, Q. J. R. Astron. Soc. 21, 400–413; 1981, Q. J. R. Astron. Soc. 22, 322–323) that the accepted values may be in error by more than 30%. We conclude that there is no basis for being suspicious of the earlier determinations and obtain a mass GM = 22,032.09 ± 0.91 km³sec⁻² or a Sun to Mercury mass ratio of 6,023,600 ± 250. The corresponding mean density of Mercury is 5.43 ± 0.01 g cm⁻³. The one-sigma error limits on the gravity results include an assessment of systematic error, including the possibility that harmonics other than J₂and C₂₂ are significantly different from zero. A discussion of the utility of the DSN radio range data obtained with Mariner 10 is included. These data are most applicable to the improvement of the ephemeris of Mercury, in particular the determination of the precession of the perihelion.     

The motion of the Martian satellites

An extensive analysis of the motion of Phobos and Deimos from 1877 to 1973 has been fulfilled. The new values of the parameters of the orbital model first developed by Struve have been determined for both satellites. The new sets of the orbital parameters compete with the solutions of similar accuracy found by Wilkins and Sinclair. A secular acceleration in longitude of Phobos is found to be equal to +(0.107±0.011)×10^?7 deg day^?2. The value of the acceleration is little affected when one or another group of oppositions is omitted. The acceleration of Deimos is determined with great uncertainty: +(0.06±0.34)×10^?9 deg day^?2. Values found for the orbital parameters seem to be in good agreement since the mass, oblateness and coordinates of the pole of Mars inferred from the motion of each satellite have similar values in both cases.