The distribution of mass in the planetary system and solar nebula

A model solar nebula is constructed by adding the solar complement of light elements to each planet, using recent models of planetary compositions. Uncertainties in this approach are estimated. The computed surface density varies approximately asr ^–3/2. Mercury, Mars and the asteroid belt are anomalously low in mass, but processes exist which would preferentially remove matter from these regions. Planetary masses and compositions are generally consistent with a monotonic density distribution in the primordial solar nebula.     

Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters

With 2 years of tracking data collection from the MRO spacecraft, there is noticeable improvement in the high frequency portion of the spherical harmonic Mars gravity field. The new JPL Mars gravity fields, MRO110B and MRO110B2, show resolution near degree 90. Additional years of MGS and Mars Odyssey tracking data result in improvement for the seasonal gravity changes which compares well to global circulation models and Odyssey neutron data and Mars rotation and precession (). Once atmospheric dust is accounted for in the spacecraft solar pressure model, solutions for Mars solar tide are consistent between data sets and show slightly larger values (k₂ = 0.164 ± 0.009, after correction for atmospheric tide) compared to previous results, further constraining core models. An additional 4 years of Mars range data improves the Mars ephemeris, determines 21 asteroid masses and bounds solar mass loss (dGM_Sun/dt < 1.6 × 10⁻¹³ GM_Sun year⁻¹).     

26Al and the partial ionization of the solar nebula

Calculation of the ionization state and consequent magnetic Reynolds number for the solar nebula shows that the presence of²⁶Al will result in strong coupling of the gas to magnetic fields. In the absence of²⁶Al,⁴⁰K will still result in substantial ionization, but the degree of magnetic coupling is much more model dependent.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.also Department of Astronomy.     

Heavy ion escape from Mars, influence from solar wind conditions and crustal magnetic fields

We have used more than 4 years of Mars Express ion data to estimate the escape of heavy ions ( and ) from Mars. To take the limited field of view of the instrument into account, the data has been binned into spatial bins and angular bins to create average distribution functions for different positions in the near Mars space. The net escape flux for the studied low solar activity period, between May 2007 and May 2011, is 2.0 ± 0.2 × 10²⁴ s⁻¹. The escape has been calculated independently for four different quadrants in the Y_MSO − Z_MSO plane, south, dusk, north and dawn. Escape is highest from the northern and dusk quadrants, 0.6 ± 0.1 × 10²⁴ s⁻¹, and smallest from the south and dawn quadrants, 0.4 ± 0.1 × 10²⁴ s⁻¹. The flux ratio of molecular ( and ) to O⁺ ions is 0.9 ± 0.1, averaged over all quadrants. The flux difference between the north and south quadrants is statistically significant, and is presumed to be due to the presence of significant crustal magnetic fields in the southern hemisphere, reducing the outflow. The difference between the dawn and dusk quadrants is likely due to the magnetic tension associated with the nominal Parker angle spiral, which should lead to higher average magnetic tension on the dusk side. The escape increases during periods of high solar wind flux and during times when co-rotating interaction regions (CIR) affect Mars. In the latter case the increase is a factor 2.4-2.9 as compared to average conditions.     

Some comments on the limb shift of solar lines

We searched for a variation with heliographic latitude of the solar limb effect by comparing the relative wavelengths of weak and strong Fraunhofer lines. The blue shifts associated with the limb effect appear 9%±5% larger in the polar radius vector than in an equatorial radius vector at cos = 0.5. This should perhaps be interpreted as an increase with latitude of either solar convection or of convective overshoot. Recent observations of poleward meridional flows of 30m s^–1 should be corrected for this limb effect variation. This correction increases this flow velocity to 70 m s^–1. A search for a similar variation in plages and in network boundaries had negative results, the variation being +1%±5% and -1%±6% respectively.Now at the Multiple Mirror Telescope Observatory, University of Arizona, Tucson, Ariz. 85721, U.S.A. The MMTO is jointly operated by the University of Arizona and the Smithsonian Institution.The Sacramento Peak Observatory is operated by the Association of Universities for Research in Astronomy, Inc. under contract AST 78-17292 with the National Science Foundation.     

Grain motions in the solar nebula

Isotopic analyses of meteorites suggest the possibility that some interaction between supernova ejecta and grains occurred in the solar nebula. In particular, the dynamics of grain motions in the solar nebula can explain the observed mixing of nucleosynthetic components. The effect of a shock wave on the motions of grains are examined. A steady-state, plane shock propagating into a uniform region of gas and dust grains is followed by a zone of gas/grain slip, in which the grains are accelerated by drag forces from the pre-shock to the post-shock gas velocity, i.e. reducing the relative velocity between the gas and grains to zero. On the basis of these calculations, it is estimated that if grains carried the isotopic anomalies investigated by Lee, Papanastassoiu, and Wasserburg (1978), then those grains could be no bigger than 2×10^–4 cm in size. A scenario is suggested in which the sluggishness of grains provides a natural way to concentrate and mix the nucleosynthetic components carried by grains in the ejecta and in the solar nebula.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Helium on Mars and Venus: EUVE observations and modeling

Long-exposure spectroscopy of Mars and Venus with the Extreme Ultraviolet Explorer (EUVE) has revealed emissions of He 584 Å on both planets and He 537 Å/O⁺ 539 Å and He⁺ 304 Å on Venus. Our knowledge of the solar emission at 584 Å, eddy diffusion in Mars' upper atmosphere, electron energy distributions above Mars' ionopause, and hot oxygen densities in Mars' exosphere has been significantly improved since our analysis of the first EUVE observation of Mars [Krasnopolsky, Gladstone, 1996, Helium on Mars: EUVE and Phobos data and implications for Mars' evolution, J. Geophys. Res. 101, 15,765-15,772]. These new results and a more recent EUVE observation of Mars are the motivation for us to revisit the problem in this paper. We find that the abundance of helium in the upper atmosphere, where the main loss processes occur, is similar to that in the previous paper, though the mixing ratio in the lower and middle atmosphere is now better estimated at 10±6 ppm. Our estimate of the total loss of helium is almost unchanged at 8×¹⁰²³ s⁻¹, because a significant decrease in the loss by electron impact ionization above the ionopause is compensated by a higher loss in collisions with hot oxygen. We neglect the outgassing of helium produced by radioactive decay of U and Th because of the absence of current volcanism and a very low upper limit to the seepage of volcanic gases. The capture of solar wind α-particles is currently the only substantial source of helium on Mars, and its efficiency remains at 0.3. A similar analysis of EUV emissions from Venus results in a helium abundance in the upper atmosphere which is equal to the mean of the abundances measured previously with two optical and two mass spectrometers, and a derived helium mixing ratio in the middle and lower atmosphere of 9±6 ppm. Helium escape by ionization and sweeping out of helium ions by the solar wind above the ionopause is smaller than that calculated by Prather and McElroy [1983, Helium on Venus: implications for uranium and thorium, Science 220, 410-411] by a factor of 3. However, charge exchange of He⁺ ions with CO₂ and N₂ between the exobase and ionopause and collisions with hot oxygen ignored previously add to the total loss which appears to be at the level of 10⁶ cm⁻² s⁻¹ predicted by Prather and McElroy [1983, Science 220, 410-411]. The loss of helium is compensated by outgassing of helium produced by radioactive decay of U and Th and by the capture of the solar wind α-particles with an efficiency of 0.1. We also compare our derived α-particle capture efficiencies for Mars and Venus with observed X-ray emissions resulting from the charge exchange of solar wind heavy ions with the extended atmospheres on both planets [Dennerl et al., 2002, Discovery of X-rays from Venus with Chandra, Astron. Astrophys. 386, 319-330; Dennerl, 2002, Discovery of X-rays from Mars with Chandra, Astron. Astrophys. 394, 1119-1128]. The emissions from both disk and halo on Mars agree with our calculated values; however, we do not see a reasonable explanation for the X-ray halo emission on Venus. The ratio of the charge exchange efficiencies derived from the disk X-ray emissions of Mars and Venus is similar to the ratio of the capture efficiencies for these planets. The surprisingly bright emission of He⁺ at 304 Å observed by EUVE and Venera 11 and 12 suggests that charge exchange in the flow of the solar wind α-particles around the ionopause is much stronger than in the flow of α-particles into the ionosphere.     

What we have learned about the Martian magnetic field

The evidence is presented for the existence of the magnetic field of the planet Mars and for the effectiveness of the dipolar part of the field as an obstacle to the solar wind at the most frequent parameters of the latter. The dipolar magnetic moment of Mars is (1.5–2.20 × 10²² G cm³. The dipole axis makes an angle i15 with the rotation axis of the panel. The magnetic north pole of Mars is located in its southern hemisphere.In terms of the precession dynamo model, the magnetic fields of the Earth and Mars are similar. This indicates that the Martian magnetic field is associated with the present-day dynamo-process in the Martian liquid core.     

Long,accurate time series measurements of radial velocities of solar-type stars

We have been measuring changes in the radial velocities (RV's) of solar-type stars to search for gravitational perturbations by planets. We transmit violet starlight through a Fabry-Perot etalon interferometer and sense changes in Doppler shift from changes in the fluxes of light on the slopes of stellar absorption lines. Our data now span 6 years. Our observations of the Sun showed earlier that both our technique and the profiles of solar photospheric violet absorption lines can be stable enough to reveal planetary perturbations. We now carry this validation to the spectra of other near-solar-type stars. Annual averages of our RV's of Draconis and Virginis are stable to ±6 m s^–1. The slope of our five-year series of RV's of Bootis A is consistent with the star's well-determined visual astrometric orbit about Bootis B. The Fabry-Perot technique of Doppler shift measurement is fully capable of detecting perturbations due to planets with masses and orbits similar to those of Jupiter.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

The Planetary Fourier Spectrometer (PFS) onboard the European Mars Express mission

The Planetary Fourier Spectrometer (PFS) for the Mars Express mission is an infrared spectrometer optimised for atmospheric studies. This instrument has a short wave (SW) channel that covers the spectral range from 1700 to (1.2-) and a long-wave (LW) channel that covers 250- (5.5-). Both channels have a uniform spectral resolution of . The instrument field of view FOV is about 1.6^° (FWHM) for the Short Wavelength channel (SW) and 2.8^° (FWHM) for the Long Wavelength channel (LW) which corresponds to a spatial resolution of 7 and 12 km when Mars is observed from an height of 250  km. PFS can provide unique data necessary to improve our knowledge not only of the atmosphere properties but also about mineralogical composition of the surface and the surface-atmosphere interaction.The SW channel uses a PbSe detector cooled to 200-220 K while the LW channel is based on a pyroelectric (L_iT_aO₃) detector working at room temperature. The intensity of the interferogram is measured every 150 nm of physical mirrors displacement, corresponding to 600 nm optical path difference, by using a laser diode monochromatic light interferogram (a sine wave), whose zero crossings control the double pendulum motion. PFS works primarily around the pericentre of the orbit, only occasionally observing Mars from large distances. Each measurements take 4 s, with a repetition time of 8.5 s. By working roughly 0.6 h around pericentre, a total of 330 measurements per orbit will be acquired 270 looking at Mars and 60 for calibrations. PFS is able to take measurements at all local times, facilitating the retrieval of surface temperatures and atmospheric vertical temperature profiles on both the day and the night side.     

A solar spectrum for PFS data analysis

A measured calibrated solar radiance in the range 1.2-, with the spectral sampling of does not exist. When studying the measured Planetary Fourier Spectrometer (PFS) spectra of the Earth's or Mars's atmosphere we discover that the most used solar spectrum contains several important errors. Here we present a “calibrated” solar radiance in the wavelength range 1.2-, with the spectral resolution of PFS , which we are going to use for studying Martian spectra. This spectrum has been assembled using measurements from Kitt Peak and from ATMOS Spacelab experiment (uncalibrated high resolution) and theoretical results, together with low resolution calibrated continuum. This is the best we can have in this moment to be used with PFS, while waiting to have good solar calibrated radiances. Examples of solar lines at Mars are given.     

Collapse of the presolar nebula

The hydrodynamical axially symmetric collapse of a 3M -cloud with an initial density of 10^–20 g cm^–3 has been investigated. In order to first arrive at an equilibrium configuration a temperature of 15 K has been assumed. During about 9 free-fall times the cloud has artificially been cooled down to the (Jeans-) critical temperature of 8 K. Thus, the dynamical collapse studied in this paper starts from an equilibrium configuration following a slow quasi-hydrostatic contraction. Two sequences corresponding to a different choice of the initial angular velocity _i = 10^–14 s^–1 (Case A) and _i = 10^–15 s^–1 (Case B) have been computed. In both cases a fast spinning, optically thick disk-like core of low mass and temperature forms for which fission into two or even more pieces is very likely to occur.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

A sensitive search for nitric oxide in the lower atmospheres of Venus and Mars: Detection on Venus and upper limit for Mars

High-resolution spectra of Venus and Mars at the NO fundamental band at 5.3 μm with resolving power ν/δν=76,000 were acquired using the TEXES spectrograph at NASA IRTF on Mauna Kea, Hawaii. The observed spectrum of Venus covered three NO lines of the P-branch. One of the lines is strongly contaminated, and the other two lines reveal NO in the lower atmosphere at a detection level of 9 sigma. A simple photochemical model for NO and N at 50-112 km was coupled with a radiative transfer code to simulate the observed equivalent widths of the NO and some CO₂ lines. The derived NO mixing ratio is 5.5±1.5 ppb below 60 km and its flux is . Predissociation of NO at the (0-0) 191 nm and (1-0) 183 nm bands of the δ-system and the reaction with N are the only important loss processes for NO in the lower atmosphere of Venus. The photochemical impact of the measured NO abundance is significant and should be taken into account in photochemical modeling of the Venus atmosphere. Lightning is the only known source of NO in the lower atmosphere of Venus, and the detection of NO is a convincing and independent proof of lightning on Venus. The required flux of NO is corrected for the production of NO and N by the cosmic ray ionization and corresponds to the lightning energy deposition of . For a flash energy on Venus similar to that on the Earth (∼¹⁰⁹ J), the global flashing rate is ∼90 s⁻¹ and ∼6 km⁻² y⁻¹ which is in reasonable agreement with the existing optical observations. The observed spectrum of Mars covered three NO lines of the R-branch. Two of these lines are contaminated by CO₂ lines, and the line at 1900.076 cm⁻¹ is clean and shows some excess over the continuum. Some photochemical reactions may result in a significant excitation of NO (v=1) in the lowest 20 km on Mars. However, quenching of NO (v=1) by CO₂ is very effective below 40 km. Excitation of NO (v=1) in the collisions with atomic oxygen is weak because of the low temperature in the martian atmosphere, and we do not see any explanation of a possible emission of NO at 5.3 μm. Therefore the data are treated as the lack of absorption with a 2 sigma upper limit of 1.7 ppb to the NO abundance in the lower atmosphere of Mars. This limit is above the predictions of photochemical models by a factor of 3.     

Observations of CO in the atmosphere of Mars with PFS onboard Mars Express

We have analyzed spectra of CO recorded with the instrument PFS onboard Mars Express in the (1-0) band. The dataset we used ranges in time from January until June 2004 (L_S=331^°.17 until L_S=51^°.61; end of Mars Year 26, beginning of Mars Year 27). The aim of this work was to determine the amplitude of the CO mixing ratio departures from the mean globally averaged value currently admitted (8±3×10^-4) [Kaplan, L.D., Connes, J., Connes, P., 1969. Carbon monoxide in the martian atmosphere. Astron. J. 157, L187-L192] as a function of season, local time and location on the planet. We therefore processed the data from 90 calibrated orbits. The globally averaged CO mixing ratio value we derive from our dataset, 11.1×10^-4, is compatible with the range found by Kaplan et al. [1969. Carbon monoxide in the martian atmosphere. Astron. J. 157, L187-L192], although somewhat higher than the “standard” value. However, the CO mixing ratio we retrieve exhibits large variations (roughly between 3×10^-4 and 18×10^-4). Such relative variations have been used on a statistical basis to derive main trends as a function of latitude for three L_S ranges: 331-360^°, 0-30^° and 30-52^°. For the first L_S range, we seem to have an enhancement of the CO mixing ratio towards the northern latitudes, probably linked to the CO₂ condensation in winter on the north polar cap. The situation for the two other L_S ranges is not so clear, mainly as we lack data on the southern hemisphere. We roughly agree with the work of Krasnopolsky [2007. Long-term spectroscopic observations of Mars using IRTF/CSHELL: mapping of O2 dayglow, CO and search for CH4. Icarus 190, 93-102] for L_S=331-360^°, thus confirming the effect of seasonal condensation of CO₂ on the north polar cap, but we have no agreement for other seasons.     

Rotation of pre-main-sequence stars in NGC 2264 and the solar angular momentum problem

Preliminary measurements of rotational velocities of pre-main sequence stars indicate that stars evolving into early F or late A spectral type have rotational velocities which are consistent with present Main-Sequence stars of similar spectral type. Stars evolving into G type, however, have rotational velocities which are as high as 100 km s^–1 and would reach the Main Sequence with velocities of 150 km s^–1. This requires the presence of a strong stellar wind to carry off considerable angular momentum in order to slow down the Sun to its present low rotational velocity.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Oxygen and carbon isotope ratios in the martian atmosphere

Oxygen and carbon isotope ratios in the martian CO₂ are key values to study evolution of volatiles on Mars. The major problems in spectroscopic determinations of these ratios on Mars are uncertainties associated with: (1) equivalent widths of the observed absorption lines, (2) line strengths in spectroscopic databases, and (3) thermal structure of the martian atmosphere during the observation. We have made special efforts to reduce all these uncertainties. We observed Mars using the Fourier Transform Spectrometer at the Canada–France–Hawaii Telescope. While the oxygen and carbon isotope ratios on Mars were byproducts in the previous observations, our observation was specifically aimed at these isotope ratios. We covered a range of 6022 to 6308 cm⁻¹ with the highest resolving power of ν/δν=3.5×10⁵ and a signal-to-noise ratio of 180 in the middle of the spectrum. The chosen spectral range involves 475 lines of the main isotope, 184 lines of ¹³CO₂, 181 lines of CO¹⁸O, and 119 lines of CO¹⁷O. (Lines with strengths exceeding 10⁻²⁷ cm at 218 K are considered here.) Due to the high spectral resolution, most of the lines are not blended. Uncertainties of retrieved isotope abundances are in inverse proportion to resolving power, signal-to-noise ratio, and square root of the number of lines. Laboratory studies of the CO₂ isotope spectra in the range of our observation achieved an accuracy of 1% in the line strengths. Detailed observations of temperature profiles using MGS/TES and data on temperature variations with local time from two GCMs are used to simulate each absorption line at various heights in each part of the instrument field of view and then sum up the results. Thermal radiation of Mars' surface and atmosphere is negligible in the chosen spectral range, and this reduces errors associated with uncertainties in the thermal structure on Mars. Using a combination of all these factors, the highest accuracy has been achieved in measuring the CO₂ isotope ratios: ¹³C/¹²C = 0.978 ± 0.020 and ¹⁸O/¹⁶O = 1.018 ± 0.018 times the terrestrial standards. Heavy isotopes in the atmosphere are enriched by nonthermal escape and sputtering, and depleted by fractionation with solid-phase reservoirs. The retrieved ratios show that isotope fractionation between CO₂ and oxygen and carbon reservoirs in the solid phase is almost balanced by nonthermal escape and sputtering of O and C from Mars.     

Circumstellar disks and planetary formation

The role of circumstellar disks in star and planetary formation is briefly reviewed. The observed disk around MWC 349 is used as an example and a table of evolutionary time scales and parameters is presented. The disk about MWC 349 is characteristic of that expected about a massive star. Disk structure about solar mass stars is more completely reviewed by Cameron (1978). The parameters for the disk indicate that there is a deduced region where conditions are appropriate for dust condensation and possible aggregation of material to planetary masses. For the purposes of the discussion we are assuming that the infrared as well as optical radiation arises from the disk which extends the known extent of the disk to 10¹⁴cm. It is not yet certain that this is the case.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris

With the collection of six years of MGS tracking data and three years of Mars Odyssey tracking data, there has been a continual improvement in the JPL Mars gravity field determination. This includes the measurement of the seasonal changes in the gravity coefficients (e.g., , , , , , ) caused by the mass exchange between the polar ice caps and atmosphere. This paper describes the latest gravity field MGS95J to degree and order 95. The improvement comes from additional tracking data and the adoption of a more complete Mars orientation model with nutation, instead of the IAU 2000 model. Free wobble of the Mars' spin axis, i.e. polar motion, has been constrained to be less than 10 mas by looking at the temporal history of and . A strong annual signature is observed in , and this is a mixture of polar motion and ice mass redistribution. The Love number solution with a subset of Odyssey tracking data is consistent with the previous liquid outer core determination from MGS tracking data [Yoder et al., 2003. Science 300, 299-303], giving a combined solution of k₂=0.152±0.009 using MGS and Odyssey tracking data. The solutions for the masses of the Mars' moons show consistency between MGS, Odyssey, and Viking data sets; Phobos GM=(7.16±0.005)×¹⁰⁻⁴ km³/s² and Deimos GM=(0.98±0.07)×¹⁰⁻⁴ km³/s². Average MGS orbit errors, determined from differences in the overlaps of orbit solutions, have been reduced to 10-cm in the radial direction and 1.5 m along the spacecraft velocity and normal to the orbit plane. Hence, the ranging to the MGS and Odyssey spacecraft has resulted in position measurements of the Mars system center-of-mass relative to the Earth to an accuracy of one meter, greatly reducing the Mars ephemeris errors by several orders of magnitude, and providing mass estimates for Asteroids 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, and 324 Bamberga.     

Interpretation of3He abundance variations in the solar wind

The ion composition instrument (ICI) on ISEE-3 has observed the isotopes of helium of mass 3 and 4 in the solar wind almost continuously between August 1978 and July 1982. This period included the increase towards the maximum of solar activity cycle 21, the maximum period, and the beginning of the descent towards solar minimum. Observations were made when the solar wind speed was between 300 and 620 km s^–1. For part of the period evidence for regular interplanetary magnetic sector structure was clear and a number of³He flares occurred during this time.The long-term average⁴He⁺⁺/³He⁺⁺ flux ratio R, was 2050 ± 200, a agreement with a previously reported result obtained using part of this data set, and in very good agreement with the previous measurements made over much shorter periods of time with the foil technique. The R values for 6-month intervals show statistically significant differences. The highest of these values is 2300 and coincides with the solar maximum of cycle 21 indicating that at solar maximum there may be changes in the character and rate of occurrence of short-term variations in R. We also find that R drops under conditions of low proton flux in the solar wind, and that it is high when solar wind speeds are lowest.At solar wind speeds above 400 km s^–1 R is nearby constant at about 2000; at lower speeds it is larger and more variable, in agreement with the idea that the sources of high and low speed wind are different. At times of sector boundary current sheet crossings, identified with coronal streamers, there is a characteristic rise in the value of R indicating an encounter with a plasma with reduced³He⁺⁺ abundance. Autocorrelations have been computed for⁴He⁺⁺ and³He⁺⁺ and indicate correlation times of about 14 and 20 hr, respectively. Periods of duration of about one day whenR is less than 1000 tend to coincide with the observation of compound streams.The possibility of detectable increases in³He⁺⁺ flux in plasma which left the Sun at the time of³He flares has been investigated, but no significant increase was seen.     

Differential rotation of the solar atmosphere as determined from millimeter data

Radiospectroheliograms obtained at millimeter wavelengths were used to determine the rotation of the solar atmosphere. Regions observed in both emission as well as absorption (associated with H dark filaments) were followed across the disk. The average sidereal rotation rate deduced from emissive regions is given by (deg day^-1)=14.152(±0.270)-4.194(±3.017)sin² B, where B is the heliographic latitude and the quoted errors are the standard deviations of a least squares fit to the data. The rate deduced from absorption regions is given by =14.729(±0.286)-1.050(±1.611)sin² B. This rate is larger than that of emissive regions at all latitudes and shows smaller differential rotation. This apparent difference in the rotation rates is probably due to the difference in the height of formation of the emissive and absorption regions. This difference could be used to estimate the difference in height between an emissive region and an absorption feature in millimeter radiation.