Fundamental properties of the planet Venus, such as its internal mass distribution and variations in length of day, have remained unknown. We used Earth-based observations of radar speckles tied to the rotation of Venus obtained in 2006–2020 to measure its spin axis orientation, spin precession rate, moment of inertia and length-of-day variations. Venus is tilted by 2.6392 ± 0.0008 deg (1σ) with respect to its orbital plane. The spin axis precesses at a rate of 44.58 ± 3.3 arcsec per year (1σ), which gives a normalized moment of inertia of 0.337 ± 0.024 and yields a rough estimate of the size of the core. The average sidereal day on Venus in the 2006–2020 interval is 243.0226 ± 0.0013 Earth days (1σ). The spin period of the solid planet exhibits variations of 61 ppm (~20 min) with a possible diurnal or semidiurnal forcing. The length-of-day variations imply that changes in atmospheric angular momentum of at least ~4% are transferred to the solid planet.
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The data sets generated and/or analysed during the current study are available from the corresponding author upon reasonable request.
Software used to obtain and process the radar echo time series is available upon request by contacting the corresponding author.
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This article is dedicated to the memory of Raymond F. Jurgens, who was instrumental in acquiring the data for this work. We thank M. A. Slade, J. T. Lazio, T. Minter, K. O’Neil and F. J. Lockman for assistance with scheduling the observations. We thank B. A. Archinal, P. M. Davis, S. Lebonnois, J. L. Mitchell and C. F. Wilson for useful comments and A. Lam for assistance with Fig. 1. The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Part of this work was supported by the Jet Propulsion Laboratory, operated by Caltech under contract with NASA. We are grateful for NASA’s Navigation and Ancillary Information Facility software and data kernels, which greatly facilitated this research. J.-L.M. was funded in part by NASA grant nos. NNG05GG18G, NNX09AQ69G, NNX12AG34G and 80NSSC19K0870.
The authors declare no competing interests.
Peer review information Nature Astronomy thanks Alexandre Correia, Attilio Rivoldini and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Representative variations in radar echo power (speckles) from observations of Venus with the Goldstone Solar System Radar and Green Bank Telescope at 8560 MHz on 2016 Nov. 26. The GBT echo was shifted in time by 20 s to illustrate the high degree of correlation between the received waveforms when the speckle trajectory is aligned with the antenna baseline.
Extended Data Fig. 2 The trajectory of wavefront corrugations sweeping over both the Goldstone and Green Bank antennas is illustrated.
Radar echoes from Venus sweep over the surface of the Earth during the 2020 Sept. 08 observations. Diagrams show the trajectory of the speckles one hour before (left), during (center), and one hour after (right) the epoch of maximum correlation. Echoes from two receive stations (red triangles) exhibit a strong correlation when the antennas are suitably aligned with the trajectory of the speckles (green dots shown with a 1 ~ s time interval).
Extended Data Fig. 3 The constraints on the spin axis orientation of Venus obtained with Goldstone-GBT observations of radar speckles are illustrated.
Each colored line represents a measurement of the epoch of correlation maximum that traces a narrow error ellipse on the celestial sphere. The orientation of each line is related to the ecliptic longitude of the projected baseline at the time of observations (Supplementary Table 2). The best-fit spin axis orientation is shown by a diamond at the intersection of the colored lines. All measurements have been precessed to the J2000.0 epoch. The black dotted line represents the trace of the spin axis orientation on the celestial sphere as a result of spin precession between 1950 and 2050.
Extended Data Fig. 4 The distribution of normalized moments of inertia from the bootstrap analysis is illustrated.
Radar speckle tracking estimates of the normalized moment of inertia of Venus suggest residual uncertainties of 7% with the data obtained to date.
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Margot, JL., Campbell, D.B., Giorgini, J.D. et al. Spin state and moment of inertia of Venus. Nat Astron (2021). https://doi.org/10.1038/s41550-021-01339-7