Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Spin state and moment of inertia of Venus


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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Space-time correlation of Venus radar speckles.
Fig. 2: Spin axis orientation of Venus.
Fig. 3: Measurements of the instantaneous spin period of Venus.

Similar content being viewed by others

Data availability

The data sets generated and/or analysed during the current study are available from the corresponding author upon reasonable request.

Code availability

Software used to obtain and process the radar echo time series is available upon request by contacting the corresponding author.


  1. Smrekar, S. E., Davaille, A. & Sotin, C. Venus interior structure and dynamics. Space Sci. Rev. 214, 88 (2018).

    Article  ADS  Google Scholar 

  2. Dumoulin, C., Tobie, G., Verhoeven, O., Rosenblatt, P. & Rambaux, N. Tidal constraints on the interior of Venus. J. Geophys. Res. Planets 122, 1338–1352 (2017).

    Article  ADS  Google Scholar 

  3. O’Rourke, J. G., Gillmann, C. & Tackley, P. Prospects for an ancient dynamo and modern crustal remanent magnetism on Venus. Earth Planet. Sci. Lett. 502, 46–56 (2018).

    Article  ADS  Google Scholar 

  4. Davies, M. E. et al. The rotation period, direction of the North Pole, and geodetic control network of Venus. J. Geophys. Res. Planets 97, 13141–13151 (1992).

    Article  ADS  Google Scholar 

  5. Mueller, N. T., Helbert, J., Erard, S., Piccioni, G. & Drossart, P. Rotation period of Venus estimated from Venus Express VIRTIS images and Magellan altimetry. Icarus 217, 474–483 (2012).

    Article  ADS  Google Scholar 

  6. Campbell, B. A. et al. The mean rotation rate of Venus from 29 years of Earth-based radar observations. Icarus 332, 19–23 (2019).

    Article  ADS  Google Scholar 

  7. Yoder, C. F. in Venus II: Geology, Geophysics, Atmosphere, and Solar Wind Environment (eds Bougher, S. W. et al.) 1087–1124 (Univ. of Arizona Press, 1997).

  8. Sánchez-Lavega, A., Lebonnois, S., Imamura, T., Read, P. & Luz, D. The atmospheric dynamics of Venus. Space Sci. Rev. 212, 1541–1616 (2017).

    Article  ADS  Google Scholar 

  9. Horinouchi, T. et al. How waves and turbulence maintain the super-rotation of Venus’ atmosphere. Science 368, 405–409 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  10. Roadmap for Venus Exploration (Venus Exploration Assessment Group, 2019).

  11. Kaula, W. M. An Introduction to Planetary Physics: The Terrestrial Planets (Wiley, 1968).

  12. Williams, J. G. Contributions to the Earth’s obliquity rate, precession, and nutation. Astron. J. 108, 711–724 (1994).

    Article  ADS  Google Scholar 

  13. Folkner, W. M., Yoder, C. F., Yuan, D. N., Standish, E. M. & Preston, R. A. Interior structure and seasonal mass redistribution of Mars from radio tracking of Mars Pathfinder. Science 278, 1749–1751 (1997).

    Article  ADS  Google Scholar 

  14. Standish, E. M. & Williams, J. G. in Explanatory Supplement to the Astronomical Almanac 3rd edn (eds Urban, S. E. & Seidelmann, P. K.) Ch. 8 (University Science Books, 2013).

  15. Konopliv, A. S., Banerdt, W. B. & Sjogren, W. L. Venus gravity: 180th degree and order model. Icarus 139, 3–18 (1999).

    Article  ADS  Google Scholar 

  16. Cottereau, L. & Souchay, J. Rotation of rigid Venus: a complete precession-nutation model. Astron. Astrophys. 507, 1635–1648 (2009).

    Article  ADS  MATH  Google Scholar 

  17. Saunders, R. S. et al. Magellan mission summary. J. Geophys. Res. Planets 97, 13067–13090 (1992).

    Article  ADS  Google Scholar 

  18. Shapiro, I. I., Campbell, D. B. & de Campli, W. M. Nonresonance rotation of Venus. Astrophys. J. Lett. 230, L123–L126 (1979).

    Article  ADS  Google Scholar 

  19. Zohar, S., Goldstein, R. M. & Rumsey, H. C. A new radar determination of the spin vector of Venus. Astron. J. 85, 1103–1111 (1980).

    Article  ADS  Google Scholar 

  20. Shapiro, I. I., Chandler, J. F., Campbell, D. B., Hine, A. A. & Stacy, N. J. S. The spin vector of Venus. Astron. J. 100, 1363–1368 (1990).

    Article  ADS  Google Scholar 

  21. Slade, M. A., Zohar, S. & Jurgens, R. F. Venus: improved spin vector from Goldstone radar observations. Astron. J. 100, 1369–1374 (1990).

    Article  ADS  Google Scholar 

  22. Goldreich, P. & Peale, S. Spin-orbit coupling in the solar system. Astron. J. 71, 425–437 (1966).

    Article  ADS  Google Scholar 

  23. Goldreich, P. & Peale, S. Spin-orbit coupling in the solar system. II. The resonant rotation of Venus. Astron. J. 72, 662–668 (1967).

    Article  ADS  Google Scholar 

  24. Gold, T. & Soter, S. Atmospheric tides and the resonant rotation of Venus. Icarus 11, 356–366 (1969).

    Article  ADS  Google Scholar 

  25. Ingersoll, A. P. & Dobrovolskis, A. R. Venus’ rotation and atmospheric tides. Nature 275, 37–38 (1978).

    Article  ADS  Google Scholar 

  26. Dobrovolskis, A. R. & Ingersoll, A. P. Atmospheric tides and the rotation of Venus. I. Tidal theory and the balance of torques. Icarus 41, 1–17 (1980).

    Article  ADS  Google Scholar 

  27. Correia, A. C. M. & Laskar, J. The four final rotation states of Venus. Nature 411, 767–770 (2001).

    Article  ADS  Google Scholar 

  28. Bills, B. G. Variations in the rotation rate of Venus due to orbital eccentricity modulation of solar tidal torques. J. Geophys. Res. 110, E11007 (2005).

    Article  ADS  Google Scholar 

  29. Hide, R., Birch, N. T., Morrison, L. V., Shea, D. J. & White, A. A. Atmospheric angular momentum fluctuations and changes in the length of the day. Nature 286, 114–117 (1980).

    Article  ADS  Google Scholar 

  30. Lebonnois, S. et al. Superrotation of Venus’ atmosphere analyzed with a full general circulation model. J. Geophys. Res. Planets 115, E06006 (2010).

    Article  ADS  Google Scholar 

  31. Cottereau, L., Rambaux, N., Lebonnois, S. & Souchay, J. The various contributions in Venus rotation rate and LOD. Astron. Astrophys. 531, A45 (2011).

    Article  ADS  Google Scholar 

  32. Parish, H. F. et al. Decadal variations in a Venus general circulation model. Icarus 212, 42–65 (2011).

    Article  ADS  Google Scholar 

  33. Margot, J.-L. A data-taking system for planetary radar applications. J. Astron. Instrum. 10, 2150001 (2021).

    Article  Google Scholar 

  34. Margot, J.-L., Peale, S. J., Jurgens, R. F., Slade, M. A. & Holin, I. V. Large longitude libration of Mercury reveals a molten core. Science 316, 710–714 (2007).

    Article  ADS  Google Scholar 

  35. Margot, J.-L. Mercury’s moment of inertia from spin and gravity data. J. Geophys. Res. Planets 117, E00L09 (2012).

    Article  Google Scholar 

  36. Stark, A. et al. First MESSENGER orbital observations of Mercury’s librations. Geophys. Res. Lett. 42, 7881–7889 (2015).

    Article  ADS  Google Scholar 

  37. Bendat, J. S. & Piersol, A. G. Random Data: Analysis and Measurement Procedures 2nd edn (Wiley, 1986).

  38. Correia, A. C. M., Laskar, J. & Néron de Surgy, O. Long-term evolution of the spin of Venus: I. theory. Icarus 163, 1–23 (2003).

    Article  ADS  Google Scholar 

  39. Correia, A. C. M. & Laskar, J. Long-term evolution of the spin of Venus: II. numerical simulations. Icarus 163, 24–45 (2003).

    Article  ADS  Google Scholar 

  40. Gross, R. in Treatise on Geophysics 1st edn (ed. Schubert, G.) 239–294 (Elsevier, 2007).

  41. Goldreich, P. & Peale, S. J. Resonant rotation for Venus? Nature 209, 1117–1118 (1966).

    Article  ADS  Google Scholar 

  42. Navarro, T., Schubert, G. & Lebonnois, S. Atmospheric mountain wave generation on Venus and its influence on the solid planet’s rotation rate. Nat. Geosci. 11, 487–491 (2018).

    Article  ADS  Google Scholar 

  43. Fukuhara, T. et al. Large stationary gravity wave in the atmosphere of Venus. Nat. Geosci. 10, 85–88 (2017).

    Article  ADS  Google Scholar 

  44. Kouyama, T. et al. Topographical and local time dependence of large stationary gravity waves observed at the cloud top of Venus. Geophys. Res. Lett. 44, 12098–12105 (2017).

    Article  ADS  Google Scholar 

  45. Mitchell, J. L. Coupling convectively driven atmospheric circulation to surface rotation: evidence for active methane weather in the observed spin rate drift of Titan. Astrophys. J. 692, 168–173 (2009).

    Article  ADS  Google Scholar 

  46. Green, P. E. Radar Astronomy Measurement Techniques Technical Report No. 282 (MIT Lincoln Laboratory, 1962).

  47. Green, P. E. in Radar Astronomy (eds Evans, J. V. & Hagfors, T.) Ch. Radar Measurements (McGraw-Hill, 1968).

  48. Kholin, I. V. Spatial-temporal coherence of a signal diffusely scattered by an arbitrarily moving surface for the case of monochromatic illumination. Radiophys. Quant. Elec. 31, 371–374 (1988).

    Article  ADS  Google Scholar 

  49. Kholin, I. V. Accuracy of body-rotation-parameter measurement with monochromatic illumination and two-element reception. Radiophys. Quant. Elec. 35, 284–287 (1992).

    Article  ADS  Google Scholar 

  50. Margot, J. L., Hauck, S. A., Mazarico, E., Padovan, S. & Peale, S. J. in Mercury: The View after MESSENGER (eds Solomon, S. C. et al.) 85–113 (Cambridge Univ. Press, 2018).

  51. Duan, X., Moghaddam, M., Wenkert, D., Jordan, R. L. & Smrekar, S. E. X band model of Venus atmosphere permittivity. Radio Sci. 45, 1–19 (2010).

    Article  Google Scholar 

  52. Dziewonski, A. M. & Anderson, D. L. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981).

    Article  ADS  Google Scholar 

  53. Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. Numerical Recipes in C 2nd edn (Cambridge Univ. Press, 1992).

  54. Williams, P. K. G., Clavel, M., Newton, E. & Ryzhkov, D. pwkit: Astronomical Utilities in Python ascl:1704.001 (2017).

Download references


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.

Author information

Authors and Affiliations



J.-L.M. conducted the investigation and wrote the software and manuscript. D.B.C. contributed to the methodology. J.D.G., J.S.J., L.G.S., F.D.G. and A.B. contributed to data acquisition. All authors reviewed and edited the manuscript.

Corresponding author

Correspondence to Jean-Luc Margot.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Random-like variations in radar echo power are illustrated.

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.

Supplementary information

Supplementary Information

Supplementary Tables 1–6 and Figs. 1–7.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Margot, JL., Campbell, D.B., Giorgini, J.D. et al. Spin state and moment of inertia of Venus. Nat Astron 5, 676–683 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing