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THE ORBITS AND MASSES OF THE MARTIAN SATELLITES AND THE LIBRATION OF PHOBOS
Open accessAbstract
This paper reports on an update to the orbits and masses of the Martian satellites Phobos and Deimos. We obtained the orbits by fitting a numerical integration to all available Earth-based astrometry through the opposition of 2003, spacecraft imaging observations through 2007, and the Doppler tracking of the Viking and Phobos 2 spacecraft; the Doppler data provide information on the satellite masses. Our dynamical model included the figure acceleration due to a librating Phobos; we determined the amplitude of the forced libration. We also took into account the secular acceleration of Phobos due to the tide that it raises on Mars and estimated the Martian tidal quality factor Q . We provide an assessment of the accuracy of the orbits and a geometrical description of the orbits in the form of mean elements.
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Phobos's rate of orbital decay is now known to be about 1.8 cm yr−1.
“Phobos’s rate of orbital decay is now known to be about 1.8 cm yr−1 (R. A. Jacobson 2010).”
From Phobos is not Hollow (2026) · cites this paper as R. A. Jacobson 2010
Section 4.4 reports a measured secular acceleration in Phobos’s mean longitude and attributes it to tides raised on Mars, supporting the claim that its orbit is changing. It does not state an orbital-decay rate of about 1.8 cm per year; the rate in the citing sentence is therefore not supported by our copy. (LLM, conf=0.82)
Experimental — accuracy not yet measuredGiven current measurements of Phobos's orbital period accurate to ∼10−4 s, the orbital period decay of 2 × 10−4 s yr−1 would be detectable within 1 yr of observation.
“Given that current measurements of Phobos’s orbital period are accurate to ∼10−4 s (R. A. Jacobson 2010), the orbital period decay of 2 × 10−4 s yr−1 would be detectable within 1 yr of observation.”
From Phobos is not Hollow (2026) · cites this paper as R. A. Jacobson 2010
Table 6 gives Phobos’s mean orbital motion, but no uncertainty from which to verify an orbital-period accuracy of ∼10⁻⁴ s. Section 6, “Accuracy of the Orbits,” discusses position and mean-motion uncertainties without quantifying period accuracy in seconds. The citation is attached to the measurement-accuracy clause, not the citing authors’ one-year detectability inference; searches for period accuracy and uncertainty did not establish the cited figure. (LLM, conf=0.72)
Experimental — accuracy not yet measuredCurrent measurements of Phobos's orbital period are accurate to ∼10−4 s.
“Given that current measurements of Phobos’s orbital period are accurate to ∼10−4 s (R. A. Jacobson 2010), the orbital period decay of 2 × 10−4 s yr−1 would be detectable within 1 yr of observation.”
From Phobos is not Hollow (2026) · cites this paper as R. A. Jacobson 2010
Table 6 gives Phobos’s mean-longitude rate, but does not give an uncertainty for its orbital period. Section 6, “Accuracy of the Orbits,” discusses position and mean-motion uncertainties without establishing period accuracy of approximately 10⁻⁴ s (searched: orbital period accuracy, seconds, and mean-motion uncertainty). (LLM, conf=0.72)
Experimental — accuracy not yet measuredPhobos is not hollow.
“Phobos is not Hollow”
From Phobos is not Hollow (2026) · cites this paper as R. A. Jacobson 2010
Section 4.2 discusses estimates of Phobos’s mass, while Section 4.3 models its gravitational effects and libration. Neither addresses whether Phobos is hollow. Searches for hollow, interior, porosity, and density found no passage establishing the claim. (LLM, conf=0.73)
Experimental — accuracy not yet measured
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Citations
Cites
Secular accelerations in the longitudes of the satellites of Mars
Sharpless, B. P. (1945) · The Astronomical Journal · doi:10.1086/105871 · Cited by 57 · cited 2×
“By analyzing the observed longitudes of Phobos between 1877 and 1941, Sharpless (1945) discovered the secular acceleration in its mean longitude.”
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Cited by
Sorted by citations
Parts, W., & Wright, J. T. (2026) · Research Notes of the AAS · doi:10.3847/2515-5172/ae6817
Metadata
- Authors
- Jacobson, R. A.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Jacobson, R. A.
- ORCID
- Jacobson, R. A.
- Venue
- The Astronomical Journal
- Publisher
- American Astronomical Society
- Published
- 2010-01-14
- Volume
- 139
- Issue
- 2
- Pages
- 668-679
- ISSN
- 0004-6256 (ISSN-L)
- 1538-3881
- OpenAlex
- W1963902468
- Cited by
- 132
- References
- 1
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 13 · 2023: 6 · 2022: 9 · 2021: 9 · 2020: 6 · 2019: 5 · 2018: 9 · 2017: 9 · 2016: 7 · 2015: 12 · 2014: 6 · 2013: 9 · 2012: 11
- FWCI
- 5.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Astronomical Journal (publishedVersion)
- Funders
- National Aeronautics and Space Administration
- California Institute of Technology
- Jet Propulsion Laboratory
- Topics
- Physical Sciences › Earth and Planetary Sciences › Space and Planetary Science › Planetary Science and Exploration
- Physical Sciences › Earth and Planetary Sciences › Space and Planetary Science › Astro and Planetary Science
- Physical Sciences › Engineering › Aerospace Engineering › Space Satellite Systems and Control
- Keywords
- Phobos, Deimos, Mars satellites, satellite orbits, satellite mass, tidal acceleration, tidal quality factor, mean orbital elements, orbit determination, Doppler tracking, astrometry, spacecraft imaging
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