Correction to: Nature Astronomyhttps://doi.org/10.1038/s41550-024-02253-4, published online 29 April 2024 In the version of the article initially published, the affiliation of Wouter van der Wal was incorrect and has now been corrected to the Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands in the HTML and PDF versions of the article.@en

We used one-way laser ranging data from International Laser Ranging Service (ILRS) ground stations to NASA's Lunar Reconnaissance Orbiter (LRO) for a demonstration of orbit determination. In the one-way setup, the state of LRO and the parameters of the spacecraft and all involved ground station clocks must be estimated simultaneously. This setup introduces many correlated parameters that are resolved by using a priori constraints. Moreover the observation data coverage and errors accumulating from the dynamical and the clock modeling limit the maximum arc length. The objective of this paper is to investigate the effect of the arc length, the dynamical and modeling accuracy and the observation data coverage on the accuracy of the results. We analyzed multiple arcs using lengths of 2 and 7 days during a one-week period in Science Mission phase 02 (SM02, November 2010) and compared the trajectories, the post-fit measurement residuals and the estimated clock parameters. We further incorporated simultaneous passes from multiple stations within the observation data to investigate the expected improvement in positioning. The estimated trajectories were compared to the nominal LRO trajectory and the clock parameters (offset, rate and aging) to the results found in the literature. Arcs estimated with one-way ranging data had differences of 5–30 m compared to the nominal LRO trajectory. While the estimated LRO clock rates agreed closely with the a priori constraints, the aging parameters absorbed clock modeling errors with increasing clock arc length. Because of high correlations between the different ground station clocks and due to limited clock modeling accuracy, their differences only agreed at the order of magnitude with the literature. We found that the incorporation of simultaneous passes requires improved modeling in particular to enable the expected improvement in positioning. We found that gaps in the observation data coverage over 12 h (≈6 successive LRO orbits) prevented the successful estimation of arcs with lengths shorter or longer than 2 or 7 days with our given modeling.@en

We processed and analyzed one-way laser ranging data from International Laser Ranging Service ground stations to NASA's Lunar Reconnaissance Orbiter (LRO), obtained from June 13, 2009 until September 30, 2014. We pair and analyze the one-way range observables from station laser fire and spacecraft laser arrival times by using nominal LRO orbit models based on the GRAIL gravity field. We apply corrections for instrument range walk, as well as for atmospheric and relativistic effects. In total we derived a tracking data volume of ≈ 3000 hours featuring 64 million Full Rate and 1.5 million Normal Point observations. From a statistical analysis of the dataset we evaluate the experiment and the ground station performance. We observe a laser ranging measurement precision of 12.3 cm in case of the Full Rate data which surpasses the LOLA timestamp precision of 15 cm. The averaging to Normal Point data further reduces the measurement precision to 5.6 cm. We characterized the LRO clock with fits throughout the mission time and estimated the rate to 6.9 × 10−8, the aging to 1.6 × 10−12/day and the change of aging to 2.3 × 10−14 /day2over all mission phases. The fits also provide referencing of onboard time to the TDB time scale at a precision of 166 ns over two and 256 ns over all mission phases, representing ground to space time transfer. Furthermore we measure ground station clock differences from the fits as well as from simultaneous passes which we use for ground to ground time transfer from common view observations. We observed relative offsets ranging from 33 to 560 ns and relative rates ranging from 2 × 10−13 to 6 × 10−12 between the ground station clocks during selected mission phases. We study the results from the different methods and discuss their applicability for time transfer.@en

The Cassini mission has provided measurements of the gravity of several moons of Saturn as well as an estimate of the tidal response, which is expressed as the degree 2 Love number k2 of its largest moon, Titan. The first estimates of Titan’s Love number were larger than pre-Cassini expectations. Interior modelling suggested it may be explained with a dense ocean, but the interpretation remains unclear. We analysed Cassini tracking data to determine Titan’s gravity field and its Love number. Our gravity results are consistent with earlier studies, but we find a lower Love number for Titan of k2 = 0.375 ± 0.06. This lower value follows from an elaborate investigation of the tidal effects. We show that a dense ocean is not implied by the obtained Love number; instead, a water or ammonia ocean is more probable. A lower density ocean can increase the likeliness of contact between the silicate core and ocean, which can leach minerals into the ocean and could promote its habitability.@en