A covariance analysis for the RAMSES Radio Science Experiment

Context: On April 13, 2029, the asteroid 99942 Apophis will have a very close encounter with the Earth, transiting the GEO ring. This flyby represents a unique opportunity to observe a well-known potentially hazardous asteroid subject to strong tidal forces. The time-varying orbital and rotational environment can lead to changes in the surface slopes. Depending on the circumstances, this mechanism may drive significant property changes in the asteroid's internal structure and granular motion on its surface. In this context, characterizing the bulk density and its mass distribution within the asteroid nucleus before and after the encounter could represent a critical step towards understanding the evolutionary history of near-Earth asteroids [1].Aim: In this work, we present the outline of a possible Radio Science Experiment (RSE) onboard the Rapid Apophis Mission for Space Safety (RAMSES) proposed by the European Space Agency, which is expected to rendezvous with the asteroid before the Earth's close encounter. The objectives of this experiment will include characterizing the overall mass, density, and porosity of the nucleus with an accuracy of less than 1%, refine the asteroid’s orientation and rotation modes to better than 1% for the dominant component and 10% for the secondary rotation components, estimating the extended gravity field and internal structure of the nucleus, and improving its heliocentric trajectory reconstruction.Methods: To reach the outlined objectives, the radio science experiment will exploit Earth-based radiometric measurements, namely Doppler, range, and ΔDOR, and optical images collected by the onboard navigation cameras. Furthermore, building on the experience gained with the RSE onboard the Hera mission [2] [3] [4], this study proposes a concept of operations involving an Inter-Satellite Link (ISL) between RAMSES and two deployable 6U CubeSats.The mothercraft is expected to rendezvous with Apophis in late February 2029. During a pre-encounter phase of roughly 40 days, the spacecraft will alternate passively safe hyperbolic orbits with hovering boxes at various altitudes between 20 km and 1 km. In the Earth close encounter phase, the spacecraft will retreat to a safe distance of roughly 15 km, hovering at a constant Sun phase angle and monitoring the evolution of Apophis with high-resolution images. In the post-encounter phase, the spacecraft will again move closer to the asteroid, mirroring the trajectories of the pre-encounter phase. The two CubeSats will be released prior to the Earth's close approach and will operate autonomously, communicating with the mother craft acting as a relay. The Orbiter CubeSat, carrying a low-frequency radar for internal structure probing, will transfer to a Periodic Terminator Orbit (PTO) at an altitude of 1.7 km from Apophis, where it will operate for roughly one month before retreating to a safe distance during the encounter. The Lander CubeSat, equipped with a seismometer, gravimeter, and magnetometer, will attempt a surface landing before the flyby to record in situ data during tidal stress.Results: The expected performance of the radio science experiment in terms of gravity and spin state estimation at the end of the Earth's close-encounter phase was assessed through a multi-arc covariance analysis using JPL's MONTE software.Preliminary results have shown that the proposed concept of operations satisfies the mission requirements in terms of mass estimation requirement with a relative accuracy of up to 0.04%. Adding Doppler and range ISL measurements, in particular for the CubeSat to CubeSat configuration, allows for the gravity field estimation up to degree and order three, which would otherwise not be possible in a Ramses-only scenario due to the mothercraft's high orbital altitude. Within this work, we also highlight the contribution of the ISL with the Lander CubeSat during the Earth encounter, which significantly contributes to the Apophis spin state reconstruction and characterization of the tidal interactions.References: [1] Findings from SBAG 29, July 11-13, 2023 (https://www.lpi.usra.edu/sbag/findings/). [2] Zannoni M. et al. (2018), Advances in Space Research, 62(8), 2273–2289. [3] Gramigna E. et al. (2024), Planetary and Space Science. [4] Gramigna E. et al. (2022), IEEE 9thMetrology for Aerospace, 430–435. [5] Pravec P. et al (2014) Icarus. [6]   Brozović, M. et al. (2018), Icarus. [7] Lasagni Manghi, R., et al. (2025). 2025 AAS/AIAA Space Flight Mechanics Meetings (https://doi.org/10.48550/arXiv.2503.19998).