Planetary Radio Interferometry and Doppler Experiment (PRIDE) to infer information on the interior structure of

Valerio Filice

1 Outline

§ Who I am § ExoMars LaRa experiment § PRIDE technique § PRIDE multi-station tracking strategy § Simulation goals, solver, setup § Simulation results § Future developments and possible limitations

2 Who I am § M.Sc. Graduate in Space and Astronautical Engineering at ‘La Sapienza’ University of Rome § M.Sc. Thesis Intern at Department of Space Engineering at Delft University of Technology § Currently Young Scientific Researcher in the ExoMars LaRa Experiment Team at Royal Observatory of Belgium § [email protected]

3 Outline

§ Who I am § ExoMars LaRa experiment § PRIDE technique § PRIDE multi-station tracking strategy § Simulation goals, solver, setup § Simulation results § Future developments and possible limitations

4 ExoMars LaRa Experiment

5 ExoMars LaRa Experiment

§ X-band transponder on the onboard the Russian surface platform of the ExoMars 2022 mission § It will remain steady and operational on Mars surface for one year (687 days) § Antwerp Space has built LaRa instrument models (thermal, structural, electrical, qualification, and flight models) § IKI (Russian Space Research Institute) integrated on the Surface Platform

6 ExoMars LaRa Experiment § Geophysics can be used as a tool for “remote sensing” of the interior § Doppler measurements will be used to obtain Mars’ orientation in space and rotation

7 ExoMars LaRa Experiment § Changes in the orientation can be divided into two components: precession and nutation § Variations in the length-of-day () exist due to angular momentum exchange between the solid and its

8 ExoMars LaRa Experiment § This experiment consists in measuring precise Doppler shifts on a two-way X-band radio between the and the LaRa transponder on the

9 ExoMars LaRa Experiment § The precise tracking from Earth over a long period of time (annual or more) allows obtaining Mars’

Precession Nutation ���

Moment of inertia Size of the core Mass redistribution of CO2 in Mars’ atmosphere and polar caps

10 Outline

§ Who I am § ExoMars LaRa experiment § PRIDE technique § PRIDE multi-station tracking strategy § Simulation goals, solver, setup § Simulation results § Future developments and possible limitations

11 PRIDE technique

§ The radioscience instrumentation consists of Telecommunications NASA Deep Space Network [DSN] subsystem on board ESA European Space the spacecraft Tracking [ESTRACK] § PRIDE is a multi-purpose, multi-disciplinary enhancement of planetary missions science return

Observables Ground stations

phase- radial open-loop referenced Doppler VLBI tracking measurement

12 PRIDE technique § -long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy

13 Outline

§ Who I am § ExoMars LaRa experiment § PRIDE technique § PRIDE multi-station tracking strategy § Simulation goals, solver, setup § Simulation results § Future developments and possible limitations

14 PRIDE multi-station tracking strategy

LaRa coherent transponder Uplink (7.162 GHz)

Downlink (8.415 GHz)

15 PRIDE multi-station tracking strategy

Nominal tracking strategy PRIDE tracking strategy § One hour per tracking session (15 § Shadow tracking when there are minutes of acquisition time) tracking passes scheduled by the § Tracking sessions twice a week (every DSN (selected passes) 3.25 days) § Network of radio telescopes from the § Three DSN ground stations: EVN and the VLBA § Goldstone § Open-loop Doppler data § Madrid § Canberra Enhancement of the amount, type and § Closed-loop Doppler data accuracy of Doppler data

16 PRIDE multi-station tracking strategy § Multi-coherent three-way

Doppler link Uplink § Master frequency standard of the uplink station § Different receiving-only PRIDE Downlink stations

The goal is to analyze the added value of having data from tens of VLBI stations added to the standard Doppler data

17 PRIDE multi-station tracking strategy

§ Orbit determination is the process of determining the parameters of a dynamical model by fitting the model on the observations

18 PRIDE multi-station tracking strategy

§ The probability density of the observation errors � has to be justified a priori by knowing the observation process or a posteriori with statistical tests

Observations from different The error distribution of stations at the same time are this technique can be described by a supposed to be correlated correlated Gaussian noise

19 PRIDE multi-station tracking strategy

§ The probability density function of the observation errors has zero mean and variance-covariance matrix, which are defined as follows:

§ The observations correlation coefficient �!" measures the degree of linear correlation between the random errors in two observations from different stations at the same time

20 Outline

§ Who I am § ExoMars LaRa experiment § PRIDE technique § PRIDE multi-station tracking strategy § Simulation goals, solver, setup § Simulation results § Future developments and possible limitations

21 Simulation goals, solver, setup

§ Investigate the accuracy of the estimated parameters achievable with the PRIDE technique w.r.t. the accuracy attainable by the nominal tracking strategy § Formal error 1� coming from the minimum variance inversion, and ratios of formal errors (errors with and without PRIDE data)

§ Operational and technical parameters related to PRIDE are taken into account: – mission duration

– observations correlation coefficient (� ∈ 0, 1 ) – number of stations involved (1,...,10 stations) – cadence of tracking sessions (2hr per week, 1,...,4 week per month)

22 Simulation goals, solver, setup

§ TUDAT is a powerful set of C++ libraries that support astrodynamics and space research

EVN and VLBA locations database ��(�) � = ��!"#

Partials w.r.t. MOPs Pathfinder model

§ Every implementation was verified, validated and tested, and they are publicly available on GitHub (https://github.com/Tudat)

23 Simulation goals, solver, setup

§ 700 days starting from the 1st of January 2021 § PRIDE three-way tracking configuration was used to create simulated Doppler § Nominal landing site: (335.45°E, 18.20°N, -2.5 km) § Doppler data are acquired within the range of [35-45]°of elevation above the local horizon of the surface platform § Uplink provided by one DSN station (DSS63, Madrid) § Solar Earth Probe (SEP) angle larger than 20° § Elevation angle at ground stations larger than 20°

24 Simulation goals, solver, setup

§ Doppler data affected by a white noise of 0.05 mm/s @ 60s for both DSN and PRIDE antennas § Highest number of observations and highest elevation angle according to the simulation constraints described

Selected EVN antennas network • CAMB32 • DARNHALL DEFFORD • JB-Mk-2 • KNOCKIN • MATERA • MEDICINA • NOTO • YEBES40M

25 Simulation goals, solver, setup Estimated parameters Uncertainty Units Mars position 1 km Mars velocity 1 Km/s Core Factor F 0.07 unitless

Free core Nutation rate �!"# 50 days Lander position (x, y , z) 10, 10, 10000 m

Seasonal Spin variations (Cosine Amplitude) �$%, � = 1, … , 4 15 mas

Seasonal Spin variations (Sine Amplitude) �&%, � = 1, … , 4 15 mas

Polar Motion (X component) ��$%, ��&%, � = 1, 2 10 mas

Polar Motion (Y component) ��$%, ��&%, � = 1, 2 10 mas

Chandler wobble (X component) ��$, ��& 50 mas

Chandler wobble (Y component) ��$, ��& 50 mas 26 Outline

§ Who I am § ExoMars LaRa experiment § PRIDE technique § PRIDE multi-station tracking strategy § Simulation goals, solver, setup § Simulation results § Future developments and possible limitations

27 Simulation Results

§ Formal error at end of mission as function of

– observations correlation coefficient �!" – number of involved stations

28 Insert a picture

29 Simulation Results

§ End of mission improvements of a-priori constraints as

function of the observations correlation coefficient �$% § Ten stations involved in the shadow tracking

30 InsertNumber of ground stations:a picture10

31 Simulation Results

§ Formal errors as function of the – mission time – tracking strategy – tracking cadence

32 Observations Correlation coefficient �!" = 0.5 InsertNumber a of pictureground stations: 10

33 Insert a picture

34 Outline

§ Who I am § ExoMars LaRa experiment § PRIDE technique § PRIDE multi-station tracking strategy § Simulation goals, solver, setup § Simulation results § Future developments and possible limitations

35 Future developments and possible limitations

§ The use of Open-loop Doppler data may be beneficial § Statistical characterization of the observations correlation coefficient § Quantify the Doppler noise in VLBI measurements for the selected antennas § Ground stations are not perfectly calibrated, there are small biases (error in station position, station clock rate, the local humidity) between station that can make difficult to properly combine Doppler data EVN Proposal E19C005, dr. Dominic Dirkx (PI), "EVN Observations of Mars landers - Enhancing knowledge of Martian interior", 2019

A conference paper was accepted for publication in the PEGASUS Student Conference 2020 36 Grazie per l’attenzione

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