ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF Simulation and measurement of the thermal behaviour of the LAGEOS- type CCRs for the LARES mission G. Delle Monache INFN-LNF, Laboratori Nazionali di Frascati dell’INFN Frascati (Rome), I-00044, ITALY for the LARES Collaboration

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF LARES: GOAL of the measurement In GR a central rotating mass drags the local space-time frame around it. The Earth drags the orbit of an artificial satellite like LAGEOS. This is the “Lense-Thirring” effect (LT) LARES: passive satellite to measure this effect with ≤1% accuracy. It will improve the 10% measurement done with LAGEOS I/II (I.Ciufolini, E.C. Pavlis, Nature 2004) LAGEOS

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF Why a thermal characterization of LARES? 1% accuracy means measuring ~ 2m/yr precession of the node of the orbit, with 2 cm/yr accuracy in a few years. Since laser ranging accuracy ~ few mm, the main experimental errors are: – Geo-potential – Thermal thrusts (TTs) due to Sun radiation and Earth IR emission. TTs give ~ 2% error on LT (Nature, Oct. 2004) – The work reported here focuses on TTs i ~ 70 o (supplementary to LAGEOS I), e ~ a ~ Km

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The LARES thermal design: options LARES diameter is 300 mm, half the diameter of LAGEOS. It can be designed following two options: 1. Scaling from the LAGEOS, but with a complete thermal characterization. TTs are measured, no attempt to reduce/eliminate them 2. New design to strongly reduce TTs and full thermal characterization to measure the residual TTs

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The LARES thermal design: tools 1. Specialized software package for thermal simulation of satellites 2. Climatic and Thermal Vacuum Test Chamber (CTVTC) The strategy is to validate simulated models with experimental tests and iterate the parametric thermal design

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The software package Thermaldesktop®, Radcad®, Sinda/Fluint ® Main features: 1.FE-FD-Monte Carlo modellers 2.Solar and IR optical material property definition

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The CTVTC (preliminary lay-out) Solar simulator (or Earth IR) Ge window tunnel (IR camera) LARES prototype 77K shield Vacuum shell Service turret

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The LARES – LAGEOS “connection” LARES CCRs will be the same of the LAGEOS, so the R&D program for the thermal and mechanical characterization of the LARES CCR assembly can be useful for the physics analysis of LAGEOS data. The R&D consists of TV-tests with Solar and Earth IR simulators. The first tests are performed on a simplified prototype with 9 CCRs housed in an AA base (the 3x3 matrix). Temperature acquisition by IR camera (0.1 K resolution) and probes.

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The 3x3 LAGEOS CCR matrix

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The 3x3 LAGEOS CCR matrix LEICA TC2002 total station POLI CMM 26 o relative orientations

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF Screw (AA) Retainer ring (AA) Upper mounting ring (KEL-F) CCR Lower mounting ring (KEL-F) AA Base (T6 6061) LAGEOS assembly The LAGEOS CCR assembly

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF The model Preliminary. 1.Volumetric IR absorption in the CCR not yet simulated 2.Thermal resistance of all interfaces simulated. Critical. It really needs to be measured Temperature of AA Base fixed (CCR IR emission evaluation)

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF Thermal gradients & thrusts CCR Thermal relaxation time,  CCR Sunlit pole of LAGEOS Figures and calculations by Victor J. Slabinski, Cel. Mech. Dyn. Astr. vol.66, (1997) 2/3 1/3

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF Optical property simulation RadCad module simulates total internal reflection

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF CCR T plot, T base =300 K, Sun on T (K) at t = secT (K) at t = 2800 sec

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF Transient simulation Temp (K) vs time (sec) The LAGEOS CCR, has never been measured. In the literature estimates vary from 2000 sec to 7000 sec, ie by 250%. This implies a 2 % error on the LT effect due the TTs. Our goal: measure  CCR at 5% accuracy. This will give a 0.04 % error on LT due to TTs. With a ≤ 0.5 K accuracy on thermometry this goal is within (statistical) reach. SUN=on, IR=off  CCR = 2400 ± 40 sec (2% error) Error on T = 0.5 K SUN=off, IR=on  CCR = 2700 ± 200 sec (7% error) Error on T = 0.5 K

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF LAGEOS T CCR (K) nodes vs time (sec): top, edge, tab, bottom

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF LARES new design: “shell over the core” The idea is to bring some of the solar radiation (the parts which are not reflected by the CCR) to the “night side” of the satellite. Also the IR radiation re-emitted by the back of each CCR propagates to the night side due to the new geometry The outer shell houses the CCRs, while the inner sphere (Tungsten made) gives mass and support to the shell. Total weight is ~100 Kg

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF LARES new design The void between shell and sphere puts the corner side of all CCRs in “radiative contact” (vacuum conducts better than Al). This should lead to a more uniform temperature among the CCRs and a lower thermal gradient along the CCR axis

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF LARES new design: back mounting This design allows the CCR “back mounting” option too. The retainer ring is replaced by a retainer seat machined directly on the shell. This removes 1/3 of the TTs according to the Slabinski paper. Details can be found in: G. Delle Monache: LARES satellite thermal design: proposal for the limitation of thermal trust – INFN LNF LARES tech note 2 G. Delle Monache: LARES thermal design: comparison between Al and Vacuum “conduction” between two plates - INFN LNF LARES tech note 1

ILRS W. Eastbourne 3 Oct G. Delle Monache, INFN-LNF Conclusions 1. The LAGEOS and LARES CCR thermal relaxation time will be measured for the first time. 2. This is mandatory for the success of the LARES mission. This will be useful also for the physics analysis of LAGEOS data. 3. This will make the perigee (not just the node) useful to test General Relativity and beyond. 4. If the new satellite design will be successfull, LARES will be a test particle subject only to the geo-potential, quasi-free from thermal thrusts