%\markright{GGonGround \underline{\textbf{Part B2}}}


\section{Proposal Part B2--Section 1}
%\label{sec:PartB2}

\setcounter{table}{1}

The Principal Investigators\\

Each of the Principal Investigators must provide a list reflecting their track record.
This can be either an 'early achievement track-record' (for PIs 2 to 12 years after their
PhD) or a '10-year track-record' (for advanced researchers) chosen by the applicants based
on which is most appropriate for their career stage.
The evaluation experts will be instructed to judge each PI against the benchmarks relevant to
his/her career stage. The experts will also pay particular attention to the joint effort of the
group that may be built around specialised infrastructure, or that allow for new combinations
of skills and disciplines, or the bringing together of researchers from different institutions,
sectors or countries.

\section{Proposal Part B2--A. Curriculum Vitae}
\label{sec:B2SectionA}

a. Curriculum Vitae (max 2 pages for each PI):\\

In addition to the standard academic and research record, the CV should include a
succinct 'funding ID' which must specify any current research grants and their
subject, as well as any ongoing application for work related to the proposal. This
facilitates the proper assessment of the proposal and the granting process in case the
proposal is retained for funding.
Any research career gaps and/or unconventional paths should be clearly explained. Peer
reviewers will take this into consideration when assessing the PI's quality and career
progression.


\section{Proposal Part B2--B Track-Record}
\label{sec:B2SectionB}
b. Track-Record\\

Early achievement track-record (max 2 pages for each PI):\\
The PI should list: his/her activity as regards:
1. Publications in major international peer-reviewed multi-disciplinary scientific
journals and/or in the leading international peer-reviewed journals, peer-reviewed
conferences proceedings and/or monographs of their respective research fields,
indicating the ten best, those without the presence as co-author of their PhD supervisor, and
information about the citation response they have attracted.
2. Granted patent(s) (if applicable).\\
3. Invited presentations to peer-reviewed, internationally established conferences
and/or international advanced schools (if applicable).\\
4. Prizes and Awards (if applicable).\\
or\\
10-Year track-record (max 2 pages for each PI):\\
The PI should list his/her activity over the past 10 years (dated from the deadline of the call)
as regards:\\
1. A list of the top 10 publications, as senior author (or in those fields where alphabetic
order of authorship is the norm, joint author), listing all authors, in major international peer-
reviewed multidisciplinary scientific journals and/or in the leading international peer-reviewed
journals and/or peer-reviewed conferences proceedings of their respective research fields,
also indicating the number of citations (excluding auto-citations) they have attracted.\\
2. Research monographs, chapters in collective volumes and any translations thereof
(if applicable).\\
3. Granted patents (if applicable).\\
4. Invited presentations to peer-reviewed, internationally established conferences
and/or international advanced schools (if applicable).\\
5. Research expeditions that the applicant has led (if applicable).\\
6. Organisation of International conferences in the field of the applicant (membership
in the steering and/or programme committee) (if applicable).\\
7. International Prizes/Awards/Academy memberships (if applicable).\\
8. Memberships to Editorials Boards of International Journals (if applicable).\\

The above mentioned page limits for sections 2a and 2b apply individually, i.e. maximum 4
pages per PI.\\
\clearpage

\section{GGonGround PartB2-Extended Synopsis}
\label{sec:B2SectionC}


{\bf The science case}. {\it General Relativity} (GR) is the best theory of gravity to-date. It governs physics at   the macroscopic and cosmic scales and has been highly successful. However, all attempts at merging gravity with the other forces of nature have failed and most of the mass of the universe is unexplained.

General Relativity  is based on the hypothesis that the gravitational force is composition independent: in a gravitational field all bodies fall with the same acceleration regardless of their mass and composition. This property is unique to gravity.  It is referred to as the {\it Universality of Free Fall} (UFF) and it is a direct consequence of the {\it Equivalence Principle} (EP). It was first subject to experimental proof by Galileo in Pisa. Newton regarded testing it as so important that reported the results of his own experiments ``{\it very accurately made}''   in the opening paragraph of the  {\it Principia}   to justify the assumption that ``{\it mass}'' and ``{\it weight}'' are equivalent --i.e. the equivalence between inertial and gravitational mass.  Einstein went much further and stated what he later referred to as the ``{\it happiest thought of my life}'':  if all bodies fall equally fast, in a freely falling frame gravity has --locally--  no dynamical effects.  UFF is therefore equivalent  to making the  ``{\it hypothesis of complete physical equivalence}'' between a gravitational field  and an accelerated frame(\cite{Einstein1907}, Ch. V {\it ``Principle of relativity and gravitation''}, Sec. $17$ {\it ``Accelerated reference system and gravitation''}).  Starting from this hypothesis --published in $1907$--  by extending it globally,  $9$ years later Einstein formulated the  {\it General Theory of Relativity},  which  is therefore founded on the UFF.    Any violation of UFF (hence of EP)  would violate General Relativity as well as all metric theories of gravity.

UFF experiments are unique tests of General Relativity in that --unlike all others-- they address the assumed composition independence of gravity which sets it aside from all other forces of nature; this fact  makes them the most deeply probing tests in the search for new physics beyond General Relativity and the current {\it impasse}. 

In the scientific community at large it is recognized that experimental evidence of a violation of the UFF (hence of EP) would make for a scientific revolution.


{\bf State of the art.} Very stringent limits to the validity of UFF and EP have been set by small size experiments in which the test masses are mechanically coupled by means of a very sensitive torsion balance which is also slowly rotating.  These experiments have reached a sensitivity to differential acceleration between the test masses of $\simeq1.69\cdot10^{-15}\,\rm ms^{-2}$, finding no violation in the field of the Earth to the remarkable level  $\eta=10^{-13}$\,\cite{Adel2008}, $\eta$ being the fractional differential acceleration of the test masses w.r.t. the Earth  (their average acceleration in the horizontal plane of the lab at the latitude of the lab is $\simeq1.69\cdot10^{-2}\,\rm ms^{-2}$). Despite the much larger free fall acceleration,  Galileo-like mass dropping tests have been by far less sensitive than torsion balances. The reasons are twofold:  a time of fall of just a few seconds and the test masses release errors.

Careful physical modeling and analysis of laser ranging data to the corner cube reflectors left on the surface of the Moon by the Apollo missions  have set a limit similar to that of torsion balances  for the Moon and Earth falling in the gravitational field of the Sun\cite{LLR2004}.

However, although a violation is expected at some point, no firm prediction exists as to the precise level at which it should occur.

Laboratory controlled experiments with slowly rotating torsion balances have reached the level of thermal noise~(\cite{adelreview2009}, Fig. 20);  lunar laser ranging tests are close to their limit\cite{EPwithlaserranging}.  Even one order of magnitude improvement may be difficult with those techniques. As for new tests based on dropping cold atoms, they have achieved $10^{-7}$, i.e. they are  $6$ orders of magnitude less sensitive than tests based on macroscopic bodies\cite{coldatoms2004}; and they have yet to match the best result $\Delta g/g\simeq3\cdot10^{-9}$ obtained in measuring the local gravitational acceleration by dropping a single species of atoms\cite{peters1999}.

It is apparent that a  radically new type of experiment is necessary to improve the current experimental limit in UFF and EP tests by several orders of magnitude thus deeply probing this physical domain so far unexplored.



{\bf The case for a test of UFF and EP in low Earth orbit}. Back in the 1970s it was realized that a torsion balance kind of experiment  in which two weakly coupled test masses orbit the Earth inside a low altitude spacecraft would be equivalent to dropping them from an ``infinitely'' tall tower, thus yielding both a stronger signal from Earth (by about $3$ orders of magnitude) and a time of fall around it as long as the mission duration (and no mass release problems). A violation signal (pointing to the center of the Earth) would appear at the (low) orbital frequency of the satellite --of a few $10^{-4}\,\rm Hz$-- to  be upconverted to higher frequency by rotation of the spacecraft in order to reduce noise~(\cite{ChapmanHanson},~\cite{WordenThesis},~\cite{WordenAA1987}).    Absence of weight and isolation of the laboratory (the spacecraft) are additional great advantages. Overall, in low Earth orbit an improvement by  $4$  orders of magnitude, down to $\eta=10^{-17}$, is within reach and the idea  has attracted the interest of NASA and of other space  agencies later on.

At an orbiting altitude $h\simeq600\, \rm km$ where the attraction from the Earth is $g(h)\simeq8\,\rm ms^{-2}$ it requires to detect a differential acceleration of the test cylinders relative to each other as small as  $a=\eta\,g(h)\simeq8\cdot10^{-17}\, \rm ms^{-2}$. If they are coupled with a natural differential period of oscillation  $T_d$, the corresponding relative displacement to be measured by the read out is $r=a\,(T_d^2/4\pi^2)$ (at the satellite orbital frequency); the weaker is the coupling, the longer is the differential period, the more sensitive is the accelerometer.

{\bf The case for ``Galileo Galilei'' (GG)}. Torsion balances are not appropriate in space. All investigators agree that the test cylinders should be ``concentric'' --with the centers of mass as close as possible to each other to reduce classical differential ({\it tidal}) effects due to the non uniformity of the gravitational field--  and should rotate, in order  to upconvert the signal to higher frequency --the higher the better. The question is:  should the concentric test cylinders be sensitive (i.e. weakly coupled) along the symmetry axis ($1$D accelerometer) and rotate around an axis perpendicular to it, or else should they rotate around the symmetry axis and  be sensitive  in the plane perpendicular to it ($2$D accelerometer)?

Although spinning around an axis which is not the symmetry axis is unnatural, the choice of coupling the test cylinders in $1$D prevailed, despite the fact that it essentially rules out fast rotation because it is well known that forcing an oscillator above its natural frequency causes the forcing signal to be attenuated. Overall, this choice made it necessary to solve the main critical issues of a high sensitive space experiment by brute force, most notably by requiring that the experiment be carried out in cryogenic conditions, close to absolute zero temperature~\cite{radiometerPRD}.

The signal to be measured asks for both weak coupling and fast spin, a situation which is known as {\it rotation in supercritical regime}: it makes fast rotation possible through autocentering, but it is well known that it cannot work in $1$D --it works only if coupling occurs in $2$D  (\cite{DenHartog},~\cite{Crandall1970}). The ``Galileo Galilei'' (GG) space experiment was proposed in the mid $1990$s by A. M. Nobili and colleagues  who realized taht this choice makes most of the critical issues disappear by design: fast rotation does not attenuate the expected low frequency signal; the centers of mass of the test cylinders center on each other by the laws of physics; most dangerous effects become DC; the experiment does not require cryogenics; fast rotation and cylindrical symmetry allow passive $1$-axis stabilization of the spacecraft and significantly reduce its size and complexity; etc... (\cite{JAS1995},~\cite{NA_GG_1998}).

Strong arguments have been published in support of the novel idea  of a differential accelerometer sensor with the proof masses weakly coupled in $2$D (rather than along a single direction as in all previous attempts) and rotating faster than their natural oscillation frequency (\cite{CQG1999},~\cite{radiometerPRD},~\cite{radiometerMicroscope}). The GG  space experiment has been investigated by ASI (Agenzia Spaziale Italiana) (\cite{}). More importantly than all that, the new sensor design allows a full-size  $1$-g version of it --with the same number of degrees of freedom and the same dynamical features-- to be built and tested on ground: the symmetry axis of the  concentric test cylinders is in the vertical direction, they are suspended  and spin around it while being  weakly coupled in the horizontal plane of the lab. GG on Ground has been set up with funding from ASI and INFN (\cite{NA_GGG_2003},~\cite{GGG_RSI_I},~\cite{GGG_RSI_II},~\cite{IJMPD}); the latest experimental results  reported in Fig.\ref{fig:GGGPictureandLSD} are at the basis of this proposal. More than any paper it demonstrates that weak coupling and sensitivity to very small forces are compatible with rapid rotation; indeed, it is rapid rotation that makes sensitivity to very small forces possible.

Surprisingly enough, the most relevant physical property of the GG novel sensor design has been discovered in 2011: 

%
\begin{figure}[ht]
\begin{center}
\includegraphics[height=6cm]{GGGpicture2011.jpg}
%\hspace{1mm}
\includegraphics[height=6cm]{XnrXsdW.jpg}
\caption{{\it Left:} the GGG experimental apparatus (at INFN lab in San Piero-Pisa, built with funding from ASI and INFN) while opening the vacuum chamber. The test masses are concentric hollow cylinders ($10\,\rm kg$ each) with the symmetry axis in the vertical direction, weakly coupled in the horizontal plane by means of high quality $CuBe$ joints in $2$D. Together they form   a very peculiar beam balance in which the beam is vertical --hence the balance  is sensitive to differential forces in the horizonal plane (it is a differential accelerometer)-- and, more remarkably, the masses of the balance are concentric. The relative displacements of the test cylinders in the horizontal plane are  read by $2$ orthogonal capacitance bridges whose plates are located halfway in between the test cylinders. The balance rotates around the vertical axis so that low frequency forces in the horizontal plane are upconverted to the spin frequency. The rotating shaft is held by ceramic ball bearings. An additional $2$D weak joint is located just below the bearings in order to reduce low frequency tilts and horizontal accelerations due to e.g. terrain microseismic noise and  bearings noise on the shaft. Note that both terrain and bearings noise are absent in the space experiment because the spacecraft is isolated  (no terrain) and  after its initial spin up  by the launcher no  motor or bearings are needed thanks  to angular momentum conservation.  The outer cylinder  is visible close to the bottom flange of the chamber. {\it Right:} Linear spectral density of the relative displacements of the concentric test cylinders in the horizontal plane of the lab in a $20\, \rm d$ run (still ongoing) after demodulation from the rotating frame (the spin frequency of the system is $0.19\,\rm Hz$). The frequency of interest is the frequency expected in space in case of violation of the universality of free fall and the equivalence principle in the field of the Earth,  which is the orbital frequency of the GG satellite around it at an altitude  $h\simeq600\,\rm km$: $\nu_{GG}=1.7\cdot10^{-4}\, \rm Hz$. At  $\nu_{GG}$ the measured displacement noise is $2\cdot10^{-7}\, \rm m/\sqrt{\rm Hz}$; after integrating for $30\,\rm d$ and with a coupling natural oscillation period  of $10$~s, the differential acceleration noise --at this frequency-- is $8.5\cdot10^{-11}\,\rm ms^{-2}$. }
\label{fig:GGGPictureandLSD}
\end{center}
\end{figure}
%


xxxxxxxxx

We propose as sensor a rapidly rotating differential accelerometer  which allows the most critical  issues involved in the space experiment to be addressed  without the need of brute force approaches, such as operating in cryogenic conditions  at extremely low temperatures. With this novel sensor the spacecraft itself is highly simplified, size and complexity are minimized thus maximizing the chances of success. Last but not least, the sensor that we propose is compatible with a ground version which shares the main physical features of the space one. By sufficiently isolating it from ground noise sources it is possible to demonstrate experimentally that the performance required in space can be achieved.

A small satellite GG (``Galileo Galilei'') and the corresponding ground experiment GGG (``GG on Ground'') have been designed in Pisa and a pre-prototype has been built~\cite{GGExpAstr2009}. They are based on the novel idea of proof masses weakly coupled in $2$-D (rather than along a single direction as in all previous attempts) and rotating faster than their natural oscillation frequency~\cite{PRLthermalnoise}. The science goal of GG in space is to improve the current best torsion balance tests by $4$ orders of magnitude, reaching the level of $10^{-17}$. Thanks to the stronger signal, this precision can be achieved if the sensor in space has a sensitivity to differential accelerations of just one order of magnitude better than torsion balances.


xxxxx


We propose an unconventional  sensor which can be run in space with 1e4 improvement by making the main critical issues disappear by design. A small satellite GG (“Galileo Galilei”) and the corresponding ground experiment GGG have been designed  and a pre-prototype has been built by solving many problems in a variety of fields.

Slowly rotating torsion balances have already reached the level of thermal noise\,(\cite{adelreview2009}, Fig. 20), which is quite remarkable because by upconverting the low frequency signal to higher frequency reduces the level of thermal noise is reduced as $1/\sqrt(\omega_{spin}$:  By rotating the balance with a period of about $20$ minutes they have improved by a factor $70$ as compared to relying on the $24$-hr rotation of the Earth, reducing the integration time by the same factor.


A giant leap by 4 orders of magnitude: opens new horizons and opportunities for research ...


It is feasible, thanks to Explorer


 An agreement exists between JPL -the Jet Propulsion Laboratory of CalTech and NASA- and ASI (Agenzia Spaziale Italiana) to submit GG to the EXPLORER program of small size missions as a NASA led mission and the partnership of ASI.


{\bf The case for GGonGround}. GG is a high precision physics experiment which can reach its final sensitivity and meet its outstanding science goal only in orbit, but that is just the final run of an experiment whose performance can and must be tested and demonstrated in the lab. The EXPLORER program is the route to space for GG. GGonGround -by synergy between two highly dedicated groups- is the route for GG to succeed within the EXPLORER competition.



{\bf The case for GGonGround Synergy Grant proposal.} As reported in Fig.\ref{fig:GGGPictureandLSD} (right), the current GGG apparatus has demonstrated a sensitivity of $8.5\cdot10^{-11}\, \rm ms^{-2}$ at $\nu_{GG}=1.7\cdot10^{-4}\, \rm Hz$, while the GG experiment orbiting around the Earth at this frequency should be sensitive to a differential acceleration of  $8\cdot10^{-17}\, \rm ms^{-2}$ in order to reach its goal. Having analyzed the noise sources which limit the current ground apparatus we can convincingly argue that it can be improved to reach a sensitivity of  $8\cdot10^{-16}\,\rm ms^{-2}$ (also in $30\, \rm d$); this requires to further reduce the bearings and local terrain noise (both absent in the space experiment), to weaken the coupling of the test cylinders and to implement a laser gauge read out replacing the current capacitance read out.


Synergy dedication to project, multidisciplinary, road map feasibility core time, resources


\begin{table}[t]\footnotesize
\begin{center}
\begin{tabular}{|l|p{3.9cm}|p{4cm}|p{2.85cm}|p{1.5cm}|}
\hline
\hline
\hline
\multicolumn{5}{|c|}{\textbf{GGonGround goal vs GG goal in space}} \\
\hline
\hline
\hline
  &Differential acceleration between test masses       &$a \, [\rm{ms^{-2}}]$                         &$r=a\frac{T_d^2}{4\pi^2}\, [{\rm m}]$&Integration time $T_{int}$\,[$\rm d$]\\
  &$a$~@~$1.7\cdot10^{-4}\, \rm Hz$                     &                                                    &                &      \\
\hline
\hline
{\bf GG goal in space}      &$a_{GG}=\eta g(h)$                                   &$8\cdot10^{-17}$                                     &$6\cdot10^{-13}$&$1$      \\
                    &(upconverted to $1\,\rm Hz$)                         &($\eta=10^{-17}\, ,\, h\simeq600\, \rm km$)            &($T_d\simeq540\,\rm s$)    &       \\
\hline
\hline
{\bf GGonGround}   &$a_{GGG}=10 a_{GG}$                                &$8\cdot10^{-16}$                                    &$3.2\cdot10^{-14}$  &$30$    \\
{\bf goal}          &(upconverted to $0.2\div 3\,\rm Hz$)                 &                                                    &($T_d\simeq40\,\rm s$)    &       \\
\hline
\hline
\hline
\end{tabular}
\begin{tabular}{|l|l|p{2.3cm}|p{2cm}|p{2.1cm}|p{4.6cm}|}
\hline
\multicolumn{6}{|c|}{\textbf{GGonGround noise budget @~$1.7\cdot10^{-4}\, \rm Hz$}} \\
\hline
Noise Source &$\Delta a$                                   &Integrated $\Delta a$   &$\Delta r$                             & Integrated $\Delta r$ & Conditions and physical data\\
             &                                              &($T_{int}=30$~d)      &($T_{d}\simeq40$~s)                     &($T_{int}=30$~d)     &           \\
             &$[10^{-13}\frac{\rm{ms}^{-2}}{\sqrt{\rm{Hz}}}]$ &$[10^{-16}\rm{ms}^{-2}]$ &$[10^{-11}\frac{\rm{m}}{\sqrt{\rm{Hz}}}]$ & $[10^{-14}\rm{m}]$     &           \\
\hline
\multicolumn{6}{|l|}{\it {Tilt noise sources:} $a_{tilt}=\frac{k_c}{mgL}\frac{k_{shaft}}{M_{tot}gL_{shaft}}g\theta_{tilt}$} \\
\hline
terrain          & 8.2&5.1 &3.3 &2.1 & $\theta_{terrain}\simeq8\cdot10^{-6}\, \frac{\rm{rad}}{\sqrt{\rm{Hz}}}$\\
\cline{1-5}
air bearing      &4.1 &2.5 &1.7 &1.0 & $\theta_{ab}\simeq4\cdot10^{-6}\, \frac{\rm{rad}}{\sqrt{\rm{Hz}}}$\\
                 &    &    &    &    & $k_c\simeq k_{shaft}\simeq0.04\, \rm Nm/rad$ \\
                 &    &    &    &    & $m=10\,\rm kg$  $L=0.5\,\rm m$ \\
                 &    &    &    &    & $M_{tot}\simeq80\,\rm kg$ $L_{shaft}\simeq4\,\rm m$\\
\hline
\multicolumn{6}{|l|}{\it Thermal noise sources\cite{PRLthermalnoise},\cite{IntegrationTime}} \\
\hline
suspensions      &1.3 &0.8 &0.5 &0.3 & internal damping, $\nu_{spin}=0.2$~Hz\\
\hline
eddy currents    &1.3 &0.8 &0.5 &0.3 & no $\mu$metal magnetic shield\\
\hline
residual gas     &0.5 &0.3 &0.2 &0.1 & 2 cm gap, $\rm{P}=10^{-4}$~Pa\\
\hline
\multicolumn{6}{|l|}{{\it ReadOut noise:} $a_{ROnoise}=(4\pi^2/T_{d}^2)r_{ROnoise}$} \\
\hline
laser gauge      &7.4 &4.6 &3.0 &1.8 & $T_{d}\simeq40$~s\\
\hline
\bf{Total noise}       &12 &7.4 &4.8  &3.0 & \\
\hline
\end{tabular}
\label{tab:GGGErrorBudget1}
\caption{GGonGround goal and noise budget  }
\end{center}
\end{table}









\begin{table}[h!]\footnotesize
\begin{center}
\begin{tabular}{p{0.5cm} p{1.6cm} p{13.5cm} }
\hline
\multicolumn{3}{|c|}{\textbf{GGonGround} Roadmap} \\
\hline
\multicolumn{3}{l}{Time (Months)} \\
\hline
\multicolumn{3}{c}{Performance achieved} \\
&$t_0$ & $a_0=8.5\cdot10^{-11}\,\rm{ms^{-2}}$ (INFN lab San Piero, Pisa; ASI and INFN funding; Fig.\,\ref{fig:GGGPictureandLSD})\\
\hline
\multicolumn{3}{c}{First 18--month period targets} \\
6&$t_0+6$ & $a_1=2.8\cdot10^{-12}\,\rm{ms^{-2}}$ ($T_d=14.8\,\rm{s} \ \ r_{capRO}=1.45\cdot 10^{-8}\,\rm{m/\sqrt{Hz}}$; can be done with capacitance read out and ball bearings,
requires weaker joints by a factor 4)\\
12&$t_0+12$ & $a_2=7.7\cdot10^{-14}\ ms^{-2}$ ($T_d=40\,\rm{s} \ \ r_{capRO}=3\cdot 10^{-9}\,\rm{m/\sqrt{Hz}}$; can be done with capacitance readout and ball bearings,
requires 10 times longer suspension shaft)\\
18&$t_0+18=t_1$ & $a_3=5.6\cdot10^{-15}\,\rm{ms^{-2}}$ ($T_d=40\,\rm{s} \ \ r_{laserRO}=2.2\cdot10^{-10}\, \rm{m/\sqrt{Hz}}$; requires preliminary version of air bearings and
 laser metrology)\\
\hline
\multicolumn{3}{c}{Second 18--month period targets} \\
24&$t_1+6$ & reduce air bearings and rotation noise \\
30&$t_1+12$ & reduce laser gauge read out noise\\
36&$t_1+18=t_2$ &  $a_4=7.7\cdot10^{-16}\,\rm{ms^{-2}}$ ($T_d=40\,\rm{s} \ \ r_{laserRO}=3.0\cdot10^{-11}\,\rm{m/\sqrt{Hz}}$; requires air bearings to full performance and
improved laser metrology)\\
\hline
\multicolumn{3}{c}{Third 18--month period targets} \\
42&$t_2+6$ & Install rotating whirl control (as required in GG)\\
48&$t_2+12$  &  Measure patch effects and demonstrate that they are not relevant; improve sensitivity to effect from Sun @ $24\,\rm h$ by Phase Sensitive Detection in preparation for analysis of space data   \\
54&$t_2+18=t_3$ & Optimize test masses different composition, manufacture test masses, measure their quadrupole moments and confirm
requirements \\
\hline
\multicolumn{3}{c}{Fourth 18--month period targets} \\
60&$t_3+6$ & Manufacture suspensions required for GG in space, measure their elastic constants and quality factors and confirm fulfilment  GG requirements\\
66&$t_3+12$ & Demonstrate on bench laser gauge read out noise to $r_{laserRO}\simeq10^{-12}\,\rm{pm/\sqrt{Hz}}\ @ \ 1\div2\,\rm{Hz}$ \\
72&$t_3+18=t_4$ & Test PZTs and inchworms to demonstrate feasibility of balancing in space\\
\hline
\hline
\end{tabular}
\label{tab:GGGRoadmap}
\caption{GGonGround Roadmap}
\end{center}
\end{table}

xxx



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xxx

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