Constraints on LISA Pathfinder’s self-gravity: design requirements, estimates and testing procedures

TLDR: The LISA Pathfinder satellite was launched on 3 December 2015 toward the Sun Earth first Lagrangian point (L1) where the LISA Technology Package (LTP), which is the main science payload, will be tested.

Abstract: LISA Pathfinder satellite was launched on 3 December 2015 toward the Sun Earth first Lagrangian point (L1) where the LISA Technology Package (LTP), which is the main science payload, will be tested. LTP achieves measurements of differential acceleration of free-falling test masses (TMs) with sensitivity below 3 x 10(exp -14) m s(exp -2) Hz(exp - 1/2) within the 130 mHz frequency band in one dimension. The spacecraft itself is responsible for the dominant differential gravitational field acting on the two TMs. Such a force interaction could contribute a significant amount of noise and thus threaten the achievement of the targeted free-fall level. We prevented this by balancing the gravitational forces to the sub nm s(exp -2) level, guided by a protocol based on measurements of the position and the mass of all parts that constitute the satellite, via finite element calculation tool estimates. In this paper, we will introduce the gravitational balance requirements and design, and then discuss our predictions for the balance that will be achieved in flight.

Figures

Figure 5: External and S/C balance masses.

Table 1: The gravitational parameter requirements and calculated values.

Figure 3: SC structure finite element model.

Figure 2: LTP and S/C hardware.

Figure 4: Internal balance mass.

Figure 1: LTP conceptual picture

Full text

Armano, M. et al. (2016) Constraints on LISA Pathfinder’s self-gravity: design
requirements, estimates and testing procedures. Classical and Quantum Gravity, 33(23),
235015.
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advised to consult the publisher’s version if you wish to cite from it.
http://eprints.gla.ac.uk/136111/
Deposited on: 2 February 2017
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Constraints on LISA Pathfinder’s self-gravity:
design requirements, estimates and testing
procedures
M Armano
a
, H Audley
b
, G Auger
c
, J Baird
n
, P Binetruy
c
,
M Born
b
, D Bortoluzzi
d
, N Brandt
e
, A Bursi
t
, M Caleno
f
,
A Cavalleri
u
, A Cesarini
g
, M Cruise
h
, K Danzmann
b
, M de
Deus Silva
a
, D Desiderio
t
, E Piersanti
t
, I Diepholz
b
,
R Dolesi
g
, N Dunbar
i
, L Ferraioli
j
, V Ferroni‡
g
,
E Fitzsimons
e
, R Flatscher
e
, M Freschi
a
, J Gallegos
a
,
C Garc´ıa Marirrodriga
f
, R Gerndt
e
, L Gesa
k
, F Gibert
g
,
D Giardini
j
, R Giusteri
g
, C Grimani
l
, J Grzymisch
f
,
I Harrison
m
, G Heinzel
b
, M Hewitson
b
, D Hollington
n
,
M Hueller
g
, J Huesler
f
, H Inchausp´e
c
, O Jennrich
f
,
P Jetzer
o
, B Johlander
f
, N Karnesis
b
, B Kaune
b
,
N Korsakova
b
, C Killow
p
, I Lloro
k
, L Liu
g
,
R Maarschalkerweerd
m
, S Madden
f
, D Mance
j
, V Mart´ın
k
,
L Martin-Polo
a
, J Martino
c
, F Martin-Porqueras
a
,
I Mateos
k
, P McNamara
f
, J Mendes
m
, L Mendes
a
,
A Moroni
t
, M Nofrarias
k
, S Paczkowski
b
,
M Perreur-Lloyd
p
, A Petiteau
c
, P Pivato
g
, E Plagnol
c
,
P Prat
c
, U Ragnit
f
, J Ramos-Castro
qr
, J Reiche
b
,
J A Romera Perez
f
, D Robertson
p
, H Rozemeijer
f
,
F Rivas
k
, G Russano
g
, P Sarra
t
, A Schleicher
e
, J Slutsky
s
,
C Sopuerta
k
, T Sumner
n
, D Texier
a
, J Thorpe
s
,
R Tomlinson
i
C Trenkel
i
, D Vetrugno
g
, S Vitale
g
,
G Wanner
b
, H Ward
p
, P Wass
n
, D Wealthy
i
, W Weber
g
,
A Wittchen
b
, C Zanoni
d
, T Ziegler
e
, P Zweifel
j
a
European Space Astronomy Centre, European Space Agency, Villanueva de la
Ca˜nada, 28692 Madrid, Spain
b
Albert-Einstein-Institut, Max-Planck-Institut f¨ur Gravitationsphysik und
Leibniz Universit¨at Hannover, 30167 Hannover, Germany
c
APC UMR7164, Universit´e Paris Diderot, Paris, France
d
Department of Industrial Engineering, University of Trento, via Sommarive 9,
38123 Trento, and Trento Institute for Fundamental Physics and Application /
INFN
e
Airbus Defence and Space, Claude-Dornier-Strasse, 88090 Immenstaad,
Germany
f
European Space Technology Centre, European Space Agency, Keplerlaan 1,
2200 AG Noordwijk, The Netherlands
g
Dipartimento di Fisica, Universit`a di Trento and Trento Institute for
Fundamental Physics and Application / INFN, 38123 Povo, Trento, Italy
h
Department of Physics and Astronomy, University of Birmingham,
Birmingham, UK
‡ corresponding author: valerio.ferroni@unitn.it

Constraints on LISA Pathfinder’s self-gravity: design requirements, estimates and testing procedures2
i
Airbus Defence and Space, Gunnels Wood Road, Stevenage, Hertfordshire,
SG1 2AS, UK
j
Institut f¨ur Geophysik, ETH Z¨urich, Sonneggstrasse 5, CH-8092, Z¨urich,
Switzerland
k
Institut de Ci`encies de l’Espai (CSIC-IEEC), Campus UAB, Carrer de Can
Magrans s/n, 08193 Cerdanyola del Vall`es, Spain
l
DiSBeF, Universit`a di Urbino ”Carlo Bo”, Via S. Chiara, 27 61029
Urbino/INFN, Italy
m
European Space Operations Centre, European Space Agency, 64293
Darmstadt, Germany
n
The Blackett Laboratory, Imperial College London, UK
o
Physik Institut, Universit¨at Z¨urich, Winterthurerstrasse 190, CH-8057 Z¨urich,
Switzerland
p
SUPA, Institute for Gravitational Research, School of Physics and Astronomy,
University of Glasgow, Glasgow, G12 8QQ, UK
q
Department d’Enginyeria Electr`onica, Universitat Polit`ecnica de Catalunya,
08034 Barcelona, Spain
r
Institut d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capit`a 2-4, 08034
Barcelona, Spain
s
NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD
20771, USA
t
CGS S.p.A, Compagnia Generale per lo Spazio, Via Gallarate, 150 - 20151
Milano, Italy
u
Istituto di Fotonica e Nanotecnologie, CNR-Fondazione Bruno Kessler,
I-38123 Povo, Trento, Italy
Abstract. LISA Pathfinder satellite has been launched on 3th December 2015
toward the Sun-Earth first Lagrangian point (L1) where the LISA Technology
Package (LTP), which is the main science payload, will be tested. With its
cutting-edge technology, the LTP will provide the ability to achieve unprecedented
geodesic motion residual acceleration measurements down to the order of 3 ×
10
−14
m/s
2
/Hz
1/2
within the 1 − 30 mHz frequency band. The presence of the
spacecraft itself is responsible of the local gravitational field which will interact
with the two proof test-masses. Potentially, such a force interaction might prevent
to achieve the targeted free-fall level originating a significant source of noise. We
balanced this gravitational force with sub nm/s
2
accuracy, guided by a protocol
based on measurements of the position and the mass of all parts that constitute
the satellite, via finite element calculation tool estimates. In the following, we
will introduce requirements, design and foreseen on-orbit testing procedures.
Keywords LISA; Pathfinder; self-gravity; differential accelerometer
PACS numbers: 04.80.Nn, 07.10.Pz, 89.20.Bb 91.10.Pp
1. Introduction
Shortly after commissioning phase of Lisa Pathfinder (LPF) [1, 2], the LISA
Technology Package (LTP) is going to be calibrated and probed with a battery
of on-flight experiments. The LISA Pathfinder differential accelerometer will orbit
around the Sun-Earth Lagrangian point L1. In addition to allowing a stable orbit
in the Sun-Earth reference frame, this provides a background gravitational gradient
seven orders of magnitude smaller than the low earth orbit occupied by GOCE
and other proposed geodesy differential accelerometers. Hence, very soon, the LPF
scientific payload, which is sketched in Figure 1, will perform the most sensitive
measurements of differential acceleration between free falling test bodies using the first
space high precision interferometer link, ever flown on-board of an orbiting satellite.

Constraints on LISA Pathfinder’s self-gravity: design requirements, estimates and testing procedures3
By measuring the differential acceleration between two test masses (TMs), one of
(a) TM interferometric link (b) TM reference axes
Figure 1: LTP conceptual picture
them being left free floating, (so nominally following a pure geodesic), and acting as
the reference of the measurement, LPF will verify whether a drag-free proof TM can
be kept along one measuring axis, x axis in Figure 1, in pure gravitational free fall
having a residual acceleration noise:
S
1/2
a
(f) ≤ 3 × 10
−14

1 +

f
3 mHz

m
s
2
1
√
Hz
; 1 mHz ≤ f ≤ 30 mHz . (1)
Fulfilling this requirement on the acceleration represents an important step
beyond the current limit [3, 4] and a step closer, factor of ten, for reaching the mission
pre-requisite to build space-born gravitational wave observatories [5, 6].
The presence of gravitational interactions between satellite and the proof TMs
modifies the local geodesic and the two TMs won’t follow the same geodesic because of
non-uniformity of the local gravitational field. This residual field needs to be balanced
by means of electrostatic actuation forces§, that invariably fluctuate themselves due
to voltage instabilities. This adds noise to the TM motion in the frequency band of
interest:
S
1/2
a,DC
= 2 λ ∆a
x
S
1/2
dV/V
= 7.8×10
−15

λ
1

∆a
x
0.65
nm
s
2



S
1/2
dV/V
6×10
−6
√
Hz


m
s
2
1
√
Hz
, (2)
where S
1/2
δV/V
is the relative amplitude stability of the applied actuation voltages and
λ is an order-unity factor dependent on the possible correlation the four amplifiers
used for x and φ actuation [7]. S
1/2
δV/V
has been measured on ground to be
between 3 and 8 ppm/Hz
1/2
for the relevant amplifiers to be used in flight. A DC
gravitational imbalance of 0.65 nm/s
2
will thus produce a relative acceleration noise
of 7.8 fm/s
2
/Hz
1/2
, and thus comfortably within the mission requirements in eqn. 1.
§ In such a context, the Drag-free attitude control subsystem (DFACS) will provide the ability to
keep the TM centered.

Constraints on LISA Pathfinder’s self-gravity: design requirements, estimates and testing procedures4
On the other hand, eqn. 2 shows that if the difference in gravitational force per
unit mass between TMs exceeds 2.5 nms
−2
, such an imbalance alone - i.e. in the
absence of any other noise - would make it impossible to achieve the mission goal,
eqn. 1. Thus the only way this mission succeeds is to balance ∆a
x
to nearly zero.
This is a crucial point for LPF and is the main driver of building the entire plan of
gravitational control for this mission, which will be described in this paper.
Other components ∆a
y
and ∆a
z
of the imbalance, and TM angular acceleration,
substitute ∆a
x
in eqn. 2 through cross-talk coefficients, and feed into noise on the
TM free fall along x. In addition self-gravity also produces through its force gradient,
a parasitic coupling between the spacecraft (S/C) and the TMs that multiplies the
read-out noise and the S/C jitter and adds-up to the other disturbances.
To control the noise budget of the mission and to specify the systemic parameters
as electrode-to-TM gaps, voltage fluctuations, and cross-talk coefficients, we set a
number of requirements on the TM imbalance, the TM unit of mass gravitational
force, the TM unit of inertia gravitational torque, and their gradients with respect to
the TM coordinates, the LPF gravitational parameters.
The main requirement applies to ∆~a, the imbalance between the TMs k; it is
expressed, the pedix
r
indicating requirement, by the inequalities:
|∆a
x
|
r
≤ 0.650 nm/s
2
; |∆a
y
|
r
≤ 1.100 nm/s
2
; |∆a
z
|
r
≤ 1.850 nm/s
2
. (3)
The first goal of the gravitational control plan is fulfilling inequalities 3.
The requirements on the other gravitational parameters are subordinate to
inequalities 3, were dealt with mostly in the design, and taken under strict control
during the system assemblage. They are all listed in the Appendix.
2. LPF
The LPF TMs are each placed inside an inertial sensor (IS) which monitors and
controls their position and attitude with respect to the spacecraft using a set of
capacitors. An high precision interferometer provides the laser link along the axis
(x axis in Figure 1) joining the two TMs for direct measuring the distance of the
nominal drag-free reference (TM1) with respect to the S/C and the TMs relative
distance, and supplementary angular measurements about the axes, y and z. Each
of the IS is enclosed inside the inertial sensor heading (ISH) with two important lock
mechanisms: the first one, the grabbing, positioning, release mechanism (GPRM) is to
hold the TMs before its final release into free-fall; the second, the caging and venting
mechanism (CVM), has the double function of constraining the TMs until LPF reaches
the desired orbit and of venting to space to provide the ultra-vacuum inside the ISH.
The two ISHs and the interferometer constitute LTP. The LTP core assembly
(LCA), placed inside the spacecraft’s inner cylinder, consists of the following main
subsystems: 2 Inertial Sensor Heads (ISH), the Venting Ducts, installed at the bottom
part of the ISHs, the Optical Bench Assembly (OBA), the LCA Assembly Integration
Equipment (AIE), and the Diagnostic instruments (DDS) included inside S/C inner
cylinder where the LCA is placed.
The LPF spacecraft will carry on-board another science payload, the Disturbance
and Reduction System (DRS) module [8], a scientific contribution from NASA. DRS
uses the sensor information supplied by LTP and a set of proprietary micro thrusters
k In practice the gravitational imbalance plus smaller non-gravitational contributions.

Frequently asked questions

Q1. What are the contributions in "Constraints on lisa pathfinder’s self-gravity: design requirements, estimates and testing procedures" ?

With its cutting-edge technology, the LTP will provide the ability to achieve unprecedented geodesic motion residual acceleration measurements down to the order of 3 × 10−14 m/s2/Hz1/2 within the 1 − 30 mHz frequency band. In the following, the authors will introduce requirements, design and foreseen on-orbit testing procedures. Potentially, such a force interaction might prevent to achieve the targeted free-fall level originating a significant source of noise. 

Q2. How many EBMs were used to compensate the imbalance?

At LTP closure, the authors used only a few EBMs per ISH, in total less than 200 g mass, to compensate an imbalance of ∆~a(EBM) = [0.16, 0.13,−0.06] nm/s2. 

Q3. What was the procedure for adjusting the compensation to the up to date imbalance?

Once the ISH integration terminated, the authors modified the IBM nominal geometry to adjust the compensation to the up to date imbalance: the procedure was to use circular and rectangular holes, which are in principle easy to machine. 

Q4. How many items were used to compensate the residual imbalance?

The EBMs preliminary design allowed for a maximum of N = 25 items (for a total EBM mass < 1 kg) and a compensation capability of a few tenths of nm/s2. 

Q5. What was the purpose of the balancing?

the authors had the SBMs to compensate any residual imbalance after the integration of LTP with the satellite, and, in addition to gravitational compensation, to balance the centre of mass of the spacecraft. 

Q6. What is the main requirement of the gravitational control plan?

The main requirement applies to ∆~a, the imbalance between the TMs ‖; it is expressed, the pedix r indicating requirement, by the inequalities:|∆ax|r ≤ 0.650 nm/s 2 ; |∆ay|r ≤ 1.100 nm/s 2 ; |∆az|r ≤ 1.850 nm/s 2 . (3)The first goal of the gravitational control plan is fulfilling inequalities 3. 

Q7. What is the procedure put into effects?

The procedure put into effects allowed to calculate with enough accuracy all the needed gravitational parameters and to project the balance masses for the needed compensation. 

Q8. How many EBMs were designed to compensate the residual imbalance?

The IBMs were in the first place nominally designed to compensate a maximum of DC imbalance of about 50 nms−2 with ten pms−2 accuracy. 

Q9. How accurate is the measurement of the self-gravity field?

Their present knowledge indicates 0.010 nm/s2 measurement accuracy, well enough to assess the field within the uncertainties of the analysis and integration. 

Q10. What was the reason for the change in the design of the LPF?

In addition, manufacturing and integration processes modified the mass distribution over the time until the construction of the satellite completed. 

Q11. What is the probability of the TMs being released?

LPF will release the two TMs from the launch-lock mechanism a few days before entering the science phase, and, at that point, the first experimental data of LPF selfgravity will become available. 

Q12. What was the common method of calculating the gravitational parameters?

Joint reviews with the personnel working on both LTP and S/C gravitational parameters occurred periodically while the refinement level passed from A to E. 

Q13. What is the purpose of the LPF flying?

LPF flying will be the test bench to validate the technique of precisely designing the self-gravity of a spacecraft without the need of on-ground experimental apparatus. 

Q14. What is the TM acceleration of a parallelepiped?

Each point massindividual contribution to the TM acceleration is expressed by the formulas of the gravitational acceleration of an homogeneous parallelepiped (dimensions Lx, Ly, Lz) due to the point-like source (of mass ms):~A = GmsLxLyLz ∇x,y,z ∫ Lx −Lx ∫ Ly −Ly ∫ Lz −Lz dx′dy′dz′√ (x′ − x)2 + (y′ − y)2 + (z′ − z)2 . 

Q15. What is the difference between the two TMs?

The presence of gravitational interactions between satellite and the proof TMs modifies the local geodesic and the two TMs won’t follow the same geodesic because of non-uniformity of the local gravitational field. 

Q16. Why is the x-acceleration of the IBM so low?

The reason of this is due to the composition (W(95%)) of the IBM, its U-shaped geometry wrapped around the TM, and its proximity to the TM (only a few tens of mm away).