Acceleration disturbances due to gravity gradients in ASTROD I

1
Acceleration disturbances due to gravity
gradients in ASTROD I
Sachie Shiomi National Tsing-Hua University,
Hsinchu, Taiwan 30013, ROC
The Astrodynamical Space Test of Relativity
using Optical Devices (ASTROD) mission consists
of three spacecraft in separate solar orbits to
carry out laser interferometric ranging. ASTROD
aims at testing relativistic gravity, measuring
the solar system and detecting gravitational
waves. Because of the larger arm length, the
sensitivity of ASTROD to gravitational waves is
estimated to be about 30 times better than LISA
in the frequency range lower than about 0.1 mHz.
ASTROD I is a simple version of ASTROD, employing
one spacecraft in a solar orbit. It is the first
step of ASTROD with several scientific goals and
simultaneously serves as a technology
demonstration mission for ASTROD. The required
acceleration noise level of ASTROD I is 10-13
ms-2 at the frequency of 0.1 mHz. In this paper
we give an overview of the sources and magnitudes
of acceleration disturbances to the ASTROD I
proof mass. We focus on local gravity gradient
noise that could be one of the largest
acceleration disturbances in the ASTROD I
experiment. We discuss possible sources of local
gravity gradients and present the results of
gravitational analyses using simplified models
for the current configuration of ASTROD I.
ASTROD I concept
Acceleration disturbances estimated assuming the
control-loop.
S. Shiomi and W.-T. Ni 2005
Two-Way Interferometric and Pulse Laser Ranging
between Spacecraft and Ground Laser Station
W.-T. Ni, S.Shiomi and A.C.Liao 2004
Local gravity gradients

• Monte Carlo simulation
• Positional fluctuations of 1 mm in the x-y plane
  are insignificant for a model of homogeneous
  spacecraft (density 35.6 kgm-3, mass 350 kg) with
  a rectangular housing at its centre (2mm gap from
  the rectangular test mass, 50?50 ?35 mm3).
• More realistic models of the spacecraft are under
  study.

Positional fluctuations of the test mass
produce dominant terms q1m, which are
proportional to q00?(fluctuation). These terms
couple to Q2m and produce unwanted acceleration
(see above equations). Therefore, the magnitude
of the unwanted acceleration is independent of
the shapes of the test mass to the first order,
but is dependent of the mass distribution of the
spacecraft (Q2m). These analyses agree with
results given by Xu and Ni.
References W.-T. Ni et al. 2002 I.J.M.P.D 11
1035-1048 X. Xu and W.-T. Ni et al. 2003
Adv.Space.Rev. 32 1443-1446 W.-T. Ni, S.Shiomi
and A.C.Liao 2004 Class. Quantum Grav. 21
S641-S646 S. Shiomi and W.-T. Ni 2005
arXivgr-qc/0506012 v1 2 Jun 2005 S. Shiomi et
al. 2001 Class. Quantum Grav. 18
2533-25415 DUrso and Adelberger 1997 Phys. Rev.
D 55 7970-7972
6th Edoardo Amaldi Conference on gravitational
waves, June 20-24, 2005 Bankoku Shinryoukan Kise
Nago, Okinawa