Pre-Phase A Report - Lisa - Nasa

46 Chapter 2 Different Ways of Detecting Gravitational Waves
of about 53 days. Two spacecraft would be close together at each corner of an equilateral
triangle, as for the LISA Cornerstone proposal, but the triangle would be about
1 000 000 km on a side instead of 5 000 000 km. An inclination of 11◦ to the ecliptic has
been mentioned for the orbits. The proposed telescope diameter was 15 cm, but we will
assume a more favourable diameter of 30 cm diameter, as in LISA, for a comparison of
the heliocentric and geocentric orbit options.
There are three main advantages expected for the geocentric option. One is that the
propulsion requirements after the initial launch for placing the spacecraft in the desired
orbits are much less. This would cut much of the cost of the interplanetary propulsion
modules for LISA, and would reduce the launch vehicle cost. The second advantage is
a simpler and less expensive telecommunications system for sending down the data. An
S-band system with small ground antennas could be used instead of an X-band system
with a large ground antenna, and the bandwidth could be much larger. This means that
less or no preprocessing and data compression would be needed on the spacecraft. Finally,
the time necessary to put the spacecraft in their final orbits would be considerably less
than the roughly one year planned for LISA.
It unfortunately is difficult to estimate reliabily the cost savings for a geocentric mission
compared with a heliocentric mission. The ESA study of both types of mission during
the first half of the M3 study led to an estimated cost difference of only about 15 %, and
the LISA mission was chosen for consideration in the rest of the study. However, the
same launch vehicle was assumed for both types of mission, so the actual savings could
be higher. Our present rough estimate is perhaps 20 % for the cost difference.
In terms of expected scientific results, a major question is the error budget allowed for the
inertial sensor. For LISA, the currently adopted requirement is 3×10−15 ms−2 / √ Hz from
0.1 to 10 mHz for an individual sensor. If a geocentric mission had the same requirement,
the overall interferometer sensitivity below about 3 mHz would be five times worse than for
LISA. In addition, the cross-over point between mainly inertial-sensor noise and mainly
distance-measurement noise would move up from 3 to about 7 mHz. If our present estimate
of the confusion-noise level due to unresolved galactic and extragalactic binaries is correct,
the loss in instrumental sensitivity would be serious for several types of signals that are
of high scientific importance. In addition, the potential information on some types of
galactic binaries would be degraded. The sensitivity at frequencies above roughly 30 mHz
would be improved for the geocentric mission because of the baseline staying shorter than
the gravitational wavelength up to higher frequencies. However, there are no sources
expected at present for which the frequency region from 30 mHz to the top of the LISA
band at 1 Hz would be important for detection.
If instead a factor five lower noise level is required for the inertial sensors in a geocentric
mission, then the question becomes how difficult it is to meet that requirement. While it
is possible that a lower noise level can be achieved if several of the potential noise sources
are on the lower end of their potential ranges, it appears difficult at present to design the
inertial sensors in such a way as to be sure of this. Thus, we regard a substantially tighter
inertial sensor requirement as a major technological hurdle that the mission would have
to overcome.
A second important technological issue for a geocentric mission is the need to keep sunlight
from getting into the telescopes when the optical axes point close to the sun. With six
3-3-1999 9:33 Corrected version 2.08