Pre-Phase A Report - Lisa - Nasa

164 Chapter 8 Technology Demonstration in Space
the location of one proof mass, then the jitter of 10−8 rad/ √ Hz corresponds to a
displacement of 2×10−9 m/ √ Hz at the location of the other proof mass. This is
within the allowable limit of item 2, so condition (i) on attitude is more restrictive
than condition (ii), etc.
4. In order to achieve the target strain sensitivity across the armlength of 5×106 km,
the interferometer displacement noise must be lower than approximately
10 −11 m/ √ Hz
across the MBW. This includes all optical effects, as well as spurious proof-mass
motions. Allowing for reasonable apportioning of errors across the various contributions,
the requirement on the optics alone becomes
over the MBW.
8.2 ELITE Mission profile
10 −12 m/ √ Hz
8.2.1 Orbit and disturbance environment
Baseline option. For the baseline GEO option (and for a shared launch into higher
orbits), the main disturbance will be radiation pressure with a nominal force magnitude
of ≈ 10 µN (solar pressure 4.644×10 −6 N/m 2 ; Earth albedo plus IR pressure ≈ 0.2 of
solar pressure), modulated at the orbit frequency due to the variation in the direction of
the line-of-sight to the Sun. This disturbance will be essentially uniform, with only slight
stochastic variations due to solar fluctuations amounting to a few percent of the nominal
values. The largest stochastic disturbance is likely to be noise in the thrusters which may
be on the order of 1 µN (rms across the MBW).
De-scoped option. For the de-scoped option which may be necessary due to cost, the
most accessible orbit would be GTO (Geostationary Transfer Orbit). For example, from
a nominal Ariane 5 launch into GTO, the resulting orbit will be low-inclination, highly
eccentric, with a perigee altitude of ≈ 600 km (velocity ≈ 9.9 km/s), an apogee altitude
of 35786 km (velocity ≈ 1.6 km/s), and an orbit period of ≈ 10.6 hours. In the vicinity
of perigee, aerodynamic drag will dominate, with a nominal magnitude of ≈ 0.1mN
opposite the direction of travel (atmospheric density ≈ 5×10 −13 kg/m 3 at 600 km, solar
maximum; drag coefficient ≈ 2.2, spacecraft projected surface area ≈ 1m 2 ). For most of
the orbit, the altitude will exceed 1000 km, and the aerodynamic drag will be negligible
compared with radiation pressure (≈ 10 µN). The comparitively large drag at perigee will
saturate the electric thrusters and the inertial sensors, requiring an undesirable switching
of electrostatic suspension forces and a corresponding reset and calibration every orbit. It
would thus be desirable to boost the orbit perigee to above 1000 km in order to overcome
this problem. Furthermore, the GTO trajectory traverses the trapped radiation belts
twice per orbit, leading to an integrated electric charge build-up on each proof mass of
about 10 −10 C per orbit. However, ground tests have shown that this high charge rate can
be managed by enhancing the performance of the discharge system.
3-3-1999 9:33 Corrected version 2.08