Spherical Versus Cubical Drag-Free Proof Masses for the LISA Satellites

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LISA

The LISA (Laser Interferometer Space Antenna) program will place three Drag-Free satellites in an earth-trailing solar orbit 20 degrees behind the earth. The satellites will be at the vertices of an equilateral triangle with a separation of 5 million kilometers. The change in distance between the satellites caused by the passage of gravitational waves will be measured by a laser interferometer. The satellites need to be Drag-Free in order to reduce the disturbances to a level where they will not mask the tiny strains in space caused by the passage of a gravitational wave. See the LISA Page of this website, The NASA LISA Page, The LISA Hannover Homepage, European Space Agency (ESA) LISA Homepage, The LISA Pre-Phase A Report, Second Edition (PDF), and The LISA STS Report (10 MB PDF).

Drag-Free Proof Mass Shapes and Single- vs. Three-Axis

There are a number of possible shapes for the Drag-Free proof masses, but the main choices are a sphere, a cylinder, or a cube.

The sphere would be a single three-axis Drag-Free reference for the two laser beams from the other satellites in the triangle.

In the case of the cylinder or the cube, there would be two proof masses in each satellite each reflecting one of the beams of the other two satellites. The cylinders and cubes would thus form two single-axis Drag-Free references inclined 60 degrees to one another, one for each beam from the sides of the triangle.

It will be argued that a sphere in a three-axis system should be included in the initial base-line design of the LISA system, and that other proof-mass shapes should only be considered when it has been shown that a sphere will not work. Not the reverse.

Reasons to Begin with a Spherical Proof Mass

1. A spherical proof mass in a three-axis Drag-Free satellite is completely free floating with no forces or torques deliberately applied to the proof mass.

2. The disturbance specification of the LISA proof mass of 3 x  10^-15 meters/sec²/Hz^1/2 is strongly supported by the DISCOS flight experience combined with the expected performance of modern Drag-Free satellites. See the discussion below or the detailed calculations of the disturbances.

3. Because of the results of DISCOS flight as explained above, a Technology Demonstration Mission for LISA would not be needed to prove the Drag-Free technology, i.e. the Technology Demonstration Flight has already occurred.

4. Placing two single-axis Drag-Free proof masses in a single satellite with the axes inclined by 60 degrees means that the second proof-mass cannot be Drag-Free at all. If the axes were inclined by 90 degrees, this would be possible; but at 60 degrees, the second proof mass has a component in the Drag-Free axis of the first. Correcting a disturbance to the first proof mass would require that the second have an applied force along its Drag-Free axis to counter this. Thus the second proof mass would not be Drag-Free.

5. Prior single-axis Drag-Free experience has demonstrated that a single-axis system is more difficult to implement and less reliable than a three-axis free-floating design. See below.

6. The satellite need be designed with only one Zero Self Gravity-Gradient point. The absence of special compensating masses could result in a significant weight saving.

7. It may be possible to improve the attitude-control reference by using the spherical proof mass as a precision Unsupported Gyroscope.

The DISCOS flight results can be used to strongly support the disturbing performance of the LISA satellites for the following reason: The flight results showed that the gradients of all fields at the proof mass were below 10^-7 / sec². If the LISA Drag-Free controller's performance is assumed to be 10^-9 meters/Hz^1/2, the component of the LISA specification of 3 x 10^-15 meters/ sec²/Hz^1/2 due to internal field gradients would be met. This leaves the external disturbances (energetic particles and the interlineations magnet field) and the internal disturbances which do not depend on the satellite motion. These two classes of disturbances can be shown to be smaller than 10^-15  meters/sec²/Hz^1/2. The flight demonstrated that the methodology used to calculate the disturbances gave the correct answers; and in particular, it showed that the gravity-gradient field at the proof mass can be determined during the design stage by calculating the gravity and gravity-gradient from every mass in the satellite. It should be pointed out that determining the gravity-gradient at the proof mass by calculation is a rigorous method and not merely an error bound or performance estimate. (See the discussion in the detailed disturbance calculations or in the DISCOS section.)

A LISA spacecraft with cylindrical or cubical proof masses would not be the first single-axis Drag-Free satellite. Five of the six Drag-Free satellites which have flown up to now were single-axis. These were TRIAD II / TIP II, TIP III, and NOVA I, II, and III. In the end the NOVA single-axis Drag-Free satellites worked as designed, but it took three flights, TRIAD II, TIP III, and NOVA I to get all of the problems solved and reach the performance which had originally been the goad of TRIAD II.

The engineers who worked on the single-axis satellites believed in the beginning that they would be simpler and easier. It turned out that they were more difficult than the three-axis version. Today they say that in retrospect, it would have been better to stick with the three-axis version.

It may well turn out that as yet unforseen problems will preclude the use of a spherical proof mass in LISA, and that we will be forced to a cubical or spherical proof mass. But for the reasons stated above, the LISA design should begin with the spherical proof mass.