Simple questions don’t necessarily have simple answers, at least if you want to get them right. Sometimes an innocent-sounding question can require a whole thesis or more to answer correctly. The answers here are a mix, a compromise between a fully detailed response and none, but they try to get the important ideas across; if for no other reason than to show that we know what we are doing. If you have a simple question that’s not in this list, let us know.
Why would the test masses fall when they are in orbit at constant height?
Well, er, um. The test masses are always falling, in orbit. That’s why weightlessness is sometimes called free fall. It is important not to confuse falling with changing height. Like a projectile, a satellite is always falling, but it is moving sideways at the same time, so after it’s gone (for example) a kilometer horizontally, it’s fallen eight centimeters or so below perfectly straight travel. But the Earth is round, and its surface curves downwards eight centimeters in the same distance. So the satellite will be the same height above the Earth as when it started. Same thing in the next kilometer, and the next...until the satellite gets all the way around, at the same height it started at. But it’s fallen all the way, it just happened to miss hitting the ground. See also, The Hitchhiker’s Guide to the Galaxy. The same is true of the test masses inside the satellite. They are falling too, nothing is holding them up. The satellite is there mostly to protect them from the wind of their motion, which although very thin at that altitude, would still seriously disturb our experiment. To keep the satellite itself from being disturbed or slowed by this air drag, we fire little jets—the helium thrusters—which exactly cancel the drag, as long as the helium lasts.
How do you pick test mass materials?
An interesting issue. How do you select materials to maximize their response to an unknown effect? There are three issues here. To maximize information return about the violation (whether any particular class of material falls faster, for example), you want to pick as many different materials as possible. The differences must be significant—it won’t do to select all similar materials. Second, to maximize certainty about the result—whether or not there is a violation—you should repeat the same experiment many times, changing at most one thing at a time, and have a few checks like the cyclic condition (below). If nothing you do changes the result, it may be real. Third, to be able to do the experiment at all, you have to pick materials that can be manufactured in the shapes and tolerances needed. There’s an additional constraint, NASA isn’t going to let you fly as many materials as you’d like—it’s expensive. Only a few pairs of materials will be allowed. The baseline mass choice, niobium, platinum-iridium, and beryllium, reflects a complex trade between these issues which emphasizes certainty in the result and manufacturablity over information return. The masses are arranged in a “cyclic condition” with one pair of masses (Pt-Ir/Be) duplicated in another accelerometer. The platinum-iridium masses are always in the center, and the beryllium masses are always outside. This prevents having a mass difference so large that it cannot be compensated by adjustments to the sensor coils. The final materials choice was based first on a selection of manufacturable materials, and then on the requirement that the materials be different in properties that might contribute to an Equivalence Principle violation, such as proton/neutron ratio, nuclear binding energy, and the like.
Beryllium & Niobium Test Masses
What is a "cyclic condition"?
This is the name given to a type of test for systematic errors. As applied to STEP, suppose we have three materials A, B, and C. The differences in acceleration A-B, B-C, and C-A between masses A and B, B and C, C and A, will add to zero if there are no systematic disturbances. If the sum (A-B)+(B-C)+(C-A) is non-zero, there is certainly a systematic disturbance. This powerful and model-independent technique for detecting systematic errors has been implemented in the arrangement of STEP test masses.
What is the reason for the shape of the masses?
It is well known that spherical objects respond to gravity like a point particle. It's less well appreciated that non-spherical objects don't usually do so when the gravity field is non-uniform and varies from one place to another. In a uniform gravity field the shape doesn't matter.
Consider a yardstick in the earth's gravity. The earth's gravity weakens with height, so if the yardstick is held vertically, one end is closer to the earth, and feels slightly stronger gravity. The high end likewise feels a little less gravity. There's a little excess which means that the yardstick falls a bit faster than a point particle at its center of mass. Some people say the yardstick's center of gravity is below its center of mass. For a similar reason (can you find it?) a thin disklike a pancake falls a bit more slowly than a point mass.
STEP's test masses are cylinders, so we can put one inside the other and be able to get to it for measurements and things. There's an optimum shape for a right circular cylinder, between a yardstick and a pancake, which has its principal moments of inertia all equal. This shape solves the problem if the gravity gradient (the change in gravity with height) is uniform, and makes the cylinder fall at the same rate as a sphere. But what if the gravity gradient is not uniform? Then there's a little more complicated shape, which still has its moments of inertia all equal, but has a belt around the middle. Actually there's a whole bunch of such shapes. And what if still higher derivatives are not uniform? You can continue as far as you like, making the non-spherical mass act as much like a sphere as you want, adding extra little belts and ridges until you get tired of it. We stopped with the belted shape, because the accuracy of manufacture becomes an issue, and because it's good enough for the sensitivity we want. Note that the gravity gradients that disturb us the most come from masses in the satellite, not from the earth as in the example. Because masses in the satellite (radios, batteries, liquid helium,...) are much closer than the Earth, their gravity gradients are as strong as those coming from the Earth. The higher-order gradients, in particular, decrease very rapidly with distance, and are a much larger concern coming from the satellite than from the Earth.
What about disturbances from higher moments of the Earth?
The biggest coupling to the differential mode is from the first order gravity gradient of the Earth. That has magnitude A" (3/2)gDx/r where g is the gravity at orbit height, r is the orbit height, and Dx is the distance between the centers of mass. The next higher moment is proportional to g(da/r)2, where a is the uncertainty in manufacture of either mass. That's a good deal smaller than A by da2/(r Dx ); depending on assumptions about the relative size of Dx and da, maybe several million times smaller (r is about 6.8´106 meters, da is a few microns, Dx less than 10-9 m). But Dx was picked to keep A from saturating the accelerometers, so A is less than about 30,000´10-17 g ; and a million or so times smaller than that is 1/30 of our estimated sensitivity. So these disturbances are not very important, but shouldn't be neglected either.
That's within one accelerometer. For comparisons between accelerometers, the higher moments of the earth are important; that's because separate accelerometers are so much farther apart-15 cm instead of ~10-9 m. In this case the disturbance is caused by small changes in the Earth's gravity gradient from point to point in the orbit, rather than higher gradients coupling directly to the test masses. These changes produce force at right angles to the sensitive direction, and are further reduced by the common mode rejection of the accelerometers, so things aren't quite so bad as the increase in length suggests. The remaining disturbance is probably a few hundred times our sensitivity, and can be further reduced during data analysis by calibration of the common mode rejection and modelling of the disturbance.
You can learn quite a lot about mass distribution in the Earth from measurements between accelerometers, and at one time STEP had a geodesy co-experiment to do just that; but it was cancelled for budgetary reasons. Too bad; the data would have enhanced the Equivalence Principle measurement as well. But we can achieve a good measurement anyway, because the disturbances from these higher Earth moments don't exactly resemble an Equivalence Principle violation. They differ in frequency (always at some harmonic of the orbit) and phase (always at the same place over the Earth), so they can be distinguished from a violation in data analysis.
Why don't you use spherical masses?
This issue has been raised several times in different versions of STEP, and we've had a lot of fun with it. The supposed advantage is that ideal spheres act like point particles, leading to a simplification in the design. For example, we had to go to a lot of effort to design the STEP test masses so they won't interact much with external gravity gradients, and they have to be made very carefully. That might not be needed with spheres, which are a simple design and fairly easy to make.
To keep the gravity gradient between the spheres from being too large, their centers of mass have to be at the same place. This can be done with hollow objects (as well as some really weird shapes), but is a particular problem with spheres. So the first problem is the inner sphere has to be put inside the outer sphere somehow; the best idea is to cut the outer one in two and reassemble it. So the outer sphere at least is no longer ideal, and you have the manufacturing problem of how to make two perfect hemispheres and joining them (much harder than simply making spheres). The next issue that has to be addressed is how to measure the position of the inner sphere. There are several techniques, from x-rays to software estimators (see the question on the usefulness of radiation sensors) that might do the job, and they are all slightly unsatisfactory, including a transparent outer sphere. The spheres have to be accurately centered on each other, and how do you manage that when you can't push on them independently? This suggests that holes are needed in the outer sphere, to push through. But you have to cut holes in the outer sphere anyway, to get any gas out-gas usually causes big disturbances-and to be able to control the charge on the inner sphere. No one has figured out how to degas without a hole, and if the inner sphere is charged you are sure to get some disturbance. If you are going to have holes, you may as well do the measurement job with SQUIDs or some other satisfying scheme. With holes in the outer sphere, especially small ones, you have to control its orientation very carefully to keep them aligned properly, and that's hard with a sphere. Finally, even without holes, you have to keep the spheres from turning at random-because they're not perfect, even if they are perfectly shaped. They will have density variations and their centers of mass will not be at the centers of the sphere, which will lead to measurement errors as the spheres turn around their centers of mass. Not to mention the gravitational couplings that you thought you'd gotten rid of when you selected the spherical geometry. All of this imperfection must be accounted for. Having done all this, the spheres are no longer spheres, they never were, quite; so you have to do a lot of calculations to use them, and come up with some good ideas, and do extremely careful machining to make them; It's not so simple as was believed, and it is looking like a development project in its own right. Which leads to the question, why bother? In the final analysis, and given the same cleverness in solving problems like those above, the performance of both perfect spheres and STEP belted cylinders is limited by density variations in the material, which is about the same in both cases; and the cylinders are much easier to make and work with.
What are STEP's pointing requirements?
STEP has no pointing requirements in the usual sense of the term. Rather, STEP uses the satellite attitude as a control input to reduce gravitational disturbances from the Earth. It does not matter what the attitude is, so long as the disturbances are minimized. We can use whatever attitude does the job. The correct attitude is found by using the gravity gradient disturbance as an error signal. This disturbance is proportional to the angular deviation from the best attitude. Changing the attitude controls the disturbance, so we implement a feedback loop which corrects the attitude until the disturbance is nearly zero. Then the satellite will automatically be pointing correctly. The "correct" attitude which minimizes the disturbances will be a fraction of an arc second from the instantaneous orbit normal, but this should not be confused with a requirement. Because the error signal is internal we wouldn't even need to know the attitude, if we didn't need to know the roll rate and phase of any Equivalence Principle signal. There are requirements on rotation of the satellite. Rotation is used in STEP to modulate the Equivalence Principle signal and distinguish it from fixed-frequency disturbances. For this the satellite must rotate up to three times orbital rate in either direction, and at constant rate during measurements. There is a requirement that the rate be constant to 1% of orbit rate, to keep the signal frequency constant and to prevent variations in centrifugal force which might disturb the measurement.
Why don't you use a torsion balance?
A torsion balance is a complex, rigid object which can't have its center of mass adjusted easily. The STEP test masses are free to move, simply shaped, and we can put their mass centers precisely at the same place, reducing many gravitational disturbances from the Earth and satellite. Moreover, the torsion fiber is redundant in space because of the weightless conditions, and it is as likely to be a source of disturbance as not, at the levels we are aiming for. The shapes and positions of our masses can be controlled much more accurately than a rigid rotor, made of two or more materials, can be made.
How does the mass centering work?
Two objects not at the same position are generally in slightly different gravity fields; the difference in their gravitational acceleration will be A =Ñg·DX, where DX is the difference in position and Ñg is the gravity gradient. The accelerometer measures A, and we work backwards to find an estimate for DX. Then we move the masses to reduce DX. This adjustment is made repetetively under computer control until DX is as small as possible. The limitation is the drag free residual acceleration in the differential mode. When the remaining acceleration from gravity gradient is smaller than the residual, no further adjustment is possible. The magnetic bearings are made in quadrants so we can adjust the masses' positions easily by changing the current trapped in them. After adjustment these supercurrents will be permanently trapped and never change. The stability of the adjustment depends on the stable supercurrents rather than a possibly variable current supply. The centering error signal A occurs at twice the frequency of the Equivalence Principle signal, and can always be distinguished from it.
How does the gravity gradient pointing work?
Any two differential accelerometers will measure slightly different common mode accelerations if they are at slightly different heights in the Earth's gravity. The difference in their common-mode gravitational acceleration will be A =Ñg·DH, where DH = L sin q is the difference in height for two accelerometers separated by L, q is the angle L makes wih the horizontal, and Ñg is the gravity gradient. This acceleration is used as an error signal in much the same way as the mass centering; but the controller uses the angle q, i.e. satellite attitude, as a control input to minimize A, rather than the distance between mass centers. Why is the gravity gradient disturbance at twice the signal frequency? It's a matter of geometry. The gravity gradient is symmetric about the horizontal plane, while the total gravity is not. So when the experiment rotates, the gravity gradient changes direction twice per rotation, and the total gravity only once. The illustration shows how the total force and difference in force between two objects change at different positions around the earth. The gravity vector always points toward the earth, and points in opposite directions on opposite sides. It changes sign once for each revolution. The gravity gradient is symmetric about a plane through the midpoint between the masses, and hence looks the same on opposite sides of the earth. It is reversed when the masses are at 90 degrees from their original position: hence, it changes sign twice rather than once. This difference between the gravity gradient force and the total gravity allows us to distinguish between the signal of an Equivalence Principle violation, which depends on total gravity, and disturbances caused by the gravity gradient.
What disturbances are caused by rotating the satellite?
So long as the rotation is smooth, none. In the rotating frame, centrifugal force is constant, and everything in the satellite is at rest so coriolis force is zero. If the rotation rate w is slightly variable, and if the masses are off-center by a distance R which varies an amount dR, the centrifugal force will vary by 2wRdw+w2dR; since the centrifugal force contributes part of the total spring constant restraining the masses, this produces a small disturbance (~10-15 m/sec^2) in the common mode, a small part of which appears in the differential mode. The rotation itself does not cause any disturbances, but it may cause some disturbances to appear at different frequencies and with different amplitudes. Chief among these are the effects of thermal distortion of the spacecraft, eccentricity of the orbit, earth gravity gradient, any helium tides, and so forth.
What disturbances are caused by the masses being off-center in the rotating satellite?
Two of the test masses define the rotation axis, and therefore can never be off-center. The others get moved to the rotation axis during the centering process, so they are also on center. The drag-free system provides all the forces and torques needed to keep the satellite's rotation axis centered on the test masses. The remaining disturbance is just the drag free residual acceleration, which has to be dealt with anyway.
What are the star tracker requirements?
The STEP star tracker needs to be able to measure angles of about 10 arc seconds. The star tracker is only a minor input to the attitude control, so the requirement is driven mostly by the need to have a very steady slow rotation. The star tracker must be able to measure the rotation in a small fraction of a turn.
Why don't we want any moving parts?
If the satellite weighs 500 kg, a part that weighs 5 gm and moves 1 cm will cause the whole satellite to move in response by 1´10-7 m. This is in the common mode of the accelerometers, and about 10-4 of it will appear in the differential mode-as big as our Equivalence Principle sensitivity. Rapid motions cannot be compensated by the drag free system and will cause broad-band disturbances, at frequencies where the common mode rejection ratio is not so good as 10-4. Slower motions can be compensated, at least in part, but may use a substantial part of the available thrust. Because many subsystem designers want to use moving parts (gyros, relays, motors, valves, thrusters) the safest and cheapest policy is to ban all but the essential moving parts in the thrusters, rather than try to account for and track a number of them.
Can't we use gyroscopes and momentum wheels?
Maybe, if they are always turned off. A well-balanced momentum wheel rotor might weigh 10 kg, and have its center of mass within 1 micron of its rotation axis. Rotation of this moving part during a measurement will directly cause a satellite motion in response, equivalent to 20% of our error budget, and possibly swamping the drag free control system. If they are initially spinning, to be caged during EP measurements, their angular momentum must be dumped via the helium thrusters, a process that could take many hours because of the low thrust available. This must be repeated every time they are turned on or off. Smaller, better balanced gyros (for attitude measurement) typically spin faster and so still cause a large disturbance.
Can we use laser gyroscopes?
One type of laser gyroscope uses a mechanical dither to prevent mode locking. These are unacceptable because of acoustic noise and mechanical motion.
Do we need magnetorquers?
Magnetorquers apply torques to the spacecraft to assist the drag free control. Otherwise part of the available thrust (which is pretty small to start with) must be used to control the satellite's attitude. Essentially the satellite with magnetorquers acts like a large compass needle in the Earth's magnetic field, except that they can be turned on and off to change the torque. Because the helium thrusters have only a limited authority, the magnetorquers can improve performance by taking over all or part of the effort needed to maintain attitude. Whether they are actually necessary will be decided during the final design of the control systems.