# Measuring a bend in spacetime

Instrumentation aboard a spacecraft launched on April 20 will attempt to detect a bending of spacetime around Earth, testing an unproven aspect of Einstein’s theory of relativity.

Instrumentation aboard a spacecraft launched on April 20 will attempt to detect a bending of spacetime around Earth, testing an unproven aspect of Einstein’s theory of relativity.

Einstein’s theory of General Relativity predicts that Earth, by rotating, twists space and time around with it, forming a mild vortex in the fabric of spacetime around our planet. Researchers call this “frame dragging.” Most physicists believe the spacetime vortex is real, but no experiment to date has been sensitive enough to detect it unequivocally.

The experimental measurement system aboard the Gravity Probe B (GP-B) spacecraft is an incredible feat of engineering, because the bending of spacetime around Earth is so subtle that even a minute interference from some outside force or a tiny internal imperfection in the spacecraft itself would mask the effect that researchers are hunting for.

Yet the idea behind the experiment is simple: Put a spinning gyroscope into orbit around the Earth, with the spin axis pointed toward some distant star as a fixed reference point. Free from external forces, the gyroscope’s axis should continue pointing at the star forever. But if the region of space through which the gyroscope orbits is slightly twisted, as Einstein’s theory predicts, the direction of the gyroscope’s axis would drift ever-so-slightly over time. By noting this change in direction relative to the star, the subtle frame-dragging effect can be measured.

It sounds like a straightforward experiment; the trick is in actually building it. The gyroscope’s axis won’t drift much, only 0.042 arcseconds over a year, according to calculations. (An arcsecond is only 1/3600th of a degree.) To measure this angle reasonably well, GP-B must have a precision of 0.0005 arcseconds.

To do so, the Gravity Probe B team had to create the roundest gyroscopes ever made, and set them orbiting Earth inside a force-free pocket. No form of atmospheric drag or magnetic forces could be allowed to penetrate the gyro-chambers. That’s tricky because Earth’s far-flung magnetic field envelops GP-B and, even at an altitude of 400 miles, Earth’s outermost atmosphere exerts drag on the spacecraft. Furthermore, it would be necessary to measure the tilt of the gyroscope’s spin axis without ever touching the gyroscope itself.

The gyroscopes in GP-B are the most perfect spheres ever made. (The experiment actually carries four gyroscopes for redundancy.) These ping pong-sized balls of fused quartz and silicon are 1.5 inches across and never vary from a perfect sphere by more than 40 atomic layers. That means that if these gyroscopes were the size of the Earth, the elevation of the entire surface would vary by no more than 12 feet! If these gyroscopes weren’t so spherical, their spin axes would wobble even without the effects of frame-dragging, thus ruining the experiment.

Being in orbit allows the spheres to float within their housings as if weightless, but without other controls, the spinning spheres would still tend to drift and bump into the walls of their containers. The reason is that the spacecraft is being slowed slightly by aerodynamic drag, while the free-floating spheres within the spacecraft’s belly are not.

The GP-B team solved this problem by developing a drag-free satellite.

Inside the spacecraft, instruments monitor the distance between one of the gyroscopes and its chamber walls with extraordinary precision – to within less than a nanometre. The spacecraft’s thrusters respond to any changes in that separation. In effect, the spacecraft chases the gyroscope and flies along the same “drag free” orbital path that it does.

The spheres must also be protected from Earth’s magnetic field. That’s because a faint magnetic signal from the gyroscopes themselves will ultimately be used to detect the all-important change in angle of their spin axes. The intrusion of Earth’s magnetic field would swamp that signal.

To block the planet’s magnetic field, the designers used superconducting bags. The gyroscope assembly is placed inside lead bags, which in turn are placed inside a large cryogenic container called a “dewar” holding 400 gallons of liquid helium. The helium cools the lead bags to 1.7 degrees above absolute zero (1.7 K, or about -271 degrees C). At this temperature the lead becomes a superconductor, thus blocking out Earth’s magnetic field. The ambient magnetic field within these bags is reduced to less than 3 micro-gauss, which is about the same as in deep interstellar space.

The extreme cold also helps create an ultra-low pressure vacuum in the gyroscope chamber; after pumping out most of the gas, the molecules of gas that remain are very cold and thus hardly moving, which means they exert almost zero pressure. In this pristine, high-vacuum environment, the spherical gyroscope could spin at its operating speed of 10,000 rpm for 1,000 years without slowing by more than 1%.

Finally, it is necessary to measure the gyroscopes’ spin without nudging the gyroscopes in the slightest.

Once again, superconductivity comes to the rescue. A superconducting sphere, when spun, will produce a weak magnetic field that is precisely aligned with the axis of rotation. The gyroscopes are therefore coated with a metallic layer of niobium of near-perfect uniformity. At the cryogenic temperature in the core of GP-B, niobium becomes a superconductor and it produces a magnetic field when the spheres are spun. By monitoring the magnetic field, engineers can monitor the spin of the gyroscopes.

To do this, the GP-B scientists use a device called a SQUID – short for “Superconducting QUantum Interference Device.” Attached to a loop of superconducting wire closely encircling each gyroscope, a SQUID functions as an ultra-sensitive magnetic field detector. SQUIDs can detect a change in this field of only 50 billionths of a micro-gauss (5 x 10-14 gauss), which equates to a change of the gyroscope’s angle of 0.0001 arcseconds.

A telescope onboard the spacecraft constantly watches a distant star named IM Pegasus. This serves as an external reference point for measuring the tilt of the gyroscopes. IM Pegasus isn’t truly a fixed point, though. It will drift ever-so-slightly during the 2 year lifetime of the GP-B mission. Fortunately, astronomers know very precisely how far it will drift, so that motion can be accounted for.

Source: NASA