Testing Einstein's Theories With Satellites Stuck in Eccentric Orbits

Illustration: ESA

In August of last year, when ESA launched its fifth and sixth Galileo navigation satellites, things went wrong. Because of a fault in the upper stage, both spacecraft ended up in elongated elliptical orbits instead of circular ones, making them unusable for navigation. Subsequent corrections of their orbits restored their function as navigation satellites, but their orbits still remained highly elliptical, with a difference of about 8,000 km between their closest and most distant points from Earth.

To the satellite navigation engineers, this was a nuisance requiring changes in the software and the technology. But for physicists, the eccentric orbits offered an unexpected opportunity. Researchers at both Sytèmes de Référence Temps Espace, or SYRTE (a department of Paris Observatory), and ZARM (the Center of Applied Space Technology and Microgravity) at the University of Bremen, Germany, convinced ESA to use the satellites to test more extensively an effect predicted by Einstein's general relativity. They hope to find out more about the extent to which time slows down when the gravitational field diminishes as one moves away from Earth.

This effect, also called gravitational redshift, or time dilation, has been previously observed; the need to correct timing signals transmitted from navigation satellites because their clocks operate slightly slower than those on the Earth's surface is a matter of routine. And the relationship between the slowing of time and the distance from Earth was tested in 1976 with the one-shot experiment, the Gravity Probe A, that reached a height of 10,000 kilometers. Using a two-way microwave link between the ground station and the Gravity Probe A, researchers directly compared the speed of the maser clock aboard the spacecraft to that on the ground, and confirmed the slowing of time with an accuracy of 140 parts in a million.

 Maser clocks are large and complicated instruments that measure time with an extreme precision, and are only carried by navigation satellites.  As their precision allows the accurate measurement of the relativistic slowing of time, the researchers at SYRTE and ZARM (ZARM had even proposed the building of a dedicated satellite in the past) jumped at the opportunity. “There are not many opportunities where you have a good clock on an eccentric orbit in space,”says Sven Herrmann, a physicist at ZARM.  “This is a combination that happened by chance; it was bad luck but also good luck.”

Unlike Gravity Probe A, the Galileo satellites don’t have a microwave link that allows direct access the maser clock frequency.  However, the researchers will be able to use the existing spacecraft-to-ground communication infrastructure, including the GNSS to perform the test.

ESA decided to go ahead with the test after a workshop in February 2015. The data taking, which will last for a year, will start in 2016.  “An important consideration for this decision was that the general relativity tests we are going to perform may be done in a transparent way, without any interference in the nominal operations of the satellites,” says ESA Global Navigation Satellite Systems Senior Advisor Xavier Ventura Traveset.

The Gallileo satellites continuously send messages about their position and the time on their clock, explains Herrmann.

We will reconstruct the data, the clock frequency, from the measured travel times. The satellite transmits a time stamp when the message leaves the satellite, and the receiver on the ground also produces a time stamp, and you calculate the travel time. If you know the position of the satellite, you can reconstruct the behavior of the clock on board the satellite. 

Precise accounting of the distance of the satellites is crucial to the determination of the maser frequencies. The researchers plan to use optical laser ranging, bouncing laser beams on retro reflectors mounted on the satellites to get an accurate measurement.  

The researchers expect that the accuracy of the relativistic slowing of time will be four times as accurate as the Gravity Probe A results. The large number of repeated measurements, as compared with Gravity Probe A’s single measurement, will give researchers a new bunch of numbers to analyze. “We have this large modulation in gravitation now, with 8,000 kilometers change twice per day...that will help us with the statistics,”  concludes Herrmann.

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