GPS takes into account mysterious black hole time warps

A black hole has been imaged for the first time. The image was captured by a world-spanning network of radio telescopes that together create the Event Horizon Telescope.

It zeroed in on the supermassive monster in the galaxy M87 to create the image.

For GNSS experts, black holes demonstrate the extremes of relativity. Time and space warp and bend in response to mass and movement, an effect we experience whenever we use GNSS.

GPS satellites move about 14,000 kilometers per hour, in a weak gravitational field about 20,000 kilometers above us. Because of relativity, the clock rates of the satellites would drift by about 38 microseconds per day, causing a positioning error of about 10 kilometers if not accounted for.

Near black holes, of course, the time-warping effect becomes extreme, slowing the closer we get to the event horizon.

As reported in Real-World Relativity: The GPS Navigation System by Richard W. Pogge, published by The Ohio State University:

“…because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

“Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly. Special Relativity predicts that the onboard atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion.

“When viewed from the surface of the Earth, the clocks on GPS satellites appear to be ticking faster than identical clocks on the ground. A calculation using general relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

“The combination of these two relativsitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38). This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds.

“If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day. The whole system would be utterly worthless for navigation in a very short time.”

To counteract the General Relativistic effect once on orbit, the onboard clocks were designed to “tick” at a slower frequency than ground reference clocks, so that once they were in their proper orbit stations their clocks would appear to tick at about the correct rate as compared to the reference atomic clocks at the GPS ground stations.

The microcomputer in each GPS receiver not only performs the calculation of position using 3D trilateration, it also computes any special relativistic timing calculations required using data provided by the satellites.

GPS indispensable to capturing image

Innovation editor Richard Langley explained that the technique used to get the black hole image relies on GPS. Known as very long baseline interferometry, the technique links two or more radio telescopes that can be many kilometers apart — even on different continents. The technique is used in both in geodesy and astronomy. GPS World discusses the method here.

VLBI was also discussed in Innovation Insights in September 2011 and September 2014. Learn more about the geodetic application of VLBI.

There is also a practical GPS link to the Event Horizon Telescope. From the second of six simultaneously published open-access papers on the result:

“All timing is locked to a 10 MHz [hydrogen] maser reference and synchronized with a pulse-per-second (PPS) Global Positioning System (GPS) signal….”

“[T]he long-term drift of the maser at the SMA compared to GPS, measured by differencing the 1 PPS ticks from the maser and local GPS receiver. The vertical width of the trace is due to variable ionospheric and tropospheric delays of the GPS signal (including the excursion near hour 200), while the long-term trend represents the frequency error of the maser. The drift measured from this plot, and its effects on the fringe visibility, are removed during VLBI correlation.”

From the third paper:

“In order to reconstruct the brightness distribution of an observed source, VLBI requires cross-correlation between the individual signals recorded independently at each station, brought to a common time reference using local atomic clocks paired with the Global Positioning System (GPS) for coarse synchronization.”

So, GPS is indispensable to the technique and the success of obtaining the image.

Image: Event Horizon Telescope Collaboration