The satellite and the navigator
Sunday, May 19, 2019
Mom was our navigator, and her GPS was a 1966 book of maps that needed no correction for millionths of seconds.
In those days, the Global Positioning System was a military secret, so when she planned a 14,000-mile summer trip, she was on her own with pencils and a few brochures. In January she wrote to 49 state tourism offices for roadmaps and roadtrips and recommendations for rambling, and spent six months scrutinizing every square map inch to develop a legacy loop of the whole country, through the Grands: from Canyon to Tetons; and the Lands: from Bad to Disney. Mom poured over detailed maps and inset flaps and accordion wraps seeking exits for Roadside America and the Corn Palace and Checkerboard Mesa. No adventure would be left unventured.
We struck out for the infinity of sweeping plains and fleeting grains, foamy seas and rosy breezes, to witness the high hopes and higher slopes of the continent. Packing little more than a can of screwdrivers and a ball of twine to keep us safe and roadbound, we loaded into the station wagon. Tim was 3, I was 5, and every night as we lay across the bench seats with nothing but a curtain of canvas stretched over the tailgate separating us from the great wild beyond, the miles ahead and the miles behind seemed precisely wrought and evenly spaced, as did the seconds on our watches. Who knew that within decades the spacing would slip and a reality of spacetime that swells and sags would be the key to better maps?
Mom and Dad flew us by the seat of our pants, not the beat of the GPS dance, never knowing for sure whether there would be scorpions in a campground washing machine in Texas, or if we would have enough gas to coast down the Rockies to Aspen, or where we could find a physician in Quebec, or how long we would be in West Virginia hunting for a fuel pump, or whether we should eat 20 pounds of cherries right now instead of tracking down a grocery, or how long we would wait for a flock of Navajo sheep to cross the road in Arizona, or would midnight be the coolest time to cross the Mohave desert, or ….
Today, we use GPS to locate everything. The satellite precision that guides a car to the exit lane and counts down to zero yardage knows exactly where the car is, thanks to Albert Einstein’s two theories of relativity.
Special relativity accounts for tiny time differences between satellite beacons, orbiting the Earth at 9,000 mph, and our cars, because time experienced by a high-speed object is magnified: the tick-tock of a satellite beat runs slightly slower than the tick-tocks in a clock moving at the speed of a car. The time lag of the satellite clock amounts to only 7 millionths of a second per day, which seems hardly worth mentioning, except that the signals between satellite and car are traveling at the speed of light, or 700 million mph. At that speed, a millionth-second of time error corresponds to a 1000-foot distance error in the figuring of your car’s location.
In addition to the speed lag from the satellite, general relativity tracks a time difference arising from the altitude of the satellites, a result of stronger near-Earth gravity slowing down ground-level tick-tocks. High-altitude clocks run faster than low altitude clocks, and at 13,000 miles up, the satellite clocks run about 45 millionth-seconds fast each day.
A pair of tiny corrections resolves these time errors in the GPS locator, which then triangulates the instant-by-instant distance to several satellites, deducing position.
Relativity skews the countdown of everything. Material falling into a gravitationally-intense black hole is sucked in so fast it nearly stops because time slows down so much. Identical birds flying at wildly different speeds would age at different rates. A baseball streaking along at 400 million mph would be 15 percent narrower and 15 percent heavier than a 90 mph pitch, and the 90 mph pitch is 7 hundred millionths narrower and heavier than the ball when it is caught.
The accordion folds of relativity permeate the universe. Everything that moves, everything that experiences gravity, joins the stretch and squeeze of shape and size and speed. The farthest reaches of visibility are forever retreating from us, speeding up and stretching away, enlarging space itself, pulling time and size with it.
Mom’s non-relativistic calculations — of gas to Aspen and doctors in Canada; of fuel pumps in Appalachia and sheep-herding speeds in Arizona — were successful in the slow and steady world of snail’s paces and low-altitude spaces. There is no relativistic objection to skipping fancy corrections on simple map projections. Here in our low, slow world far from the satellites, where a million millionths tick by each second, and 32 million million millionths clock each year, the circus-lens bending of length and time have little effect.
Six months and flat maps provide the same navigational ramblings as a few millionth-seconds with a satellite.
Our navigator Mom passed away June 1 of last year, 32 million seconds ago. Seems like a lifetime.
Follow @jmoseshall on Facebook. Joy Moses-Hall teaches physics and astronomy at Pitt Community College. She has a PhD in oceanography and is the author of the novel Wretched Refuge.