Tag Archives: global positioning system

Physicists disagree

physicists

Getting back to our satellites—traveling around Earth at 17,000 miles per hour, a satellite’s time slows down, according to Einstein. Also according to Einstein, since gravity is weaker up where the satellites are, time moves a little faster. If that’s the case, wouldn’t a satellite’s GPS signal be inaccurate?

As I researched this question online, I got 2 answers to it: yes and no.

Yes. The satellites’ times slow down, but those amazing scientists who put the satellites up there in the first place cleverly adjusted their signals to compensate for it. Each satellite carries an atomic clock and sends a time & location signal at the speed of light, slightly adjusted (through programmed computer chips) for Einstein’s Special Theory. The clock takes into consideration both the slowing down because of speed and the speeding up because of weak gravity.
https://www.physicscentral.com/explore/writers/will.cfm

https://physicstoday.scitation.org/doi/abs/10.1063/1.1485583?journalCode=pto

No. The satellites’ times slow down, but since they’re all zooming along at 17,000 miles per hour, all their times will be slowed down by the same ratio. So, it doesn’t matter. If all the satellites’ times agree with each other, the GPS system will be accurate. Or, the slowing down is cancelled out by the speeding up caused by weak gravity, so it’s what they call a ‘wash.’ Or, Einstein’s theories are a bunch of baloney so we shouldn’t pay any attention to them.
http://www.alternativephysics.org/book/GPSmythology.htm
View at Medium.com

Um. I don’t know what to say here, gang. As you must be aware, I’m just some shmo who is learning as I write this. If you put me on the spot for which is the right answer, I’m going with the bloggers who have better proofreading/grammar skills and citations. If any of my loyal readers want to chime in, please do!

UPDATE: Regarding a satellite’s time difference because of relativity, our indefatigable physics consultant, Ms Physics, says:

Infinitesimal difference, yet a difference. You need to approach the speed of light 3.0 x 10^8 m/s (670,616,629 mph) to have a significant difference. Any way John you remember the precision of the Cesium clock, these differences would really become significant in GPSA calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

A microsecond is one-millionth of a second. https://www.simetric.co.uk/si_time.htm

This is why I stick to drawing pictures and let others do the heavy brain-work.

I borrowed parts of this composition for my sketch. I removed the horses and put everybody in lab coats.

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Einstein’s Special Theory of Relativity


As you move faster, time slows down for you. Even though that’s true when you’re riding in a car, the slowdown is so teeny-tiny that it’s not worth measuring. But, if you were to travel to another galaxy at almost the speed of light, time would slow down—for you—to the point where you would age more slowly than your pals back on Earth.

When you got back from your trip, your friends would be old and wrinkly but you’d be ready to graduate from high school.

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Classical Relativity

Believe it or not, we’re coming to the end of The Western Civ User’s Guide to Time & Space. I would be cheating you customers if I didn’t spend a little time talking about TimeSpace.

The name Einstein has come to be shorthand for genius. It’s still difficult to imagine the abstract way he trained his brain to think about time and space. Back in 1905, Albert Einstein published his theories about Relativity. He had 2 theories, a Special and a General Theory. But first, let’s talk about Classical Relativity.

Classical Relativity: everything moves relative to everything else.

If you’re riding in a train going 45 miles per hour and throw a ball from the back of the car to the front, the ball seems to you to travel at 10 mph. To a cow standing in a field watching you throw the ball, the ball is traveling at 55 mph: 45 mph for the train plus 10 mph for the ball.

A speedometer can say we’re driving an automobile at 45 miles per hour, but that 45 mph is the car’s speed relative to the surface of good ol’ Planet Earth. Earth is also spinning around and circling the Sun. The Sun also circles around in the Milky Way, taking us along with him. The Milky Way circles around in the Universe. Even the Universe is moving—it’s expanding. How fast something is moving can only truly be measured as it relates to something else. That’s Classical Relativity.

I once tried talking my way out of a speeding ticket using this concept but the trooper wasn’t buying it. Just kidding! Actually, I started sobbing uncontrollably and he walked away in disgust.

UPDATE: My pal Ross sent this interesting article about how a fighter jet ran into its own bullets (the jet landed safely). It seems air-friction slowed the bullets but the jet’s engines allowed it to speed up. At any rate, probably I should redraw the above cartoon with the kid inside a box car, instead of standing on a flat car. https://arstechnica.com/tech-policy/2019/04/dutch-f-16-takes-cannon-fire-from-itself/?fbclid=IwAR1aIR4z2buoa-58GgXSQGUIlqAji6qFpE0MsXSAqC2gYGi6kUBg4UBYYLg

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Einstein

So atomic clocks saved the day—yay! Satellites are synchronized with each other to nanosecond accuracy. Their signals let our GPSs figure out where we are because even though those satellites are hurtling through space at 17,000 miles per hour, their atomic clocks will always show the correct time, right? Nothing’s gonna interfere with each satellite’s time, nothing! No sir! Not one thing!

Okay, maybe one thing: Einstein.

I can see you loyal-yet-exasperated readers flinging your half-eaten peanut-butter-and-jelly sandwiches across the room and yelling, “Oh, come off it, Manders! Have you finally gone around the bend? Should we have you fitted for a straight-jacket and a drool-cup? What’s Einstein got to do with my global positioning system?”

Listen, and I will tell you all about it.

Please continue to hold while I sort this thing out

Remember how mechanical clocks are prone to lose time? It’s because they’re made out of physical machinery—pendulums or mainsprings and gears. We replaced those mechanical parts with a quartz crystal, zapped it with electricity to make it vibrate and got digital clocks. Digital clocks are more reliable, but they still lose 15 seconds every month.

To make the even-more-reliable atomic clock, we replaced the quartz crystal with atoms. Atoms vibrate on their own. We’re building a clock that’s as free of physical, mechanical parts as we can manage in this bad old fallen world.

Here’s what I’m getting from my exhaustive research so far: somehow cesium atoms are funneled down a tube. How do they get the atoms out of the cesium? I don’t know. The atoms are exposed to radiation—radio microwaves like the kind you use to heat up your old cold French fries—which makes them switch back and forth between energy states. The idea is to tune the radio waves to sync up with the atom’s own vibrations at 9,192,631,770 times every second. It’s not easy to get this exactly right—like tuning in a jazz station from 2 counties over on an old radio with dials. There’s a detector at the end of the tube. When the radio waves are at the exact right frequency (the same frequency as the atoms’ vibrations), the atoms change energy states and bounce off the detector—which means one second has passed. Then what? I dunno. How does the detector know when the atoms change from State B back to State A ? I dunno.

Back to my research. Thanks for your patience. Please continue to hold.

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Atoms. They’re small.

Here’s something: before I can even begin to figure out how atomic clocks work, it may be helpful to understand what an atom is. An atom is the smallest thing that exists. Anything you can touch is made out of atoms. Lots of ‘em. There is literally nothing physical that’s smaller than an atom.

An atom is made out of subatomic particles, but these can’t be separated so they don’t count as being smaller than a whole atom.* These particles have Greek names (like Aristotle hahajustkidding). In the middle of the atom are neutrons and protons stuck together in a clump, called a nucleus. Around the nucleus are electrons, circling like the moon circles Earth.** The electrons don’t fly away from the nucleus because the neutrons and protons exert a magnetism kind of like gravity.

So, no, I still haven’t figured out how the atomic clock works. This is taking longer than I thought. I’ll be back as soon as have more info. Please continue to hold.

 

https://www.britannica.com/science/atom

*Ms Physics chimes in: “Atomos (Greek) ‘indivisible’ later proved incorrect!” Well, yes, that’s true. I don’t want you kids getting any ideas. Please, if you manage to isolate an atom—DON’T SPLIT IT!

 

 

** Another Western Civ Irregular Jeffrey K takes exception to me comparing an atom’s nucleus to a planet and electrons to orbiting moons. He says “Electrons don’t really orbit like planets– more like moths around a flame (without the usual fatalities). Also electrons are magnetic but the rest is held together by nuclear forces.” I said “So far as I know, nobody’s seen an atom because they’re so teensy.” So he sent me this:

 

https://www.school-for-champions.com/science/atoms_solar_systems.htm#.Xyk9hB17nzI

 

 

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Just a second

Before I got side-tracked into digital clocks and watches, we were talking about satellites and the Global Positioning System. I mentioned that the satellites that send us navigational signals need to have an incredibly accurate clock aboard. Even a second’s difference in time between satellites’ clocks would change significantly your GPS data—and give you the wrong location.

So you’re thinking, “Well, Manders, those quartz crystal clocks lose or gain only 15 seconds a month. That seems pretty accurate to me. How you gonna improve on a system that measures 32,768 oscillations per second? How you gonna do that? How?”

To which I reply, with a rueful smile, “My friend, there is another clock yet to come, whose sandals the quartz crystal clock isn’t fit to lace. I speak of a clock that loses only one second every 100 million years!”

Really.

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Satellites and hamster balls

Satellites are useful for a whole bunch of purposes: talking on your cell phone; keeping an eye on the weather; broadcasting television and radio stations; seeing what your enemy is up to in times of war; communicating with people when there’s an emergency…but you probably guessed why I decided to talk about satellites.

Satellites serve the same purpose the stars did for Galileo and Maskelyne. They give you information you need to find your location on Earth. Satellites communicate with the Global Positioning System (GPS) on your phone or in the car. They constantly send out 2 bits of information: time and distance.

Most satellites orbit fairly close to the Earth, like 11,000 miles above its surface. When a satellite sends out information, its range is like a sphere—the satellite in its sphere is like a hamster in a hamster-ball.

Well, maybe not exactly, but you get the idea.

These spheres overlap. In fact, we want 3 or 4 satellite spheres to overlap. If you’re looking at your GPS device, satellites are telling it when you’re within their spheres.

So if you’re in the overlap of 2 spheres, you have a general idea where you are.

A third sphere makes that overlap even smaller, right? The smaller the overlap, the more accurately you know your position.

Then there’s a fourth sphere: Earth. You’re inside that overlap, and on the surface of the Earth.

 

trilateration noun

: the measurement of the lengths of the three sides of a series of touching or overlapping triangles on the earth’s surface for the determination of the relative position of points by geometrical means (as in geodesy, map making, and surveying)

triangulation noun

1 : the measurement of the elements necessary to determine the network of triangles into which any part of the earth’s surface is divided in surveying broadly : any similar trigonometric operation for finding a position or location by means of bearings from two fixed points a known distance apart

While the satellites are telling your GPS device where they are, they’re also zipping along at hundreds of miles an hour. Their positions change from second to second. All 3, 4 or 5 satellites need to tell you their positions at the exact same moment or it doesn’t work. They need a clock that’s even more accurate than Harrison’s chronometer.

https://spaceplace.nasa.gov/gps/en/
https://thesciencegeek.org/2017/01/29/gps/                                                               mmmmmmmm

https://www.loc.gov/everyday-mysteries/item/what-is-gps-how-does-it-work/

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Who needs a GPS?

Here’s something fun: a chart of Jupiter’s moons, showing where they will be on today’s date according to your location. Of course, Galileo proposed finding your location by observing Jupiter’s moons: you find their positions and note your local time. Those 2 bits of information are enough to tell where you are on Earth.
https://in-the-sky.org/jupiter.php

Here’s where you can get an app for observing Jupiter’s moons. https://skyandtelescope.org/observing/jupiters-moons-javascript-utility/

Here’s an animated chart you can download: http://shallowsky.com/galilean/