GPS, How does it work? | ICT #12
Summary
TLDRThe video script delves into the fascinating world of GPS technology, explaining how it utilizes a constellation of 24 satellites and the concept of trilateration to pinpoint locations. It highlights the critical role of atomic clocks and Einstein's theory of relativity in ensuring accuracy, as even tiny time discrepancies can lead to significant location errors. The script clarifies that GPS doesn't require an internet connection but can benefit from it for faster startup. It concludes by emphasizing the importance of these complex technologies in our everyday lives, from food delivery tracking to car navigation.
Takeaways
- 🌐 GPS is a critical technology that relies on a network of 24 satellites to provide location services worldwide.
- 📍 To accurately pinpoint a location, GPS uses a minimum of four satellites, employing the mathematical concept of trilateration.
- ⏱️ Atomic clocks on satellites are crucial for GPS as they provide precise timekeeping, essential for calculating distances based on signal travel time.
- 📱 The time error of mobile devices is a significant concern in GPS accuracy, as even a tiny error can lead to substantial location inaccuracies.
- 🔄 Albert Einstein's theory of relativity is integral to GPS, accounting for time dilation effects due to the speed and gravity experienced by satellites.
- 📊 Trilateration in 3D space requires three satellites to narrow down a location to two possible points, with a fourth satellite used to determine the correct one.
- 📶 The GPS system measures the distance between the satellite and the receiver by sending a signal with a timestamp, which the receiver uses to calculate distance.
- 🕰️ Receivers in smartphones use crystal clocks, which are less accurate than atomic clocks, necessitating a correction for the time offset in GPS calculations.
- 🌌 GPS does not require an internet connection to function, but internet assistance can speed up the GPS startup process by providing satellite information more quickly.
- 🛰️ Modern GPS receivers often use a combination of GPS and other navigation systems to enhance location accuracy and reliability.
Q & A
How many satellites are required for GPS to track a location?
-At least four satellites are required to track a location using GPS.
What is the role of trilateration in GPS technology?
-Trilateration is a mathematical technique used in GPS to determine someone's position by measuring distances from at least three satellites to the receiver.
Why do GPS satellites carry atomic clocks?
-GPS satellites carry atomic clocks to provide highly accurate time measurements, which are essential for calculating distances and positions with precision.
How does the speed of light affect GPS calculations?
-The speed of light is crucial in GPS calculations because the time it takes for a signal to travel from a satellite to a receiver is used to calculate the distance, and any delay, even in microseconds, can result in significant location errors.
What is the significance of Albert Einstein's theory of relativity in GPS?
-Einstein's theory of relativity is significant in GPS because it accounts for the time dilation effects on the atomic clocks due to their high speed and the weaker gravitational field at the satellites' altitude, ensuring more accurate positioning.
Why do GPS receivers need at least four satellites to determine a location?
-GPS receivers need at least four satellites to determine a location because, in addition to the three spatial coordinates, they also need to calculate the time offset of the receiver's clock, which requires an extra measurement.
How does the GPS system compensate for the inaccuracies in a smartphone's clock?
-The GPS system compensates for the inaccuracies in a smartphone's clock by using the fact that the time offset is the same for all satellites, treating the time offset as an additional unknown to be solved along with the three spatial coordinates.
Does GPS require an internet connection to function?
-GPS does not require an internet connection to function. However, an internet connection can speed up the GPS startup process by downloading satellite location information more quickly.
What is the impact of special relativity on the GPS satellites' atomic clocks?
-According to special relativity, the atomic clocks on GPS satellites moving at high speeds slow down by about seven microseconds every day due to their motion.
How does general relativity affect the GPS satellites' atomic clocks?
-General relativity causes the atomic clocks on GPS satellites to tick slightly faster at their altitude due to experiencing a weaker gravitational field, resulting in a faster rate by about 45 microseconds every day.
What is the net effect on the atomic clocks in GPS satellites due to relativity?
-The net effect on the atomic clocks in GPS satellites due to relativity is a daily offset of about 38 microseconds, which is accounted for by adjusting the clocks' rates using a relativity equation.
Outlines
📡 Understanding GPS Technology
The first paragraph introduces GPS as an essential technology in our lives, utilizing a network of 24 satellites to determine location. It explains the concept of trilateration, which requires at least four satellites to pinpoint a location by measuring distances. The paragraph also touches on the significance of atomic clocks and the impact of time errors on GPS accuracy. It highlights the role of Einstein's theory of relativity in GPS, adjusting for time dilation caused by the satellites' speed and gravity. The summary emphasizes the need for precise time measurements and the practicality of using four satellites to determine location without an atomic clock in mobile devices.
🌌 The Role of Relativity in GPS
The second paragraph delves into the nuances of GPS accuracy, emphasizing the importance of Einstein's theory of relativity. It discusses how the theory of special relativity accounts for time dilation in fast-moving atomic clocks aboard satellites, and how general relativity corrects for the slightly faster ticking of these clocks due to weaker gravity at their altitude. The paragraph clarifies that GPS does not require an internet connection but can be augmented by it for faster startup. It also mentions that modern receivers use multiple navigation systems for enhanced accuracy. The video concludes by stressing the importance of relativity and other mathematical concepts behind the functioning of GPS.
Mindmap
Keywords
💡GPS
💡Satellites
💡Trilateration
💡Atomic Clock
💡Relativity
💡Time Offset
💡Speed of Light
💡Assisted GPS
💡US Department of Defense
💡Navigation Systems
Highlights
GPS is an integral part of our lives with various applications.
GPS uses 24 satellites orbiting Earth, requiring at least four for location tracking.
GPS technology employs atomic clocks for precise timekeeping.
Einstein's theory of relativity is crucial for accurate GPS functioning.
Trilateration is the mathematical technique used to determine location in GPS.
Two satellites are needed for 2D trilateration, and three for 3D.
Satellites measure distance to the receiver to determine location.
The Earth's surface is used as a third reference to eliminate incorrect location possibilities.
Four satellites are required to account for the time offset of the receiver's clock.
Receivers use the time difference between sent and received signals to calculate distance.
Time measurement must be extremely accurate due to the speed of light.
Smartphones use crystal clocks which are less accurate than atomic clocks.
Time offset is a significant factor in GPS calculations and is mitigated by using four satellites.
GPS receivers do not need an atomic clock due to the use of four satellites.
GPS systems must account for time dilation effects described by relativity.
GPS compensates for relativity effects to maintain accuracy.
GPS was developed by the US Department of Defense and is free for public use.
Modern GPS receivers use multiple navigation systems for enhanced accuracy.
GPS does not require an internet connection for operation.
Assisted GPS uses internet downloads to speed up satellite location information.
Transcripts
- [Narrator] GPS has already become
an integral part of our lives,
And you can see a few useful applications
from these examples.
(upbeat music)
GPS is really an interesting technology.
It uses a system of 24 satellites
continuously orbiting the Earth,
and requires at least four satellites
to track your location.
It uses at atomic clock,
and the time error of your mobile phone
is also a matter of great concern.
Moreover, Albert Einstein's theory of relativity
plays an important role in GPS technology.
Finally, a real-life application
for the theory of relativity.
Let's put aside all these complications,
and understand the technology of GPS
is a step-by-step and logical manner.
Let's assume that your friend
wants to find out your location,
and you have a mobile phone
which has an integrated GPS receiver.
In GPS, an interesting mathematical technique
called trilateration is used to locate someone's position.
Let's first understand trilateration
in a two-dimensional way.
At least two satellites are required
to find out your position in two-dimensional trilateration.
Using some engineering techniques,
the satellites measure the distance
between you and the satellites.
We will see the techniques for doing this later.
Now things are easy.
The first satellite knows you are at a distance of R1.
So, you should be somewhere on this circle.
The second satellite knows you are at a distance of R2,
so you should be on this circle as well.
This means your actual location
should satisfy both these circles.
In short, you should be on the intersection points.
Now there is a small issue.
There are two intersection points.
So, which is your final position?
For this you take the Earth's surface as the third circle,
and eliminate the improbable solution.
In the three-dimensional world,
you can also use the same approach.
Here, instead of two satellites, we need three satellites.
In the three-dimensional world
the satellite knows you are somewhere on a sphere.
With the use of a second satellite
your position narrows down to a circle.
Note that the intersection of two spheres gives a circle.
Now, with the help of a third satellite,
you will be able to narrow down your location
to just two points.
Here, the intersection of a circle
and a sphere gives two points.
Just like in the previous case,
using the Earth as the forth surface
we find the correct point, the three spacial coordinates.
Now, let's see how the distance between you
and the satellite is measured.
All the satellites are equipped
with a very accurate atomic clock.
The satellite sends an intermittent
radio signal down to Earth.
This radio signal will contain the exact time
the signal was sent, and the position of the satellite.
Assume the receiver also has a very accurate clock.
The receiver on Earth receives the signal.
A typical smartphone GPS receiver is shown here.
Since radio waves travel at the speed of light,
your receiver receives the signal
after a certain time duration.
By finding out the difference
between the sent and received times,
and multiplying it by the speed of light,
you will be able to find out
the distance between you and the satellites.
Since the satellite has already sent you its coordinate,
you can easily build a sphere
around the satellite's center point,
and find out your position, as explained before.
One thing to note here,
is that the time measurement has to be very accurate.
Even an error of microseconds will give an error
in the range of kilometers,
since the speed of light is so huge.
Here comes the main issue.
Your receiver does not have a highly accurate clock.
Your mobile phones or laptops,
work on crystal clocks that are not accurate
when compared to atomic clocks.
Having an atomic clock in a smartphone,
is simply impractical.
You can easily see how inaccurate
your smartphone clock is compared to an atomic clock,
by checking the time settings.
We call the difference between to actual time,
and the time measured by your mobile phone, as time offset.
This time offset will cause a huge error
in GPS calculations.
How do we overcome this issue?
The good news is that the time offset of your smartphone,
with all three of the satellites is the same,
since the satellites all keep the same time.
The time offset value of your device
becomes the new unknown.
This means, apart from the three spacial coordinates,
we have to solve the time offset value
of your receiver as well.
We need an extra satellite measurement
to solve this fourth unknown,
and that is why we need four satellites
to measure your location.
This way we avoid the need of an atomic clock
in your mobile device.
If you check your current GPS constellation,
it will be clear that at least four satellites
can see your location at any point in time.
Please hold on, this video is not yet over,
we have one more issue to solve.
Even with all these advanced technologies,
this GPS system will not give you the right location.
Here comes the importance
of Einstein's theory of relativity.
Time is not absolute,
it depends upon many other factors.
According to the theory of special relativity,
a fast moving clock will slow down.
The atomic clocks,
which are moving at speed of 14,000 kilometers per hour,
will slow down by seven microseconds every day, due to this.
At an altitude of 20,000 kilometers above the Earth,
the satellites experience one quarter
of the Earth's gravity,
thus, according to Einstein's general relativity theory,
the clocks will tick slightly faster.
In this case, around 45 microseconds every day.
This means a net 38 microseconds offset
is created every day in the atomic clock.
To compensate for this,
a theory of relativity equation is integrated
into the computer chips,
and adjusts the rates of the atomic clocks.
Without this application of the theory of relativity,
the GPS would have produced an error
of 10 kilometers every day.
GPS is navigation system
developed by the US Department of Defense,
and is completely free for the public.
However, there are accurate alternatives
available in many countries nowadays.
Modern receivers simultaneously make use of GPS
and other navigation systems,
to get the most accurate position.
Now, a quick question.
Does GPG require an internet connection?
GPS does not require an internet, or cell phone signal.
However, with their help,
GPS startup can be greatly speeded up.
Satellite location information
can be downloaded by the internet,
rather than direct satellite downloads, which are very slow.
Such GPS systems are known as assisted GPS.
So, the next time you track your food delivery,
or navigate your car,
please keep in mind how important the theory of relativity,
developed by Einstein,
and the other mathematical ideas are, behind GPS.
Thank you for watching the video,
and please, don't forget to press the support button.
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