How is the distance to a satellite measured in a GPS?

Answer 1

Triangulate the distance with geometry. If you know the distance between two points in a triangle and the angle between those two and the third, you can calculate the distance between all three.

We know the distance to the sun (the nearest star) because we dropped mirrors all over the moon and used them to bounce signals off and then time how long they take to go there and back, calculate the distance and then we've got two sides of the triangle and can figure out the third.

We can do the same with other stars.

Answer

The method outlined above is called "parallax". It is how we establish distances to stars near earth. Since the earth is moving around the sun (and as the guy above says we know the distance to the sun) we can use the "width" of the earths orbit as what we call the baseline. (the bottom of the triangle.) near earth stars (near still being very far away, the order of parsecs) will appear to move against the background of distant stars. We can take measurements from each "end" or the orbit and use them to calculate (as above) the distance to the star.

This is best demonstrated by holding your finger up in front of your face and looking at it through one eye at a time, the distance between your eyes serving as the baseline. if you could measure the apparent movement of your finger and you knew the distance between your eyes you could work out how far your finger was from your face.

Once we have the distance to a few nearby stars like this we start to use more outlandish methods.

Stars tend to fit into various types depending on colour (which indicates temperature) and age. If we know the distance to a star (by parallax) and we know what type it is we can use what is called the "standard candle" method to work out the distances to further away stars of the same type.

So - I know that a "type G2V" (the sun) is X bright if it's Y far away... i assume that a G2V which appears much dimmer is much further away - we know that brightness decreases related to the square of distance (can't remember the full equation of the top of my head) so you can use this method to pin down distances for loads of stars provided you can get a fixed reference the "standard candle" - obviously this method has issues, mostly to do with the light from stars being dimmed for reasons other than distance like dust in the way. However it's the best we've got!

Answer 2

Astronomical distances are calculated in "light-years". That is the distance a beam of light travels in one year. Light travels at (in round numbers) 186,000 miles per second. You do the math. It is too early for me.

Answer 3

In order to calculate the distance of stars, Astronomers use two basic methods. One method for stars estimated to be within 100 light years away, the parallax method is used. Astronomers triangulate two imaginary lines from two different observation points meeting at an astronomical object that measures the object's distance from Earth. The closer the imaginary lines, the further out the star is. If a star is estimated longer than 100 light years away, astronomers use the Cepheid variable stars. These stars are contained in the constellation Cepheus located in the northern sky. Cepheid variable stars have become reliable guides for the far reaches of space due to its predictable luminosity and pulsation periods. Comparing the apparent brightness of the star to the true brightness allows the astronomer to calculate the distance to the star.

Answer 4

A thorough answer would take a long time. I'll try to give a simplified answer.

There's more than one way these distances are measured or estimated. The distance to most stars is estimated, not measured.

As stars are further away, distance is measured using different methods. This use of different methods as the distance increases is called the "cosmic distance ladder."

Method 1:

The distance to close stars is measured using trigonometry -- a method called triangulation. This is difficult to explain without pictures. The angular location of the star in the sky is measured. Then six months later, when the earth is on the opposite side of the sun, it's measured again. The difference in these two angles is used to calculate the distance. This only works for nearby stars.

Method 2:

For intermediate distances a method based on brightness is used. Certain stars brightness pulsates -- they get brighter and dimmer in a rhythmic manner. The maximum brightness of these stars can be calculated based the rate at which they get brighter and dimmer -- the rate their brightness pulsates. Stars get dimmer the further they are away, so by calculating how bright they really are using the above method and then measuring how bright they appear to us, the distance to them can be estimated. The method cannot be used for distant stars. This method is less accurate than method 1 and more accurate than method 3.

Method 3:

For very distant stars they use a method called "red shift" to estimate their distance. It's believed the universe is expanding and the further away stars are the faster they're moving away from us. As a star moves away from us the color of the light from it changes -- becomes redder and redder the faster it's moving away. By measuring the color of the light from a star they know how fast it is moving away. Then they make calculations about how distant an object is that's moving away that fast.

Answer 5

Very easily. The GPS receiver measures how long it takes a certain radio signal to travel from the GPS satellite(s) to itself, and from that, the receiver calculates the distance. It can do that because it knows precisely how fast the radio signal travels.

If you have signals from at least 3 satellites, the process of trilateration (not triangulation) pinpoints the location where the 3 distances 'cross' each other. If you have 4 satellites 'locked in', then you will find out your altitude, too. (The process is not quite this simple, but to go on would be confusing.)

The hard part is measuring the precise time it takes for a certain radio signal to travel from the GPS satellite to your GPS receiver. Well, hard if you do it, but very easy when the GPS receiver does it!

First, each GPS satellite carries an on-board atomic clock. This clock is outrageously accurate, but even so, ground stations connected to the US Navy atomic clock system keep each satellite precisely at the correct time. Your GPS receiver has an on-board high-precision clock of its own.

Second, when your GPS receiver first makes contact with the constellation of GPS satellites, it is sent an 'almanac' that lists where each satellite is, what it's precise time is, and other goodies. After reading the almanac, the GPS receiver sets itself to the precisely same time as the satellite constellation.

Thirdly, when the GPS receiver gets a signal from the satellites, there is information in it that says precisely at what time the radio signal left each satellite, which is identical for all the satellites. Then your GPS receiver 'looks at its watch' and subtracts the 'sent' time from the 'received' time. The data in the almanac are updated by the satellite constellation every few hours so that your GPS receiver will always know where the satellites are and what their precise time is.

Go back to the beginning and reread what your GPS receiver can do once it knows the precise travel time of the radio signal.

Answer 6

There are two basic methods to determine the distance of stars from the Earth. The first, used for relatively nearby stars, is called parallax: The star is first observed from one point in the Earth's orbit, and then, six months later, from the opposite point in the orbit. Since the two observations are made from points that are about 300 million kilometers apart, a nearby star will appear to be in a slightly different direction; thus it will seem to shift in front of the background stars and galaxies. The size of the shift is called the star's parallax; if the parallax is one arc-second (one 3600th of a degree), then the star's distance is one "parsec", which is about 3.26 light-years. A star twice as far away will have half the parallax. This method is useful for measuring distance within our stellar neighborhood, out to a few hundred light-years.

Greater distances are measured using various "standard candles", that is, astronomical objects that have a known luminosity. If any source of light is moved twice as far away, it will appear only one fourth as bright, so its distance can be determined. Within our galaxy, a type of variable star called an RR Lyrae star can be used to estimate distances. RR Lyrae stars are not all the same brightness, but their brightness varies in a consistent way depending on the period of their variability. Over greater distances, extending to nearby galaxies, another type of variable star called a Cepheid can be used in just the same way. Over even greater spans of distance, astronomers rely upon so-called Type I-a supernovae, which reach a maximum brightness that can be determined by studying how quickly they brighten and then fade away.

For much more information on the topic of determining astronomical distances, see the Wikipedia article "Cosmic distance ladder".
Astronomers measures the distance to the stars that are less than 1000 light-years from the earth using parallax method.

Answer 7

Triangulate the distance with geometry. If you know the distance between two points in a triangle and the angle between those two and the third, you can calculate the distance between all three.

We know the distance to the sun (the nearest star) because we dropped mirrors all over the moon and used them to bounce signals off and then time how long they take to go there and back, calculate the distance and then we've got two sides of the triangle and can figure out the third.

Answer 8

The satellites send predetermined signals out. a gps device has an "almanac" so it knows when each signal originates. It uses GPS time as a constant and compares the timing of the different signals to triangulate positions.

Answer 9

For "nearby" stars out to about 500 light years, we can calculate the distance by observing the parallax; how much does a star appear to "jump" as compared to the very distant background stars, when we make two observations 6 months apart.

Beyond that, we measure the spectrum of the star and figure out how bright it ought to be for its size and temperature, and measure how bright it is in the sky. These calculations are somewhat imprecise and prone to a bit of error.

Answer 10

The distance to a satellite is measured in miles.