Relative Velocities

[Jay-qu]

Ok I just thought this up and I cant work through it, it seems to make no sense to me.. :cup:

 

You are sitting on the surface of the Earth. There is a geostationary satellite in orbit directly over your head. Do you agree that this satellite will not move relative to yourself on the surface of the Earth? Assuming it is stationary, now consider the velocities of the two objects. You sitting on Earth have a much smaller circle to go around in 24 hours, while the satellite must complete a circle of much bigger radius. Hence the satellites velocity is much larger.

 

So how the hell do you have to objects travelling at different velocities but relatively remain stationary? (I am thinking the answer may have something to do with radial velocities, because both objects would be equal in that respect)

 

Jay

[Janus]

The answer lies in the different reference frames from which you make your judgement.

 

In the first case, you are making your measurement from within a rotating, or non-inertial reference frame.

 

In the second case, you are measuring from an non-rotating, inertial frame.

 

So the satellite is either stationary with respect to you (as seen from the Rotating frame) or has a different velocity from you (as seen from the inertial frame), but it cannot be both at the same time, because you can't measure from both frames at the same time.

[Jay-qu]

How is the second case an inertial frame? I thought it to was rotating..

[Janus]

How is the second case an inertial frame? I thought it to was rotating..

 

The satellite and the Earth are rotating, but the frame from which you are considering them from isn't.

[Erasmus00]

Both sattelites have the same angular velocity

 

[math]\omega = \frac{v}{r}[/math]

 

This ensures they remain geosynchronous even though one has a faster linear velocity.

-Will

[arkain101]

For you on the earth you have say 1400km to travel If you made it into a strait line. (if we assume the earths circumfrance at your posistion is 1400km).

 

The Satalite lets say has to travel 140,000km in its pathway.

 

We view them both going in a strait line. The velocities will be different in order for them to reach the finish line at the same time and that is whats happening in your scenario.

 

You could imagine that you were holding a super long light string that was connected to the satalite and compare that to a miniature scale of a ball on a short string on earth.

 

If you wing it over your head the ball moves faster than your arm.

If you hold your arm out and look down your arm, down the string, down to the ball and rotate your body everying looks at rest but everything is of course at very different velocities. But what you see and what is happening are not always in sync with eachother.

 

I suddenly got to wondering while typing here, what would happen if someone were to perform the following experiment.

 

Lets say we had a Very very long cable made out of that new super structure material that is 4000 times lighter than steel and 1000 times as strong or whatever. And we hook this string up to a planet and attatch a small video camera and satalite to the end of it.

 

Lets say we attatch this cable to mars, and we let out thousands and thousands of miles of it slowly bit by bit from one of the poles untill its cyntrifugal force peaks over the gravity force and the cable goes into orbit. At this point the satalite at the end (very light) would be traveling Incredibly fast! At least depending on where you look.

 

So we look from mars, and we look down the string, and let say we can with a telescope see the entire cable all the way down to the end. If the end of the cable was approaching very high velocity, somewhere close to C, (in thought experiment sense) would we begin to see the string curve? from the Relativistic Dialations?? or... would it still act as though it was at rest just because we view it as so??

 

As we view from earth the satalite could be measured to be moving at incredible speeds and would produce sufficient tests of time dialation. Its just a matter of forces in the engineering and if the materials will hold up.

 

 

 

Come to think of it, this would be a really interesting experiment to perform. I wonder how fast we could get an object traveling by hitching a ride like this with a long cable.

[arkain101]

This reminds me of an easy experiment anyone can perform.

 

Materials:

 

One Extension Cord for a 120V House outlet fixed with its own LED light in the outlet of the cord.

 

Other things might work.

 

What you do:

 

The LED light in the extension cord is flashing at around 60 hertz. When you look at it, it looks as though the light is simply just on and glowing.

 

A)

Fix the cord like a lassoo and hold out about 10 feet of it in front of you and begin to spin your body around and around as to make it so the plug appears to be at rest the LED light will continue to glow as though it was at complete rest infront of you with nothing moving.

 

Have an observer stand away from this experiment and ask him to note what he observes.

 

Second part)Fix the cord like a lassoo again but keep your body stationary and begin to spin the cord over your head and note what occurs. What should occur is the LED light will now be in motion relative to you. Distance or space will fill the the spaces for when the light is off and a fixed bulb will form in several places around your head, if you are able rotate it at a constant rate. You should see several lights that are not moving and are equally seperated by a distance of no light. This allows you to see the actuall frequency in action, all from the act of how you view it.

 

The faster you spin the cord the larger the distance between the lights will be and the less lights in the circle you will actually see that are at rest!!

 

If you spin it at a slow enough speed you will see up to 60 lights sitting at rest.

If you spin the cord at a fast enough speed you will see one light.

 

It may be better to rig up a device to rotate the LED light for you so you can have more consistant results and have the ability to see whats going on easier when your arm isnt flailling around.

[Qfwfq]

How is the second case an inertial frame? I thought it to was rotating..

Actually, it isn't even necessary to say why it's inertial, it's a kinematic matter and not one of dynamics. It's enough to say that in Earth coordinates both velocities are zero.

[Jay-qu]

hhmmmmm.. I get how it works and why it works, it just an interesting anomaly to me that two objects can have different velocities but remain at the same distance from each other.

[Qfwfq]

Constant distance but varying direction.

 

[math]\Delta \vec{v} = \vec{\omega}\cross\vec{r}[/math]

 

We need an online LaTeX manual

[arkain101]

yah it is definetly a bit of a concept to think about.

 

Curved and angled things can act a little stranger than our comman day thoughts.

 

Like when you draw a large triangle on a sphere, you can have a triangle with three 90 degree angles.

[bilge]

The reason of the problem space-time is only the limited velocity of light. Relative velocities are not influential.