Twin Paradox, Paradox?

[EWright]

Since I apparently offended some people by proposing a possible paradox that included a reference to the age of the Universe (apparently there are too many posts per week on that subject so be sure to never reference it or they won't address your actual question) I'll pose another scenario instead.

We're all familiar with the Twin Paradox, in which one twin travels into space at a significanty fraction of the speed of light and when he returns he has aged much less than his twin back on earth.

Now consider that the same twin leaves earth is a space ship but does not travel distantly. Instead he assumes a high-earth orbit, but still at a significant fraction of the speed of light. Relativity tells us that he should still age less than his twin on earth because of the speed at which he is traveling. But consider that during his entire trip he is receiving a light speed signal in the form of a microwave television signal from the north pole or a satellite that is traveling at earth's same speed. The twin on the spaceship can view this signal in a monitor. Now, althought time should slow for the twin in the space ship, causing him to age less, the electromagnetic signal he is receiving should travel at a constant speed of c along its entire path of travel. And because he is traveling in a high earth orbit rather than far from earth, the signal does not need the significant time to reach him that it would if he traveled far from earth, so there should be no significant delay in it reaching him. Therefore, the twin in the spaceship should receive the signal at the same rate that it is transmited because the light-speed signal muyst remain CONSTANT between the two points at all times. If the signal, visible in his monitor, is of constant events on earth and has a visible time code to the frame (30 frames per second), how does the traveling twin perceive the image and time coded relationship in relation to his own clock?

(disclaimer: I am posing this as a thought experiment, not a proof of anything.)

[Tormod]

Could you please do as I suggested and visit our astronomy and cosmology forum? This topic has been discussed many times over there.

You could also try to search for "twin paradox" in our search field.

And no, you are not offending anyone - you are simply ignoring common courtesy which is to find out what is already being discussed before you post.

[EWright]

I am proposing an altered scenario to the twins paradox. Are you telling me that my exact scenario has been proposed already?

[Tormod]

I am telling you that your scenario is similar to others that are being discussed, yes. It would be tremendously better for the site if you would join in those discussion rather than start new threads on topics that are already being discussed.

[EWright]

So much for trying to introduce new concepts using old analogies.

[Erasmus00]

Originally Posted by EWright

So much for trying to introduce new concepts using old analogies.

Please actually pay attention to what Tormod said. You are free to discuss your ideas, simply roll on over the Astronomy section, find the thread where they are discussing the twin paradox, and post there. That way, all the talk of the twin paradox and variations there of are in one area. You are still free to discuss your ideas.
-Will

[Tormod]

Originally Posted by EWright

Now consider that the same twin leaves earth in a space ship but does not travel distantly. Instead he assumes a high-earth orbit, but still at a significant fraction of the speed of light.

It is actually impossible to orbit the Earth at a significant fraction of the speed of light and still stay within a distance where relativistic effects would not be perceived.

A "high-earth" orbit cannot be higher than a geostationary orbit, at 35,800 kilometers, because at this height the speed of the orbit perfectly matches the rotation of the Earth, so that any satellite placed in this orbit always hovers above the same spot on the Earth.

Now, the escape velocity for Earth is 11200 meters per second, or about 25,000 miles per hour. The escape velocity of the Solar System is about 1,000 kilometers per second. That is 1/300th of the speed of light. So even at 1/299th of the speed of light, your space craft would never return.

In order for an object to be in a similar orbit at higher speed you would need constant maneuvering, which would actually mean that A) you are not in an orbit, and B) you would need to draw an immense circle in space to be able to follow a path all the way around without increasing the distance from Earth.

The amount of fuel needed for maneuvers is another issue completely.

I have not calculated what distances you would need to be at but I think you'd have to be far, far outside of our solar system. And, importanly, you would no longer orbit the Earth but the entire solar system.

The time for transmissions from Earth to this spacecraft would be immense.

So this thought experiment cannot work in real life.

[EWright]

Originally Posted by Tormod

It is actually impossible to orbit the Earth at a significant fraction of the speed of light and still stay within a distance where relativistic effects would not be perceived.

A "high-earth" orbit cannot be higher than a geostationary orbit, at 35,800 kilometers, because at this height the speed of the orbit perfectly matches the rotation of the Earth, so that any satellite placed in this orbit always hovers above the same spot on the Earth.

Now, the escape velocity for Earth is 11200 meters per second, or about 25,000 miles per hour. The escape velocity of the Solar System is about 1,000 kilometers per second. That is 1/300th of the speed of light. So even at 1/299th of the speed of light, your space craft would never return.

In order for an object to be in a similar orbit at higher speed you would need constant maneuvering, which would actually mean that A) you are not in an orbit, and B) you would need to draw an immense circle in space to be able to follow a path all the way around without increasing the distance from Earth.

The amount of fuel needed for maneuvers is another issue completely.

I have not calculated what distances you would need to be at but I think you'd have to be far, far outside of our solar system. And, importanly, you would no longer orbit the Earth but the entire solar system.

The time for transmissions from Earth to this spacecraft would be immense.

So this thought experiment cannot work in real life.

Nice of you to side step the actual, tho hypothetical, question. Whether you could stay in orbit or not is not the issue here. The usual "Twins Paradox" scenario is just as impossible to pull off because it still requires reaching an impossible speed. So put a nuclear powered latteral side booster on the space ship to keep it in orbit if you must. Why can we remove all objects from the universe to "prove" hypothetic SR theories, but I can't propose a space ship engineered to orbit the earth at a significant fraction of light speed? The question at hand is how would the light-speed signal be perceived by the twin on the ship if it must be constant for both those on earth and the person on the ship, yet time must slow for the person in orbit?

[Erasmus00]

Your orbit isn't inertial, and so handling the problem is a bit subtle. I suggest a treatment along the lines of what is traditionally done for the Sagnac effect. Calculate the interval from the earth's frame, which will give you a proper time measurement for your orbiting frame.
-Will

[Boerseun]

EWright:

I see what you're trying to say. If you can actually rig up a system like this, the time signal would come from Earth, which is standing still for all practical purposes, and hit the spaceship perpendicular to its direction of flight say, once every second.

The spaceship will see the timesignal coming from Earth, and everything on Earth will appear (from the spaceship's point of view) to be moving at a hectic rate, including radiosignals beamed off the planet. So, as time slows down relativistically on the spaceship, it should seem as if the signal speeds up. The crux of your story seem to be the fact that the signal is hitting the spaceship perpendicular to its motion - but keep in mind that the spaceship is flying at a right angle to the direction the radio waves are travelling, and intercepts the wave in an ever-increasing sweep as the spaceship's speed increases.