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If someone were transported out into empty space, idk like hundred of thousands of miles straight "up," would they fall into the sun? It would depend on their velocity right? If they were moving at an orbital speed e.g. similar to earths velocity, they would go into orbit. So to make them "fall" you'd also have to give them a huge rocket to deccelerate them...

But velocity is a relative thing. In order to say the earth is going so many miles per hour in a direction tangential to it's orbital path, one must picture the solar system with some kind of reference frame to measure distances upon.

Thus to justify the earth not falling into the sun vs some unlucky friend teleported and decelerating as described above, I must arbitrarily pick a universal reference frame, perhaps one where the distant stars (since they are so seemingly immutable..) are stationary upon my arbitrary frame, or at least dang near so. But distant stars being stationary doesn't seem to have anything to do with the physics of the earth, sun, and my unlucky friend... so why bother mentioning them? (I guess I just don't want them whizzing around my head at insane velocities? Umm never mind that)

Plus I remember reading somewhere that there is no universal reference frame. Perhaps that was in something to do with Einstein's theories, which I only have a vague notion of, so if you want to answer in terms of GR keep it simple please/ty.

So basically my question (s) is/are summed up as follows: Am I over looking something, or is that thought experiment kind of paradoxical? Is this one of the paradoxes that sparked the new theories of relativity? Can one planet being in orbit and another object, eg that thing we sent to investigate mercury, degenerate orbit from said mother planet, in terms of reference frames? Or is that a meaningless question?

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Fortunately, you don't need any special relativity or general relativity. All you need to describe orbital motions (to a high enough degree for NASA to use) is classical mechanics.

The key in classical mechanics is that rotating reference frames are not inertial. The laws of physics as you know them only hold in an inertial frame. Over time scales of a year, the Earth's frame isn't inertial either. However, to a very good approximation, the frame with the sun at the origin with close to zero velocity IS inertial. (it's better to choose the center-of-mass frame of the solar system)

It is in this sense that the earth has an orbital velocity of ~30km/s. This is very well defined.

Basically, you can't take the notion of "there is no preferred reference frame" on face-value. If you're in a centrifuge, you're going to prefer a different reference frame pretty quickly :)

(there are other interesting asides I could get into)

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Orbital velocity is measured relative to the object that it is orbiting. If you went at the same orbital velocity to observe something, while I would see to have no speed, neither would you (in your own reference frame) and therefore there is nothing paradoxical about it.

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