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This is about validating the science from a science fiction novel.

My understanding is that speed is all relative. So while I am in a car on the freeway my speed relative to another passenger is zero, relative to a street sign is 75, relative to a car travelling the opposite direction is 150, and relative to some point off the planet it is much greater.

Now two cars traveling at the same speed and direction would have a relative speed of 0, but because of imperfect roads and wind resistance, the speed relative to earth would still impact the car's interactions. For example, walking between a board connecting the two cars would be much easier at 10 km/h than at 100 km/h. But the relative speed of the cars compared to a distant star has no measurable impact.

So how does this translate to two spaceships? Is a space ship traveling at 1000 km/h relative to a star in the solar system any more likely to strike debris at a faster speed, than one that is stationary relative to the star? Likewise, is it more difficult for two ships traveling at 1000 km/h relative to a star (both with the same heading, speed, etc.) to dock, than two ships stationary relative to that star?

It would seem like acceleration would be the only influence, unless solar winds have a bigger impact then I imagine. Without resistance, it would require just as much effort from the maneuvering thrusters to maintain a specific speed as it would be to hold still.

Theoretically, no mater how fast, or in what direction I am traveling, there is some point, at some distance, in space, to which I am stationary (relatively).

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Your assertion that only relative speeds matter is absolutely correct. However, you might want to look at the velocity addition of special relativity for space ships or whatever else travelling at relativistic speeds. For speeds high above our everyday experience, two things which, relative to us, travel in opposite directions with a speed $v$ will not see the other as travelling with speed $2v$ in their stationary frames.

If we assume that debris in a star system is stationary with respect to the star, then a ship travelling at some non-zero velocity w.r.t. to the star will of course be more likely to hit that debris. If the debris is moving, e.g. as some kind of asteroid belt, the minimal impact will be achieved at a velocity such that ship and debris are stationary w.r.t to each other.

Two ships docking (at each other's ports, I assume) will never care what their velocity relative to some other object is - except if they enter some zone in which gravitational or other influences of that objects might play a role, of course.

Lastly, I want to make two other remarks: First, "no matter how fast" is a statement that makes physicists uncomfortable, since nothing that has mass can ever travel at the speed of light (or even faster than that). Second, you cannot be stationary w.r.t. to a "point", since a point has no velocity at all. You can only be stationary w.r.t. other objects, and there is one obvious object w.r.t. which you are stationary: You. No observer will ever, in their own frame of reference, think that they are moving.

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    $\begingroup$ Good comment about "no matter how fast". Thanks. $\endgroup$ – Jim McKeeth Jul 12 '14 at 22:38

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