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In order to understand my question, the following references must be studied.

There is an article that you might want to read, the article was written by Sebastian von Hoerner, "The general limits of space travel ", Science, 1962.

There is also a clear presentation of the basic ideas in Paul Nahin's book "Time Machines", in the technical note 6 "A high speed rocket is a one way time machine to the future".

Basically, this is relativistic analysis of space travel at 1 g constant acceleration (in the rocket reference frame).

If we assume that gravity modification effects can be achieved (big IF, but it is worth a thought), then we can assume that around the rocket (from all directions) the effect of gravitation is cancelled, except for a solid angle in the desired direction of travel. Only the matter in the universe contained in that solid angle will interact gravitationally with the rocket. In this case, the acceleration (in the rocket reference frame) will be inverse proportional to the square of the distance to the source of gravitation (approximations are necessary here, as there are many independent sources in that solid angle). The calculations made by von Hoerner have to be extended for variable acceleration (inverse proportional to the square of the distance to the source of gravitation). If you have a look at them, the calculations are not trivial and the differential equations that appear are not linear (this is an interesting problem, all by itself).

Another article that is worth a look is:

"The interplanetary transport network", by Shane D. Ross, American Scientist, May - June 2006.

This is basically an article about low energy transit orbits in the many - body problem.

The conclusions are directly related to my question. It seems to me that, if gravitational shielding effects become a reality, then space travel to the stars within our galaxy would be possible. In other words, Kepler - 186f (for example, situated at 500 ly from Earth ) could be reached in a human life span (in rocket years, due to time ditation), but it would take thousand of years (in Earth years) to bring that information back to Earth. Colonization is possible, extending our "sphere of knowledge", not so much.

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closed as primarily opinion-based by TildalWave Apr 28 '14 at 16:20

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ The bulk of your post seems to be unrelated to the thrust of your question. $\endgroup$ – Deer Hunter Apr 27 '14 at 19:54
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    $\begingroup$ This appears to be a counterfactual question: "if the laws of physics were not as they are, could we do X?" And yes, if gravity were a nonconservative force, you could extract work from it. $\endgroup$ – Mark Apr 27 '14 at 21:23
  • $\begingroup$ Gravity is so far not that well understood to even attempt speculating on effects of an antigravity field. This means the realm of this question is entirely within the theoretical physics. If you agree, we can migrate this to Physics for you, assuming it's not a duplicate there. FWIW I also discuss constant 1 g acceleration approaching 1 c and some relativistic effects in the second part of How fast will 1g get you there? Problem is, that a collision with even a speck of dust at near 1 c releases close to $\frac{1}{2}mc^2$ of kinetic energy. $\endgroup$ – TildalWave Apr 28 '14 at 16:33
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I'm going to attempt an answer here.

From the rockets frame of reference it is travelling at 1g continuously. Assuming you don't want to slow down as you approach (not the smartest of assumptions but I'll run with it) you are simply looking at a 1g acceleration though the rockets travel of 500ly. With this information alone, and assuming an initial velocity of 0m/s you can use SUVAT equations:

S = u*t+0.5*a*t^2

Which can be re-arrange to a couple of equations, but only this one is positive:

t = (sqrt(2*a*S + u^2)-u)/a

However, as you've noted, 'a' will depend on distance from the target. Since gravitational acceleration is proportional to 1/r^2 you can treat the point value of a as:

a = c/(s-(u+a*t))/m

Where c represents Gm1m2 in the gravitational acceleration equation and m is your mass.

So there you have two equations which you can put into a time step on something like excel, you can choose the values you use yourself. But if the acceleration is purely based on the gravitational pull of the target planet, then you defiantly wont get there inside a human lifetime.

Look at it another way. If you could place a 1kg mass at 1AU from the sun (Earth distance from the sun). It would take a very, very long time for that mass to reach the sun because it's so far away. You get around 0.0059m/s acceleration towards the sun at this distance; and you're 149.6 million kilometres from the sun. That's very far, and you're going very slowly. That's around 187 kilometres per year (if you had constant acceleration), so about a million years travel from the earth to the sun if you had that constant acceleration, of course it increase exponentially so it wouldn't take a million years.

Finally, something that stands out here is orders of magnitude. Always have a think through them before you worry about the specifics of the equations.

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  • $\begingroup$ It is clear that the acceleration would be too small initially, so it would take too long to reach the stars, but there is a small window of possibilities that has to be explored, non-collision singularities in the n-body problem (the Newtonian and relativistic cases). This coupled with the initial assumption (the existence of gravity modification technology, a big IF), could lead to some interesting scenarios. In other words, reasonable speeds could be reached using the gravitational potential energy available in our solar system (once again, IF gravity modification effects are possible). $\endgroup$ – Cristian Dumitrescu May 3 '14 at 16:45
  • $\begingroup$ Is there something I can add to this question for you? $\endgroup$ – ThePlanMan May 3 '14 at 16:53

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