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I recently calculated using $E = 0.5mv^2$ that one kilogram of mass traveling at one tenth of the speed of light would have a kinetic energy of 449.4 trillion joules. Relativistic effects are insignificant at this speed. This is the amount of energy equivalent to an earthquake of 7 on the Richter scale or a large hydrogen bomb.

This is an enormous amount of energy from the perspective of designing a propulsion system to accelerate this 1 kg space craft to this speed from rest even if it is started from space outside of earth's gravity. Conventional chemical rockets would be out of the question and much slower accelerations using alternate propulsion systems would be needed and even then present a very significant challenge to eventually obtain said velocity.

We know that Voyager 1 and 2 have used gravity assist flybys of planets Jupiter, Saturn, Uranus, and Neptune to eventually increase their velocities to 17000m/sec for Voyager 1 and 15000m/sec for Voyager 2. While this is fine escaping the solar system and enter deep space, it is still very slow for reaching Proxima Centauri, the closest star group after our sun, in any practical time. Even at one tenth the speed of light, 29,979,246 m/sec, this would take 40 years. 40 years is still a long time but a practical and manageable long term goal.

I was wondering if a great many chained gravity assists within our solar system could be used to eventually accelerate the 1 kg space craft to said speed. This article explains gravity assists well, and how they can be used to speed up or slow down spacecraft relative to the solar frame of reference.

I have in mind oscillating gravity assists on planets in orbits on opposite sides of the sun, back and forth to eventually reach this speed. I realize that the spacecraft can only gain speed if it the exit trajectory of the gravity assist is in the forward orbital tangent from the planet. This would present a challenge if we would like to keep oscillating the gravity assists from planet to planet, but it doesn't seem impossible.

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    $\begingroup$ It's not really the case that relativistic effects are insignificant at 0.1c; they'd be rather noticeable in quite a lot of different aspects of design, though likely not overwhelming. $\endgroup$
    – Nathan Tuggy
    Commented Nov 6, 2017 at 15:45
  • $\begingroup$ Why opposite sides of the sun? Why not just jump back and forth between, say, Jupiter and Saturn a few times? $\endgroup$
    – corsiKa
    Commented Nov 6, 2017 at 22:34
  • $\begingroup$ After reflecting on the question, it would be far too time consuming to have to wait between planets in general. It would be far more time efficient to use the hundreds of moons of Saturn for smaller but much more frequent gravity assists. The trick would be to keep accelerating with Saturn satellite orbital without heading in the wrong direction and escape Saturn. There would have to be a few regressive gravity assists to keep the craft within bounds but as long as the speed keeps increasing in balance we could more quickly obtain the 0.1c . $\endgroup$
    – 0tyranny0poverty
    Commented Nov 6, 2017 at 22:45
  • $\begingroup$ @0tyranny0poverty: The amount the trajectory can be curved by gravity assist is directly proportional to speed of flyby and inversely to flyby body mass. The moons, being relatively light, would be unable to turn the craft towards next moon, preventing its escape from Saturn's SOI. $\endgroup$
    – SF.
    Commented Nov 7, 2017 at 11:23

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Accumulating 0.1c (30000 km/s) with gravity turns alone within the bounds of Solar system isn't possible. Reason is: system escape velocity (sometimes referred to as third cosmic velocity) is about 42km/s (at Earth orbit, and the farther the lower). Once craft reaches this speed, it still can accumulate a bit more with right escape path, but generally not much more.

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    $\begingroup$ I think I get it. Once the escape velocity is surpassed, energy must be used in order to keep the craft within orbits of system. The energy expenditure defeats purpose. $\endgroup$
    – 0tyranny0poverty
    Commented Nov 7, 2017 at 4:15
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    $\begingroup$ @0tyranny0poverty: Or otherwise, gravity assists are opportunities which you can help a little to occur through modifying your trajectory. The higher your velocity the less you can change your trajectory on a reasonable budget and so the less likely you are to find another assist. Past escape velocity you can still use some assists to delay departure but you can no longer wait an orbit or two for an encounter; you must encounter multiple planets within a single orbit just to remain within the system. And there's only so many planets... $\endgroup$
    – SF.
    Commented Nov 7, 2017 at 7:21

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