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If you have the energy for a constant 1G thrust, how long would it take to get to the planets in our solar system? How long for the 5 nearest solar systems?

Assuming turn over and decelerate at halfway.

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This would probably be better on Physics.SE, not here. –  Undo Jul 30 '13 at 0:56
    
"1g of thrust" pointed straight up will balance gravity, and result in you floating. "1g" (as I read it), is the acceleration caused by the Earth's gravity; if that's how you actually define it, then your acceleration decreases as you get further (and 'feel less pull') from Earth. Of course, you don't need to point straight up, and TidalWave's assumption that what you meant is 9.8m/s/s is probably correct - but note that even so, his answer provides you with a minimum, eg assuming you could turn off gravity and the atmosphere (and the assumptions he mentions at the top). –  hunter2 Jul 31 '13 at 9:28
    
@hunter2, you are correct 1g of thrust will not get you off the planet. The assumption is that the starting point is in orbit, 1g of thrust during a long trip provides thrust & simulated gravity. –  James Jenkins Jul 31 '13 at 10:24
    
Fair enough. Again, his answer makes several assumptions and is a minimum (on which I'm not going to improve), but OK. // IMO, it would make more sense to use rotation for 'ship gravity' (tethered-module ship), but that's just IMO. –  hunter2 Jul 31 '13 at 10:33
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up vote 9 down vote accepted

Not assuming any time taken for orbital maneuvering, turning halfway 180° to decelerate, assuming closest distance of planets (and Luna) to the Earth, and not accounting for fuel burn (i.e. literal constant 1g acceleration):

  • The Moon / Luna:
    Closest to Earth (Supermoon): 356,577 km
    Travel time (at 9.80665 m/s2, no deceleration): 2h 22m 12s
    Travel time (at 9.80665 m/s2, decelerating halfway): 3h 20m 24s

  • Mercury:
    Closest to Earth: 77.3 million km
    Travel time (at 9.80665 m/s2, no deceleration): 1d 10h 52m 48s
    Travel time (at 9.80665 m/s2, decelerating halfway): 2d 1h 19m 12s

  • Venus:
    Closest to Earth: 40 million km
    Travel time (at 9.80665 m/s2, no deceleration): 1d 1h 5m 2s
    Travel time (at 9.80665 m/s2, decelerating halfway): 1d 11h 28m 48s

  • Mars:
    Closest to Earth: 65 million km
    Travel time (at 9.80665 m/s2, no deceleration): 1d 7h 58m 5s
    Travel time (at 9.80665 m/s2, decelerating halfway): 1d 21h 13m 1s

  • Jupiter:
    Closest to Earth: 588 million km
    Travel time (at 9.80665 m/s2, no deceleration): 4d 0h 11m 2s
    Travel time (at 9.80665 m/s2, decelerating halfway): 5d 16h 2m 2s

  • Saturn:
    Closest to Earth: 1.2 billion km
    Travel time (at 9.80665 m/s2, no deceleration): 5d 17h 25m 1s
    Travel time (at 9.80665 m/s2, decelerating halfway): 8d 2h 20m 24s

  • Uranus:
    Closest to Earth: 2.57 billion km
    Travel time (at 9.80665 m/s2, no deceleration): 8d 9h 6m 0s
    Travel time (at 9.80665 m/s2, decelerating halfway): 11d 20h 24m 0s

  • Neptune:
    Closest to Earth: 4.3 billion km
    Travel time (at 9.80665 m/s2, no deceleration): 10d 20h 7m 48s
    Travel time (at 9.80665 m/s2, decelerating halfway): 15d 7h 52m 48s

  • Pluto:
    Closest to Earth: 4.28 billion km
    Travel time (at 9.80665 m/s2, no deceleration): 10d 19h 31m 12s
    Travel time (at 9.80665 m/s2, decelerating halfway): 15d 7h 1m 12s


The interstellar travel however comes with a major problem once approaching a significant fraction of the speed of light, with your mass increasing as you go faster and faster due to effects described in general relativity. Neglecting this (one really can't if you're a body with mass, but for the sake of argument let's pretend for a while), you'd reach the speed of light after roughly 4.582 trillion kilometers or approximately 353 days and 20 hours.

You'd then (again hypothetically) travel the rest of the distance at the speed of light. Our closest star neighboring our Solar system is Proxima Centauri, a red dwarf star in the Alpha Centauri system, about 4.24 light-years (40,112,640,416,000,000 km) away from Solar system in the constellation of Centaurus. So you'd be (hypothetically, I can't stress this enough) travelling part of this distance accelerating to light speed (4,582,376,136,279.04 km in 353.83 days), decelerating same distance and same amount of time to zero speed, and the rest (40,103,475,663,727,441.92 km) travelling at the speed of light (4.2390 years). Your one-way excursion to the closest neighboring star system would take 6 years, 64 days, 11 hours, 11 minutes and 17 seconds *.

Calculating for other stars (that we have approximate distance from Sol in light years for) should be relatively easy, just assume you need to add roughly 1.9407 years to the distance in light years for the acceleration and deceleration part of your voyage.

Again, this is completely neglecting that your mass would be reaching infinity as you approach the speed of light, which just can't be, unless you're a massless particle to start with.


* Amount of time as perceived by an outside observer stationary to the reference time frame. The hypothetical subject accelerating with a constant force of 1 Earth's sea-level gravity to the speed of light would perceive a year and 342 days and a half have passed regardless of the distance travelled. This would require infinite amount of energy, an object with a non-zero rest-mass would become infinitely massive, and would create a tear in spacetime consuming its surroundings with the speed of light. In a nutshell, the Universe would spill its guts out - which would not be a nice image to behold at all.

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I'll go crawl back to my corner now... ;) –  TildalWave Jul 30 '13 at 2:05
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There would be some slight difference depending on the speed of each planet at the time of launch, but this should be close enough. –  PearsonArtPhoto Jul 30 '13 at 2:07
    
To anyone interested in what would happen, if a non-zero rest-mass particle were to travel at the speed of light, here's a few amusing answers (my favorite is #5, but they all describe much the same): scienceline.ucsb.edu/getkey.php?key=1571 –  TildalWave Jul 30 '13 at 14:32
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