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The Trip to Saturn

  1. Apr 19, 2012 #1
    If I am in a spaceship and it begins a constant acceleration of 9.81 m/s^2, would I be able to stand up in the spaceship and it would feel the same as gravity? (This is assuming the fact that my feet were placed in the direction of the thrust source.)

    I've done some equations, and a ship with this hypothetical acceleration capacity (regardless of fuel source, and assuming it could compensate for its mass increase due to relativity)...

    My calculations put it at reaching Saturn in 225 days...

    Here is the data I am using:

    Distance to Saturn = 1,321,416,800 km

    After 24 hours of continued acceleration (+9.81 m/s every second) the velocity would be roughly 848,000 m/s

    By day 100 it would be 84,800,000 m/s

    And by the day you reached Saturn (day 225) it would be 190,800,000 m/s or roughly 426 million miles per hour -- and 63.64% of the speed of light.

    Are these numbers totally wrong? Someone smarter please help me. Thanks!
     
  2. jcsd
  3. Apr 20, 2012 #2
    The velocity after time t, is gt, but the distance you've reached after a time t = (1/2)gt^2 and this should be equal to the distance to saturn.

    this gets you t ^2 = 2(1.321 * 10^12)/9.81, so t = 5.19 * 10^5 s = 144 hours = 6.01 days.
    If you want to decelerate as well, you'd accelerate for half the distance, wich you reach in 4.25 days, and then decelerate for the same time, reaching saturn after 8.5 days.
     
  4. Apr 20, 2012 #3
    I adjusted my equations and found the error (was multiplying by 60 instead of 86,400 -- that certainly does change the results.) To "free fall" to Saturn with the assumption of Earth's gravity (and no friction) would take 6 days :) I find that kind of interesting. So at the end of the "fall" you'd only be going 1.70% light speed. That makes a ton more sense than what crazy results I had. Thank you.
     
  5. Apr 20, 2012 #4
    IF you could accelerate at 9.81m/s2, you could cross the width of the universe well within your lifetime. It's interesting, but it's a BIG "if".
     
  6. Apr 20, 2012 #5

    HallsofIvy

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    Since the person standing in the spaceship is motionless with respect to the spaceship, there would be no "mass increased due to relativity".
     
  7. Apr 21, 2012 #6
    I was speaking of the fuel source/acceleration problem, that as the ship increased in velocity it would also increase in mass because of relativity, meaning it would need more energy to sustain its acceleration. I was told that this is one of the main problems with accelerating up to 99% of the speed of light.
     
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