# Infinite Acceleration

1. Sep 18, 2007

### Xori

If you're on a spaceship that's accelerating at g (9.8 m/s/s), you would feel a force similar to the gravity here on Earth, correct?

Now what happens if you go off into space and keep this acceleration constant?

What happens as you approach the speed of light, which should take under a year. Does your acceleration slow due to your mass increasing, or are you able to keep up your acceleration forever because you can never reach the speed of light relativey to your original starting point?

2. Sep 18, 2007

### neutrino

3. Sep 18, 2007

### Xori

So in theory if you had the energy to keep going at 1g, you could do it forever, you would just never reach the speed of light?

However, you would be able to cross distances at a much faster speed than speed of light because of time dilation?

Would you continue to to feel the effect of g the whole time inside the spaceship?

4. Sep 18, 2007

### JesseM

Constant "proper acceleration"--acceleration as felt by the person on the ship--is different from constant coordinate acceleration in a given inertial frame. If your proper acceleration is constant, your coordinate acceleration in the frame you started off from will be constantly decreasing as you approach the speed of light, so you'll never make it to that speed. This is related to the fact that velocities don't add the same way in relativity--if I'm on a ship and I shoot a missile at 0.6c relative to me, and in your frame my ship is moving at 0.5c in the same direction, you won't see the missile moving at 0.5c + 0.6c = 1.1c, instead you'll see it moving at only (0.5c + 0.6c)/(1 + 0.5*0.6) = 1.1c/1.3 = 0.85c. And the faster my ship is moving relative to you, the less difference in speed between my ship and the missile in your frame, even if the missile is always shot out at 0.6c relative to me. You can imagine breaking acceleration up into a series of jumps in velocity, in which case constant proper acceleration means that each jump in velocity is the same amount as seen in the ship's previous rest frame. So, if you pick a single inertial rest frame to observe the ship's movement, the difference in the ship's velocity before and after the jump gets smaller and smaller as the ship's velocity before the velocity gets bigger, in just the same way that the difference between the missile's velocity and the ship's velocity would get smaller and smaller the larger the ship's velocity when the missile was fired.

5. Sep 18, 2007

### JesseM

Yes.
The coordinate speed of light is only constant in inertial frames, and from the perspective of any inertial frame, your speed is always slower than light. In any frame where you get to a destination in less than x years, it must be true that the distance between Earth and the destination has shrunk to under x light-years in that frame due to length contraction.
Yes, constant proper acceleration means constant G-force felt inside the ship.

6. Sep 18, 2007

### Bob Walance

Point your 1g rocket ship away from the Earth. After 5 years then rotate it 180 degrees. Let 10 more years go by and then rotate it again. At the 20th year you make a soft landing back at home sweet home. Your friends will all be about 340 years older.

Bob

7. Sep 18, 2007

### Wonderballs

If you timed it so that you turned around in exactly 5 years, on your "10 year" return trip; you would collide with earth. And you too, would be dead with your friends because your landing gear broke.... just playing :)

8. Sep 19, 2007

### Bob Walance

No, you need to think about it a little more.

If your speed when you leave (with respect to Earth) is zero, then at the end of 5 years it would be +V, then rotate, after 5 more years it's zero and after another 5 it's -V, then rotate back, and finally after five more years (20 years total) it's back to zero and you land safely (don't forget to turn off the engine just as you land).

Bob

9. Sep 19, 2007

### Wonderballs

I was just being particular about the way you worded your statement, you had said "Let 10 MORE years go by", meaning you dont turn around after the 10th year only on the 5th, 15th and 20th.

10. Sep 19, 2007

### Capuchin

Please note that this is not "infinite acceleration" as your topic states. It is 1g acceleration.

An infinite acceleration would get you to the speed of light instantly.

11. Sep 19, 2007

### Wonderballs

/i think he is refering to the fact that he never stops accelerating...ever.

12. Sep 19, 2007

### JesseM

I think that's exactly what Bob Walance meant--if your velocity is +v by the 5th year, and then you turn around and continually accelerate in the opposite direction for 10 years, then your velocity in the positive direction will be continually decreasing, so after 5 years your velocity will be back to 0, then after 5 more years it'll be -v...there's no need for another turnaround during this period.