How long would it take to accelerate a person to the speed of light without dying?

Factual Questions
1

A co-worker of mine told me today that if people could travel at the speed of light, it would take just over 3 minutes to get from Earth to Mars. I countered that the time it would take to safely accelerate a human body to the speed of light (i.e. without crushing it to death) would negate some (or most?) of the benefit of actually travelling at the speed of light.

So now I’m curious…exactly how long would it take to accelerate a person to the speed of light? What’s the maximum force that a human body can withstand for the time it would take to get up to speed? And what’s the distance you’d have traveled during the acceleration, and how much further would there be to go in my Earth-to-Mars example once you actually achieve the speed of light?

All of this is hypothetical, of course. Assume we have the technology of a vehicle that could withstand the stresses as well as the capability to actually achieve that kind of speed.

2

…an infinitly long time… isn’t c a limit?

3

Yes, you’ll have to rephrase the question to suggest a fraction of the speed of light. 99.999% for example. You can’t actually get to C. A specific fraction less than 100% would be necessary to answer your question.

Also, you’ll have to state whether you want the time relative to the spacecraft, or relative to Earth. That whole time dilation thing, don’tcha know.

4

Going by classical physics

Velocity = g * time where g is the acceleration constant.

In “weightless” space, a person would be continuously subjected to a force of one ‘g’ if the person were accelerated at 32 ft/sec[sup]2[/sup]. Since this is equaivalent to Earth’s gravity, the person would be subjected to no undue stress.

The speed of light is about 300,000 kilometers per second which equals 984,000,000 feet per second.

Since v=g*t then
t = v/g
t= 984.000.000/32
t= 30,700,000 which is roughly speaking one year ( 1 year is about 31.5 million seconds).

As someone else mentioned, it isn’t as straightforward as this because as we approach light speed, relativistic changes occur.
Here is a website for calculating relativistic changes:
http://www.1728.com/reltivty.htm

So, uniformly accelerating a spaceship cannot be done with the same amount of force. At 50% the speed of light, the mass of the ship increases by 15%. At 90 % the speed of light, the ship’s mass has increased by 229%. So, you would need to expend 2.29 times the amount of fuel to continue the accelleration at 32 fett/sec[sup]2[/sup]. Eventually this would be very impractical because at 99% light speed, the ship’s mass has increased seven-fold.

So, let’s suppose we have a ship that has enough fuel to account for the relativistic changes in mass, then the answer would be about a year IF you wanted to go at 99% light speed (your mileage may vary).

To tell you the truth that surprises me. I thought it might take a century or more so it is practical in terms of a person’s lifetime. However, constructing a spaceship that could accelerate at 32 feet/sec[sup]2[/sup] would be impossible by today’s technology. Among other things it would require enough fuel to burn continuously to maintain a one ‘g’ acceleration for one full year.

One more thing how far would you have travelled by the time you reach 99% light speed? IF you headed in a straight line, you would be 2.8 TRILLION MILES from where you started. This is roughly one half of a light year so this seems about right.

5

Well, ignoring time dilation and the fact that you can’t actually reach c at the moment…

Assuming that 1 g = 10 m/s^2 and that c = 300,000,000 m/s, we get:

v = a t
t = v / a
t = 300,000,000/10 = 30,000,000 seconds or 347.222 days.

So, with an acceleration of 1 g it would take you almost a year to reach lightspeed. I think you would reach Mars a bit before that, even without reaching c.

6

Or, you could just read what wolf_meister said while I was looking for a calculator…

Of course, you could cut the time in half by accelerating at 2 g (or by two-thirds at 3 g and so on) but that raises the question of if a human being could survive 2 g for nearly 6 months. (And another 6 months to slow down on the other end.) Anyone know of any studies on the effects of long-term higher-than-normal acceleration on humans?

7

What increment of g could a human be continuously subjected to? 3g? 4g? That’d quicken the acceleration substantially, wouldn’t it?

8

By the by, how much time would the astronaut experience during that 347.222 days? Is it calculable?

9

OK, just as an academic exercise, 90% the speed of light is good enough.

But, at some point you will need to start decelerating. You would need a certain amount of fuel to burn to start slowing down. Otherwise the landing will be most unpleasant.

10

You could do that. However, there’s a more realistic way to look at it. You could accelerate uniformly in your own reference frame without having to worry about mass dilation. However, 1g of acceleration in your reference frame would not be the same as 1g of acceleration in Earth’s reference frame. If I understand Equation 15, when you do this, the speed-acceleration formula changes from:

v = at

to:

gamma × v = at

For v = 0.9c, gamma × v = 2.065c, and so it will take 2.000 years to reach this speed at 1g of acceleration. To reach v = 0.99c, it would take 6.799 years.

Now, Earl Snake-Hips Tucker is right, you’d want to start decelerating halfway through your trip. This exercise is common enough that the answer is given in Eq. 16-17 of the page I linked to. However, the formula makes no sense. I’ll try to find something better.

11

[aside]

I love these discussions! Especially Achenar’s post: “We’ll need to figure out A, B and C. Equation Z lays it all out because it’s so common a question. Unfortunately, I don’t understand a lick of it. Be right back.” Ha! I wouldn’t have Clue #1 where to start if I were to try to answer.

[/aside]

12

Just a minor note, probably what Jadis’ coworker was marveling at was that Mars is only three light minutes away * right now *. It’s as close as it’s been in something like 50,000 years and the astronomers are having a field day.

Although 56,000,000 km is still a long drive, what surprises me is that it looks like it only takes 29 hours or so of 1 G acceleration. 42 hours if you want to survive the landing.

13

Just make sure you have intertial dampeners on your spaceship. Then you can accelerate to 99.999c in about 1.3 seconds. Add a few seconds for the calculations so you dont wind up hitting a star or asteroid,that could end your trip real quick.

14

Ha ha. :slight_smile: I do understand the math, but there’s definitely a typo or something with those equations. If you look, you’ll see that they use the variable G which isn’t defined or used anywhere else. Plus, they take the hyperbolic sine of a number which isn’t unitless.

Anyway, this problem is given a good treatment in the first half of the Relativistic Rocket FAQ. I’ll copy equations from there. Say an astronaut wants to travel a distance d at an acceleration a. The time it takes in Earth’s reference frame is:

t = sqrt((d/c)[sup]2[/sup] + 2d/a)

The time it takes in the astronaut’s frame is:

T = (c/a) arccosh(ad/c[sup]2[/sup] + 1)

The maximum speed she would reach would be:

v[sub]MAX[/sub] = at (1 + (at/c)[sup]2[/sup])[sup]-1/2[/sup]

Okay, now in real life, you’d want to make d equal to one-half your journey, and double your result. This is because you’d be accelerating for the first half, and decelerating for the second half.

Thus, if our astronaut wanted to travel a total distance of 78.3221 million km at 1g of acceleration, then it would take 2.068705 days to us, but only 2.068701 days to her - a difference of about a quarter of a second. Relativistic effects don’t come into play over such a small distance; the maximum speed she’d reach is only 876.4 km/s = 0.00292c.

We could make the effects more prominent by increasing the acceleration - say to 8g. Then the trip would take about 17.6 hours, and the difference in perceived times would be a whopping 0.36 seconds.

15

I’m fascinated by the responses here (even if I don’t necessarily understand all of the math and theories)…thanks, guys.

One thing I don’t see answered (and maybe it’s because no one really knows), but how many Gs of force can a human body withstand for an extended period of time? All of the calculations so far are assuming 1 G, which would be no more stress on the human body than standing on Earth…but could the body stand more? I know that fighter pilots and astronauts are subjected to high Gs for short periods of time…but is it possible to withstand them for longer periods?

16

Here’s one answer, apparently from NASA: http://quest.arc.nasa.gov/saturn/qa/new/Effects_of_speed_and_acceleration_on_the_body.txt .

My WAG is that the human frame could probably support 2 G’s for a sustained period – this is based mostly on some of the physical specimans my height I’ve seen wandering around my supermarket carrying approximately twice my body mass and appearing to function pretty normally despite being in-far-from peak condition. The human frame seems capable of carrying twice “normal” body weight for a considerable length of time. Probably the long-term effects would more or less mirror morbid obesity as well – considerable stress on the cardio-vascular system, limited mobility, high blood pressure, circulation and back problems. The cases may not be totally analogous – I imagine blood would tend to pool in the extremities under high acceleration and capillaries might not be up to the strain of carrying “heavier” blood, but pressure suits and fluid baths could be used to minimize these effects.

Actually, if extreme obesity is a good model for how well humans can withstand acceleration, the link http://www.dimensionsmagazine.com/dimtext/kjn/people/heaviest.htm describes several people who lived relatively long, somewhat healthy lives weighing almost 1/2 ton! So 3-4 G’s might not be completely out of the question, provided mobility is not an issue.

I imagine you wouldn’t want to just spike the acceleration – you’d probably want to ramp it up over a few hours, days, or even weeks to give the astronauts time to acclimate.

17

…on foot?

18

Old thread, but I think I may be able to add something…
The energy requirements to accelerate a ship the size of the Enterprise to only half the speed of light is roughly 2000 times the total annual energy used in the world today (2011). Source “The Cosmic Perspective” by Bennett
We would also need to devise some type of energy shield protecting the space ship.
As the ship travels through interstellar gas at near-light speed, ordinary atoms and ions will hit it like a deadly flood of high-energy cosmic rays.

Well, I guess we are still waiting for the “Galactic Civilization” to contact us. I wonder if they have cool video games?

19

Then you smack into that space rock you had absolutely no means of detecting in time to avoid by changing course.

20

The real question is, at what rate can a ZOMBIE be accelerated to the speed of light? My guess is it takes at least 8 years…