# Accelerating to light speed

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#### ahook12

##### Guest
I have calculated that if you accelerate at 1 g for 1 year you reach light speed (300,000,000 Meters per/sec). can someone check my math to see if this is correct.

Thanks, Allen

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#### Astro_Robert

##### Guest
I guess simply: 1G ` 10 m / s^2. 1 year ~ 31.5 Million seconds. So 10 m / s^2 * 31.5 M-secs ~ 300 M m/s. It may work out mathematically...

However, and it is a big however, as one approaches relativistic speeds, the 'thrust' required to achieve 1G acceleration would go up dramatically. This would be impossible to actually achieve with any technology we can even imagine.

Surely, any civilization attempting high relativistic speeds would find some other way, although I do not believe any have yet been proven to be viable. I do root for the discovery of some effective means of travelling cosmic distances as I feel the universe would be a much more interesting place. However, it does seem to be rather unlikely.

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#### ahook12

##### Guest
I was not suggesting that this would be a good way to get to light speed, but only saying this is a very strange coincidence that accelerating at 1 g for 1 year = light speed.

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#### ramparts

##### Guest
I mean, it's a coincidence but I don't see why it's particularly strange. Some familiar numbers, when combined, are similar to another familiar number. If you play around with enough familiar numbers you're bound to find all sorts of coincidences like this

(By the way, accelerating at g for one year wouldn't leave you at the speed of light, it would leave you at 1.03 times the speed of light. Accelerating at g for about 354 days would leave you right at c. It's not an exact thing.)

As Astro_Robert began to talk about, though, there are a lot of reasons why this has nothing whatsoever to do with physics. For one thing, what we call g is only the gravitational acceleration on the Earth's surface. The acceleration would be lower at higher altitudes and higher at lower altitudes, so if you were actually accelerating at g, it wouldn't be very long at all before the acceleration you felt became very different from its surface value (9.8 meters per second^2).

Second, this calculation doesn't take into account relativistic effects, so if, say, a rocket ship were accelerating at g for a full year, it would most certainly not reach the speed of light. The reason is that according to relativity, as you start moving, you effectively gain mass from that motion (you have kinetic energy, so think E=mc^2, although that equation isn't quite the relevant one here). Now, you can't apply a constant acceleration, you can only apply a constant force. Recall that force is dependent on both mass and acceleration (F=ma), so if your mass is constant, then so is your acceleration, but if you're getting heavier, then the same force will accelerate you less and less. So if your rocket ship has a constant force of mg (where m is the rocket's rest mass), then as it gets faster, the actual acceleration you feel will be less than g. As it turns out, this constantly-shrinking acceleration approaches a limit - it means that no matter how much force you apply, you can get arbitrarily close to but never reach the speed of light

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#### kelvinzero

##### Guest
In terms of coincidences, how about the speed of light being so close to 3x10^8 m/s, instead of something as ugly and hard to remember as pi. I think the actual value is more like 2.998*10^8. The error is less than a thousandth of the value.

The definition of the meter is really pretty arbitrary if you look it up.

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#### kg

##### Guest
Actually you can accelerate at 1G for as long as you like and you will NEVER get to the speed of light. No matter how fast you think you are going a photon coming up from behind you will still pass you like you like are standing still (er... at the speed of light). What will happen in the spaceship frame of refrence is that the distance you travel to get to where you are going shortens along with the time it takes to get there. There was a neat caculator kicking around here somewhere to help figure this out with...

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#### emperor_of_localgroup

##### Guest
ahook12":1co0jxsf said:
I have calculated that if you accelerate at 1 g for 1 year you reach light speed (300,000,000 Meters per/sec). can someone check my math to see if this is correct.

Thanks, Allen

It may be just a coincidence, but an interesting curiosity raising coincidence.

It may bring back an old question 'are all our measurements earth or solar system dependent'? Measurements which include constants of physics?

I see there 's a small discrepancies in numbers, which may have come from the fixed numbers we use for 'g' (usually 9.81 in metric system), or for mass or radius of earth.

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#### ramparts

##### Guest
Emperor - No, it's not that it "may be" a coincidence. It is a coincidence. And not a very interesting or curious one, at that. In order for this to be anything more than a coincidence, there has to be a relationship between the mass of the Earth, the radius of the Earth, the time the Earth takes to travel around the sun, and the speed of light, things which have absolutely no common factor. And that's ignoring special relativity which makes this calculation meaningless anyway. Sometimes a coincidence is just a coincidence (and not even a very good one; the number ahook calculates is close to but not exactly the speed of light).

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