How many Gs would you be under if you accelerated steadily from 0 to 99.9% of c over a one year period?

Answer 1

The non-relativistic equation of motion for constant acceleration is v=aT.

The relativistic version of this can be shown to be v = c tanh (aT/c).

Plugging in numbers gives an acceleration of about 3.7g.

Answer 2

v = at
v = speed: at a constant acceleration, the speed increases at a constant rate. The speed after a time t is simply the acceleration multiplied by the time. Just make sure all units are compatible.
I am using international units: metres and seconds.

v = 0.999 c = 299,493 km/s
t = 31,556,952 (average Gregorian year)

a = v/t = 299,492,000 m/s / 31,556,952 s
a = 9.4905 m/s^2

one g = 9.80665
(lower case g for 'standard gravity' on Earth at 45 N)

a = 0.96776 g

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Badass, you got it OK.

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The problem in 'real life' is maintaining the acceleration. As the speed (v) appraches the speed of light (c), the total energy of the moving object would increase greatly so that it would behave as if it had more mass (if we used the old Newtonian approach -- which I will do here).

Remember F = m a
The force needed to accelerate an object depends on its mass. Well, as the object approaches the speed of light (if we insisted on using this equation) we'd have to consider that the mass increases
m = mo / SQRT(1 - v^2/c^2)

So that more and more force is needed to maintain the same acceleration.

At a speed of 0.998 c, the force we need to maintain an acceleration of 9.49 m/s^2 is 250 times the force we needed when we started with the same acceleration from rest.

At a speed of .999 c, the force is 500 times as much as when we started.

At .9999 c, it will be 5,000 times as much...

and so on.

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However, for the people inside the spacecraft, since their time is dilated (they are living 500 times slower than us when they reach 0.999), they would preceive everything differently.

See pseudospin below.

Answer 3

v = a * t
a = v / t

v = 0.999 * 3 * 10^8 m/s
t = 60s * 60 min/s * 60 mins/hr * 24 hrs/day * 365 days/yr

a = 3*0.999 * 10^8 / (6*6*6*24*365 * 10^3)
= 2.997 * 10^8 / (1892160 * 10^3)
= 2.997 * 10^8 / (1.892160 * 10^9)
= 1.58390411 * 10 ^-1

since G = 9.8 m/s

then # Gs = 1.58390411 * 10 ^-1/9.8
= 0.016162287 G

Answer 4

I got about .97 g's, or 9.5 m/s^2, with a high chance that I mixed up a few zeroes.

Answer 5

9 Gs.

Answer 6

1g nearly