Dear PF Forum,
What is the limit of acceleration?
I've been reading old threads, and I found this.

G = 6.673 x 10^{-11} N m^{2}/kg^{2}
Solar mass = 1.989 * 10^{30}kg

And I tried to plug in some numbers....
In a distance 30 km from a 10 solar mass object the acceleration is...
##a = \frac{GM}{r^2\sqrt{1-\frac{2GM}{c^2R}}}##
##a = \frac{6.673*10^{-11}*10*1.989*10^{30}}{10^{10}\sqrt{1-\frac{2*6.673*10^{-11}*30*1.989*10^{30}}{9 * 10 ^{16} * 30000}}}##
##a = 22725433875431.4000## or 2 trillion km per second squared. (if my calculation is correct. But I calculate it carefully, sorry if I make a mistake here)
Which seems much higher than the speed of light, 300 thousands km per second
But, of course that statement above is unreasonable, irrelevant. Because acceleration is in length per time squared. And 300 thousands km per second is in our units, our km, our second.

So is there a limit for acceleration as in limit for velocity in this universe is the speed of light? (beside expansion of galaxy)
Thank you very much.

I am not sure what exactly is confusing you. What Peter's quote shows is that while there is a limit on velocity, there is no limit on the rate at which velocity can increase. Obviously for an extremely high value for a, the time during which an object can have this acceleration is very small.

I haven't thought about Peter equation, until I tried pluggin some numbers and ##a=\frac{2,000,000,000,000}{s^2}## came up. Of course you're right, "there's no limit on the rate at which velocity can increase". Just want to discuss it with someone else, I'm afraid I make mistake.
Yes, yes, I understand. Thank you.

Well acceleration is not speed. And as the speed increases so does the mass ([itex] m_{v}=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/itex]), so you need to modify the formula to take that into account.

I am not expert but I have read somewhere, if we assume velocity of object can't exceed velocity of light - c. Then maximum change in velocity can be 2c per second. Hence acceleration can't exceed 2c, i.e. 2*c is limit of the acceleration.

I'm no expert either. . But I think there is no limit for acceleration.
You can accelerate ten times the speed of light (whatever it means) say 3 millions km/second squared, but only for 0.1 sec I think. - Hence acceleration can't exceed 2c
Now, I think this is a false statement?
Intutitively we would have said that accelerate at 600 thousands km / second squared is accelerate 2 times the speed of light. But again I think this is a wrong statement. And doesn't make any sense either.

When I first created this thread, I just realize that acceleration can be very high (may be there is a limit?)
But thinking it over again, I realize that it doesn't make any sense for acceleration having a limit.

Perhaps @Svein is trying to show the relation between acceleration and mass. But either way, I understand now. Intuitively we can get confused seeing 600 thousands km / m^{2}. Seems like twice the speed of light. But it's irrelevant.

You mean km/s^{2}, right?
I suppose you did not yet understand that acceleration and velocity are different quantities and comparing them is meaningless.
Like comparing your height with your weight and saying that your weight (140 lb) is twice as much as your height (70").