- #1
Stephanus
- 1,316
- 104
Dear PF Forum,
What is the limit of acceleration?
I've been reading old threads, and I found this.
Solar mass = 1.989 * 1030kg
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.
What is the limit of acceleration?
I've been reading old threads, and I found this.
G = 6.673 x 10-11 N m2/kg2PeterDonis said:You are doing the wrong calculation. ...the correct GR formula is...
$$
a = \frac{GM}{R^2 \sqrt{1 - \frac{2GM}{c^2 R}}}
$$
According to this formula, ##a## increases without bound as ##R \rightarrow 2GM/c^2##, i.e., as the horizon is approached...
Solar mass = 1.989 * 1030kg
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.