Brewer
Mar19-08, 05:15 PM
1. The problem statement, all variables and given/known data
http://i54.photobucket.com/albums/g99/brewer86/Capture.jpg
2. Relevant equations
d\tau = dt\sqrt{1-\frac{r_s}{r}}
and
\frac{dr}{d(ct)} = 1 - \frac{r_s}{r}
3. The attempt at a solution
First of all I worked out the Schwarzschild radius to be 2.964*10^4m.
From this I plugged it into the first of the two equations above, along with d\tau = 30, and dt = 300 (years in both cases, but it'll cancel), and rearranged to give r as 2.994*10^4m, i.e. 300m outside the Schwarzschild radius.
From here I plugged these new numbers into the second equation that I've given in order to give \frac{dr}{d(ct)} = 0.01. I assume that this means a fraction of c.
I'm not entirely convinced though. Can someone check what I've done please. Have I used the correct meanings of d\tau and dt? Is the second equation that I've given the correct one to use? If not could someone point me in the right direction?
Thanks for anyone who helps out.
http://i54.photobucket.com/albums/g99/brewer86/Capture.jpg
2. Relevant equations
d\tau = dt\sqrt{1-\frac{r_s}{r}}
and
\frac{dr}{d(ct)} = 1 - \frac{r_s}{r}
3. The attempt at a solution
First of all I worked out the Schwarzschild radius to be 2.964*10^4m.
From this I plugged it into the first of the two equations above, along with d\tau = 30, and dt = 300 (years in both cases, but it'll cancel), and rearranged to give r as 2.994*10^4m, i.e. 300m outside the Schwarzschild radius.
From here I plugged these new numbers into the second equation that I've given in order to give \frac{dr}{d(ct)} = 0.01. I assume that this means a fraction of c.
I'm not entirely convinced though. Can someone check what I've done please. Have I used the correct meanings of d\tau and dt? Is the second equation that I've given the correct one to use? If not could someone point me in the right direction?
Thanks for anyone who helps out.