Schwarzschild Radius help

Sep 2018
7
0
I have been trying to calculate the radius of a blackhole using Scharzschild Radius:

R = 2GM/C2

But when I compare my answers to sample question problems, I am consistantly getting different answers.

For example
A black hole with M (solar) = 3.7 x 10^6M

I plug in:
(2x(6.67x10^-11)(3.7 x 10^6))/(3x10^8)^2

But the answer I get is: 5.48e-21
The sample problem says it should be: 0.08 au or 16R

I have the same issues with every other one too
And it doesn't matter what I do -whether I convert Msolar to KG or try to break down the equation further, I still get different answers to those provided.

I am not sure where I am going wrong.
 
Oct 2017
611
312
Glasgow
You've missed out the solar mass (1 solar mass = \(\displaystyle 2 \times 10^{30}\) kg), which needs to be included so the units are in SI. You should have

\(\displaystyle R = \frac{2 \times 6.67 \times 10^{-11} \times 3.7 \times 10^6 \times 2 \times 10^{30}}{(3 \times 10^8)^2} = 1.482 \times 10^{9} m = 0.0099 AU\)
 
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