Universal Gravitation and X-ray pulses

[Antepolleo]

I'm having a little bit of a problem with this one. Here's the question:

X-ray pulses from Cygnus X-1, a celestial x-ray source, have been recorded during high-altitude rocket flights. The signals can be interpreted as originating when a blob of ionized matter orbits a black hole with a period of 4.7 ms. If the blob were in a circular orbit about a black hole whose mass is 18 * MSun, what is the orbit radius?


Here's my train of thought. I used one of Kepler's laws:

$$\begin{equation*}<br /> \begin{split}<br /> T^2 = \frac{4\pi^2r^3}{GM_{blackhole}}\\<br /> r = (\frac{T^2GM_{blackhole}}{4\pi^2})^(\frac{1}{3})\\<br /> \end{split}<br /> \end{equation*}$$

I changed the milliseconds to seconds, and I got a answer of 110196.285 meters. I'm letting the mass of the sun be 1.991 x 10³⁰ kg.

I enter this into webassign, but I doesn't like it. What am I doing wrong?

 

[gnome]

I don't see anything wrong in what you did (other than keeping too many significant digits). Try rounding the answer to 110 km.

 

[chroot]

Kepler's laws won't apply when you're this close to a black hole. I'll have to think about this one a bit. Although the title of this thread suggests you're supposed to be using Newtonian mechanics...

- Warren

 

[Antepolleo]

These questions were in the "Universal Gravitation" chapter. It's got to have something to do with either Kepler's laws, or the law of universal gravitation.

 

[Antepolleo]

Originally posted by gnome
I don't see anything wrong in what you did (other than keeping too many significant digits). Try rounding the answer to 110 km.

Heh, it was a decimial problem. Thanks for pointing that out.

If only all of these problems would be so simple!