GM What is the orbital period of a bit of matter in an accretion disk that is located 3 x 105 km from a 29 M. black hole? (Hint: Use the circular orbit velocity formula, V. = V

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**Question:**

What is the orbital period of a bit of matter in an accretion disk that is located \(3 \times 10^5\) km from a \(29 \, M_{\odot}\) black hole? *(Hint: Use the circular orbit velocity formula, \( V_c = \sqrt{\frac{GM}{r}} \).*

**Answer:**  
[ ] s

In this problem, you are tasked with finding the orbital period of matter in an accretion disk around a black hole. The mass of the black hole is \(29 \, M_{\odot}\), where \(M_{\odot}\) represents the solar mass, and the distance from the black hole is \(3 \times 10^5\) km. The hint provided suggests using the formula for circular orbit velocity:

\[ V_c = \sqrt{\frac{GM}{r}} \]

In this formula:

- \(G\) is the gravitational constant.
- \(M\) is the mass of the black hole.
- \(r\) is the distance from the black hole.

You will need to integrate this formula into the calculation for the orbital period to find the answer.
Transcribed Image Text:**Question:** What is the orbital period of a bit of matter in an accretion disk that is located \(3 \times 10^5\) km from a \(29 \, M_{\odot}\) black hole? *(Hint: Use the circular orbit velocity formula, \( V_c = \sqrt{\frac{GM}{r}} \).* **Answer:** [ ] s In this problem, you are tasked with finding the orbital period of matter in an accretion disk around a black hole. The mass of the black hole is \(29 \, M_{\odot}\), where \(M_{\odot}\) represents the solar mass, and the distance from the black hole is \(3 \times 10^5\) km. The hint provided suggests using the formula for circular orbit velocity: \[ V_c = \sqrt{\frac{GM}{r}} \] In this formula: - \(G\) is the gravitational constant. - \(M\) is the mass of the black hole. - \(r\) is the distance from the black hole. You will need to integrate this formula into the calculation for the orbital period to find the answer.
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