A 1.5 M neutron star and a 0.7 M white dwarf have been found orbiting each other with a period of 10 minutes. What is their average separation? Convert your answer to units of the Sun's radius, which is 0.0047 AU
A 1.5 M neutron star and a 0.7 M white dwarf have been found orbiting each other with a period of 10 minutes. What is their average separation? Convert your answer to units of the Sun's radius, which is 0.0047 AU
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Question
A 1.5 M neutron star and a 0.7 M white dwarf have been found orbiting each other with a period of 10 minutes. What is their average separation? Convert your answer to units of the Sun's radius, which is 0.0047 AU.
![**Binary Star System Analysis**
**Problem Statement:**
A 1.5 \(M_{\odot}\) neutron star and a 0.7 \(M_{\odot}\) white dwarf are orbiting each other with a period of 10 minutes. Determine the average separation of the two stars. Convert the answer into units of the Sun's radius, which is 0.0047 AU.
**Methodology:**
Utilize the version of Kepler's third law for binary stars:
\[ M_A + M_B = \frac{a^3}{p^2} \]
- \(M_A\) and \(M_B\) are the masses of the neutron star and white dwarf in solar masses.
- \(a\) is the average separation in astronomical units (AU).
- \(p\) is the orbital period in years.
**Conversion Note:**
A year is equivalent to \(3.2 \times 10^7\) seconds.
**Calculation:**
(Insert your value in the box below)
- **[ ] solar radii**
This exercise provides a practical application of gravitational dynamics in binary star systems, employing Kepler's laws to deduce real celestial measurements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0530e16-0f9d-4caf-90d6-684cf5a3ef1c%2F402051bf-71df-4450-bce8-53a9bce3aaae%2F8umbwzi_processed.png&w=3840&q=75)
Transcribed Image Text:**Binary Star System Analysis**
**Problem Statement:**
A 1.5 \(M_{\odot}\) neutron star and a 0.7 \(M_{\odot}\) white dwarf are orbiting each other with a period of 10 minutes. Determine the average separation of the two stars. Convert the answer into units of the Sun's radius, which is 0.0047 AU.
**Methodology:**
Utilize the version of Kepler's third law for binary stars:
\[ M_A + M_B = \frac{a^3}{p^2} \]
- \(M_A\) and \(M_B\) are the masses of the neutron star and white dwarf in solar masses.
- \(a\) is the average separation in astronomical units (AU).
- \(p\) is the orbital period in years.
**Conversion Note:**
A year is equivalent to \(3.2 \times 10^7\) seconds.
**Calculation:**
(Insert your value in the box below)
- **[ ] solar radii**
This exercise provides a practical application of gravitational dynamics in binary star systems, employing Kepler's laws to deduce real celestial measurements.
Expert Solution
Step 1
The expression for the Kepler’s third law for binary stars is as follows:
Use equation (1) to solve for the average separation between the stars.
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