A 1.4 M. neutron star and a 0.5 M. white dwarf have been found orbiting each other with a period of 16 minutes. What is their average separation? Convert your answer to units of the Sun's radius, which is 0.0047 AU. (Hints: Use the version of Kepler's third law t binary stars, M. + Ma =; make sure you express quantities in units of AU, solar masses, and years. Note: a year is 3.2 x 10' s.) solar radii

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### Binary Star Problem:

**Given:**
- A 1.4 \(M_\odot\) neutron star and a 0.5 \(M_\odot\) white dwarf orbit each other.
- Orbital period: 16 minutes.

**Question:**
What is their average separation? Convert your answer to units of the Sun's radius, which is 0.0047 AU.

**Hint:**
Use Kepler's third law for binary stars:

\[ M_A + M_B = \frac{a^3}{P^2} \]

- **Convert quantities into**:
  - AU (Astronomical Units)
  - Solar masses
  - Years

**Note:** A year is \(3.2 \times 10^7\) seconds.

**Answer Format:**
- Provide the answer in **solar radii**.

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This problem requires converting the given data and using Kepler's third law to find the average separation of the two stars in solar radii.
Transcribed Image Text:### Binary Star Problem: **Given:** - A 1.4 \(M_\odot\) neutron star and a 0.5 \(M_\odot\) white dwarf orbit each other. - Orbital period: 16 minutes. **Question:** What is their average separation? Convert your answer to units of the Sun's radius, which is 0.0047 AU. **Hint:** Use Kepler's third law for binary stars: \[ M_A + M_B = \frac{a^3}{P^2} \] - **Convert quantities into**: - AU (Astronomical Units) - Solar masses - Years **Note:** A year is \(3.2 \times 10^7\) seconds. **Answer Format:** - Provide the answer in **solar radii**. --- This problem requires converting the given data and using Kepler's third law to find the average separation of the two stars in solar radii.
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