The parallax method has been used for measuring distances of stars, which are

Options

A. lass then 100 light years away
B. more the 100 light years away
C. neither less nor more then 100 light years away
D. none of above

Answer

To solve the question regarding the parallax method for measuring distances of stars, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understanding Parallax**: The parallax method involves observing a star from two different positions in Earth's orbit around the Sun. The apparent shift in position of the star against the background of more distant stars is measured.

2. **Defining the Parameters**:
- Let’s denote the distance from the Earth to the star as \( L \).
- The distance between the two observation points (the baseline) is \( x \), which is typically the diameter of Earth's orbit (about 2 AU or approximately \( 3 \times 10^{11} \) meters).
- The angle of parallax formed at the star due to this baseline is \( \theta \).

3. **Using the Parallax Formula**:
- The relationship between the distance \( L \), the baseline \( x \), and the angle \( \theta \) can be expressed as:
\[ \theta = \frac{L}{x} \]
- Rearranging this gives:
\[ L = x \cdot \theta \]

4. **Limitations of the Method**:
- The angle \( \theta \) must be small for the approximation to hold true. If \( L \) is too large (greater than 100 light years), the angle \( \theta \) becomes too large, and the simple linear relationship breaks down.
- Thus, the parallax method is effective for measuring distances to stars that are less than 100 light years away.

5. **Conclusion**:
- Therefore, the parallax method is used for measuring distances of stars that are **less than 100 light years** away.

### Final Answer:
The parallax method has been used for measuring distances of stars which are **less than 100 light years**.

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