Question

match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer. view available hint(s) decreases increases remains the same 1. as the distance to the object increases, parallax blank. 2. as the size of baseline increases, parallax blank. 3. as the distance to background objects increases, parallax blank. (image shows earth with points a, b, and two star views labeled \as seen from a\ and \as seen from b\)

Explanation:

To solve this, we recall the concept of parallax: Parallax is the apparent shift in position of an object when viewed from different points (baseline). The formula related to parallax (in angular terms) is \( \theta \approx \frac{b}{d} \) (for small angles), where \( \theta \) is parallax, \( b \) is baseline, and \( d \) is distance to the object.

1. As the distance to the object increases, parallax...

From \( \theta \approx \frac{b}{d} \), if \( d \) (distance) increases (with \( b \) constant), \( \theta \) (parallax) decreases.

2. As the size of baseline increases, parallax...

From \( \theta \approx \frac{b}{d} \), if \( b \) (baseline) increases (with \( d \) constant), \( \theta \) (parallax) increases.

3. As the distance to background objects increases, parallax...

Background objects are very far, so their distance \( d \) is extremely large. From \( \theta \approx \frac{b}{d} \), as \( d \) becomes very large, \( \theta \) (parallax) becomes negligible and remains the same (since the shift is too small to notice, or effectively constant for practical purposes).

Final Matches:

1. decreases
2. increases
3. remains the same

Answer:

To solve this, we recall the concept of parallax: Parallax is the apparent shift in position of an object when viewed from different points (baseline). The formula related to parallax (in angular terms) is \( \theta \approx \frac{b}{d} \) (for small angles), where \( \theta \) is parallax, \( b \) is baseline, and \( d \) is distance to the object.

1. As the distance to the object increases, parallax...

From \( \theta \approx \frac{b}{d} \), if \( d \) (distance) increases (with \( b \) constant), \( \theta \) (parallax) decreases.

2. As the size of baseline increases, parallax...

From \( \theta \approx \frac{b}{d} \), if \( b \) (baseline) increases (with \( d \) constant), \( \theta \) (parallax) increases.

3. As the distance to background objects increases, parallax...

Background objects are very far, so their distance \( d \) is extremely large. From \( \theta \approx \frac{b}{d} \), as \( d \) becomes very large, \( \theta \) (parallax) becomes negligible and remains the same (since the shift is too small to notice, or effectively constant for practical purposes).

Final Matches:

1. decreases
2. increases
3. remains the same