Let A be the Area Swept by the line joining the earth and the sun during Feb-2007. The Area Swept by the same line during the first week of that month is

Options

A. A/4
B. `(7A)/29`
C. A
D. `(7A)/30`

Answer

To solve the problem, we need to determine the area swept by the line joining the Earth and the Sun during the first week of February 2007, given that the total area swept during the entire month is \( A \).

### Step-by-Step Solution:

1. **Understand the Concept**: According to Kepler's Second Law (the law of areas), a planet sweeps out equal areas in equal times. This means that if we know the total area swept in a certain time period, we can find the area swept in a shorter time period by using a proportional relationship.

2. **Identify the Total Area**: Let \( A \) be the total area swept by the line joining the Earth and the Sun during February 2007. February has 28 days.

3. **Calculate the Area Swept Per Day**: Since the area swept is uniform over the month, we can find the area swept per day by dividing the total area by the number of days in February:
\[ \text{Area swept per day} = \frac{A}{28} \]

4. **Calculate the Area Swept in the First Week**: The first week of February consists of 7 days. Therefore, the area swept during the first week can be calculated by multiplying the area swept per day by the number of days in the week:
\[ \text{Area swept in the first week} = \text{Area swept per day} \times 7 = \left(\frac{A}{28}\right) \times 7 \]

5. **Simplify the Expression**: Now, simplify the expression:
\[ \text{Area swept in the first week} = \frac{A \times 7}{28} = \frac{A}{4} \]

6. **Final Answer**: Thus, the area swept by the line joining the Earth and the Sun during the first week of February 2007 is:
\[ \frac{A}{4} \]