If the area swept by the line joining the sun and the earth from Feb 1 to Feb 7 is .A., then the area swept by the radius vector from Feb 8 to Feb 28 is

Options

A. A
B. 2A
C. 3A
D. 4A

Answer

To solve the problem, we will use Kepler's second law, which states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Area swept from February 1 to February 7 is \( A \).
- The time interval from February 1 to February 7 is 7 days.

2. **Calculate the Area Swept per Day:**
- Since the area swept in 7 days is \( A \), the area swept in 1 day can be calculated as:
\[ \text{Area per day} = \frac{A}{7} \]

3. **Determine the Time Interval from February 8 to February 28:**
- The number of days from February 8 to February 28 is 21 days.

4. **Calculate the Total Area Swept from February 8 to February 28:**
- The total area swept in 21 days can be calculated by multiplying the area swept per day by the number of days:
\[ \text{Area for 21 days} = 21 \times \left(\frac{A}{7}\right) \]
- Simplifying this gives:
\[ \text{Area for 21 days} = \frac{21A}{7} = 3A \]

5. **Final Answer:**
- Therefore, the area swept by the radius vector from February 8 to February 28 is \( 3A \).