According to Kepler's laws of planetary motion, specifically his second law (the law of areas), a planet sweeps out equal areas in equal times. This means that while it is at its slowest orbital speed, it sweeps out an area \( A \) in 45 days.
When the planet is at its fastest orbital speed, it will sweep out more area in a shorter duration. Since the time is shorter (40 days instead of 45 days), the planet will sweep out a smaller area compared to the area it sweeps out in the longer duration.
Using this reasoning:
- In 45 days, it sweeps out area \( A \).
- In the time period of 40 days, at its fastest speed, it will not sweep out the entire area \( A \) but rather less than that.
Thus, the area swept out in 40 days at maximum speed will be less than \( A \).
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