Explanation:

To find the ratio of the maximum speed to the minimum speed of the Earth in its orbit, we need to understand the concept of eccentricity and its relation to the speed of the orbiting object.

1. Eccentricity:
The eccentricity of an orbit is a measure of how much it deviates from a perfect circle. It is a dimensionless parameter that ranges from 0 to 1. A value of 0 represents a perfect circle, while a value of 1 represents a highly elongated orbit.

2. Relation between Eccentricity and Speed:
The speed of an object in its orbit is not constant throughout the orbit. It varies depending on the distance between the object and the center of attraction (in this case, the Sun). The speed is highest when the object is closest to the center of attraction and lowest when it is farthest away.

3. Kepler's Second Law:
Kepler's second law states that a planet sweeps out equal areas in equal times. This means that as a planet moves closer to the Sun, it covers more area in a given time interval, indicating a higher speed. Similarly, as it moves farther away, it covers less area in the same time interval, indicating a lower speed.

4. Application to Earth's Orbit:
The Earth's orbit around the Sun is not a perfect circle but an ellipse, with the Sun at one of the foci. The eccentricity of Earth's orbit is given as 0.0167.

The Earth's speed is highest when it is closest to the Sun (perihelion) and lowest when it is farthest away (aphelion). The ratio of the maximum speed to the minimum speed can be calculated using the formula:

Ratio = (1 + e) / (1 - e)

where e is the eccentricity.

5. Calculation:
Plugging in the given value of eccentricity (e = 0.0167) into the formula, we get:

Ratio = (1 + 0.0167) / (1 - 0.0167)
= 1.0167 / 0.9833
≈ 1.033

Therefore, the ratio of the maximum speed to the minimum speed of the Earth in its orbit is approximately 1.033.

Conclusion:
Hence, the correct answer is option B) 1.033.