The average distance between the Sun and the Earth is approximately 150 x 10^6 kilometers, which corresponds to Option 4. This distance is commonly referred to as an astronomical unit (AU).

The precise average distance between the Sun and the Earth is known as the mean distance or semi-major axis of Earth`s orbit. It is a result of the elliptical shape of Earth`s orbit around the Sun, with the Sun located at one of the foci of the ellipse. Earth`s orbit is not a perfect circle but rather an ellipse with the Sun slightly off-center.

The semi-major axis of Earth`s orbit is defined as half of the longest diameter of the elliptical orbit. It is an important astronomical measurement used to calculate the distances of other objects in the solar system. The average distance of 150 x 10^6 kilometers is calculated by taking the mean of the closest point (perihelion) and the farthest point (aphelion) of Earth`s orbit.

The perihelion occurs when Earth is closest to the Sun, while the aphelion is when Earth is farthest from the Sun. The actual distance between these two points can vary slightly due to the gravitational influences of other celestial bodies, such as other planets in the solar system.

It is worth noting that the average distance between the Sun and the Earth is not a fixed value. Due to various factors such as gravitational interactions and the influence of other celestial bodies, Earth`s orbit experiences small perturbations over time. These perturbations can cause the average distance to change slightly over long periods, but for practical purposes, the value of 150 x 10^6 kilometers is widely accepted.

In conclusion, the average distance between the Sun and the Earth is approximately 150 x 10^6 kilometers (Option 4). This value is based on the mean distance or semi-major axis of Earth`s elliptical orbit around the Sun and is commonly used as a reference in astronomical calculations.