Final answer:
The distance between Earth and the Sun varies throughout the year due to Earth's slightly elliptical orbit, with a change being more subtle if the orbit was closer to a true circle. The area swept by Earth in one day is derived by dividing the total area of the orbit by the orbital period of 365.26 days.
Step-by-step explanation:
The distance between the Earth and the Sun changes as the Earth makes a complete orbit around the Sun due to the slightly elliptical nature of Earth's orbit.
While Earth's orbit is nearly circular, the semi-major axis is 152 million km and the semi-minor axis is 147 million km, indicating there is a small variation in distance throughout the year.
If Earth's orbit were more circular, with the major axis almost as long as the minor axis, the shape of the orbit would be even closer to a true circle, and the distance variation would be minimal.
Earth's orbital period is 365.26 days. According to 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, the area swept by an Earth-to-Sun line in one day would be a fraction of the total area of the ellipse.
To calculate this daily swept area, we consider the entire orbit area and divide by the number of days in the period.
Assuming Earth's orbit as an ellipse, the formula for the area of an ellipse (A = π × semi-major axis × semi-minor axis) yields the total area. This total area divided by the orbital period gives the area swept in one day.