Introduction:
The distance between the Earth and the Sun is a crucial factor in determining the length of a year. If the Earth were to be placed at one-half of its present distance from the Sun, it would significantly impact the duration of a year. In this response, we will explore the effects of this change and calculate the new number of days in a year.

Understanding the current number of days in a year:
Currently, a year is defined as the time it takes for the Earth to complete one orbit around the Sun. This duration is approximately 365.25 days. The extra 0.25 days account for the additional time it takes for the Earth to catch up to its starting point due to the leap year system.

The impact of a change in distance:
When the Earth moves closer to the Sun, it experiences a stronger gravitational pull. This increased gravitational force results in a higher orbital speed for the Earth. As a consequence, the time required for the Earth to complete one revolution around the Sun decreases.

Calculating the new number of days in a year:
To determine the new number of days in a year, we can apply Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun.

Let's assume the current average distance between the Earth and the Sun is represented by "d". If the Earth is moved to one-half of its present distance, the new average distance would be "d/2".

Using the proportionality relationship from Kepler's Third Law, we can set up the following equation:

(T/365.25)^2 = (d/2)^3

Simplifying the equation, we find:

T/365.25 = (d/2)^(3/2)

Solving for T, the new orbital period, we have:

T = 365.25 * (d/2)^(3/2)

Substituting the values, we can calculate the new orbital period and subsequently the number of days in a year.

Conclusion:
By applying Kepler's Third Law of Planetary Motion, we can determine the new number of days in a year if the Earth were to be placed at one-half of its present distance from the Sun. This calculation takes into account the change in gravitational force and orbital speed caused by the altered distance. Remember, the estimated value we obtain might not be an exact representation due to various factors affecting the Earth's orbit.

558.45??