The correct answer is option 3: 1 and 3.

Let`s break down each statement to understand why it is correct or incorrect:

1. The earth is nearest to the Sun at Perihelion, which generally occurs on January 3.

- This statement is correct. Perihelion is the point in the Earth`s orbit where it is closest to the Sun. It generally occurs on January 3.

2. The earth is farthest away from the Sun at Perihelion, which generally occurs on July 4.

- This statement is incorrect. Perihelion is when the Earth is closest to the Sun, not farthest away.

3. The earth is farthest away from the Sun at Aphelion, which generally occurs on July 4.

- This statement is correct. Aphelion is the point in the Earth`s orbit where it is farthest away from the Sun. It generally occurs on July 4.

4. The earth is nearest to the Sun at Aphelion, which generally occurs on January 3.

- This statement is incorrect. Aphelion is when the Earth is farthest away from the Sun, not nearest.

Therefore, the correct statements are 1 and 3, which makes