The orbit of the Earth around the Sun being elliptical means that the distance between the Earth and the Sun varies throughout the orbit. The two important points to determine are:

1. Perihelion (the closest point to the Sun).
2. Aphelion (the farthest point from the Sun).

For an ellipse, the following formulas apply:

• The perihelion distance $r_{\text{min}}$ is given by: $r_{\text{min}} = a(1 - e)$
• The aphelion distance $r_{\text{max}}$ is given by: $r_{\text{max}} = a(1 + e)$ where:
• $a$ is the semi-major axis (92.9 million miles),
• $e$ is the eccentricity (0.017).

1. Perihelion (closest distance):

$r_{\text{min}} = 92.9 \times (1 - 0.017) = 92.9 \times 0.983 = 91.3 \text{ million miles}$

2. Aphelion (farthest distance):

$r_{\text{max}} = 92.9 \times (1 + 0.017) = 92.9 \times 1.017 = 94.5 \text{ million miles}$

Conclusion:

• The closest the Earth gets to the Sun (perihelion) is approximately 91.3 million miles.
• The farthest distance from the Sun (aphelion) is approximately 94.5 million miles.

Would you like further details or clarification?

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Here are some related questions for further exploration:

1. What is Kepler's First Law of planetary motion, and how does it apply to Earth's orbit?
2. How does the Earth's distance from the Sun affect the seasons?
3. How do we calculate the orbital period using Kepler's Third Law?
4. How does the eccentricity of other planets' orbits compare to Earth's?
5. How does the speed of the Earth vary in its elliptical orbit?

Tip: Eccentricity measures how "stretched out" an orbit is. The closer $e$ is to 0, the more circular the orbit.