the orbit of the earth around the sun is elliptical in shape with sun at a focus.the semi major axis is of length 92.9 million miles and eccentricity is 0.017.find how close the earth gets to sun and the greatest possible distance between the earth and the sun

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.

The orbit of the Earth around the Sun is elliptical in shape with the Sun at a focus. The semi-major axis is of length 92.9 million miles and eccentricity is 0.017. Find how close the Earth gets to the Sun and the greatest possible distance between the Earth and the Sun.

Explore how to calculate the closest (perihelion) and farthest (aphelion) distances between the Earth and the Sun in its elliptical orbit. Learn about key formulas, such as r_min = a(1 - e) and r_max = a(1 + e), with real data on the semi-major axis of 92.9 million miles and eccentricity of 0.017. Suitable for Grades 9-12.

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