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The question in the image asks:

**Exercise 9:**  
All planets revolve around the sun in elliptical orbits. Uranus's furthest distance from the sun is approximately \( 3.004 \times 10^9 \) km, and its closest distance is approximately \( 2.749 \times 10^9 \) km. Using this information, what is the average distance of Uranus from the sun?

### Solution:

The average distance of a planet in an elliptical orbit from the sun is the arithmetic mean of its closest (perihelion) and furthest (aphelion) distances from the sun. This can be calculated as follows:

\[
\text{Average distance} = \frac{\text{Closest distance} + \text{Furthest distance}}{2}
\]

Given:
- Closest distance = \( 2.749 \times 10^9 \) km
- Furthest distance = \( 3.004 \times 10^9 \) km

Now, let's calculate the average distance:

\[
\text{Average distance} = \frac{2.749 \times 10^9 + 3.004 \times 10^9}{2}
\]

\[
\text{Average distance} = \frac{5.753 \times 10^9}{2} = 2.8765 \times 10^9 \, \text{km}
\]

Thus, the average distance of Uranus from the sun is approximately **\( 2.8765 \times 10^9 \, \text{km} \)**.

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Would you like further details on this, or do you have any other questions?

### Related Questions:
1. How is the elliptical orbit of a planet determined mathematically?
2. How does the average distance affect the orbital period of a planet?
3. What is Kepler’s First Law of Planetary Motion regarding elliptical orbits?
4. How do we calculate the eccentricity of a planet's orbit?
5. How does the distance of Uranus compare to that of other planets in the solar system?

### Tip:
In elliptical orbits, the **semi-major axis** is often used to determine a planet's average distance from the Sun, and this can simplify orbital period calculations using Kepler's Third Law.

All planets revolve around the sun in elliptical orbits. Uranus's furthest distance from the sun is approximately 3.004 × 10^9 km, and its closest distance is approximately 2.749 × 10^9 km. Using this information, what is the average distance of Uranus from the sun?

Learn how to calculate the average distance of Uranus from the sun using its closest and furthest distances (3.004 × 10^9 km and 2.749 × 10^9 km). This problem involves key concepts like arithmetic mean and Kepler's laws. Suitable for high school students in Grades 9-12.

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