A new planet in orbit about the Sun has a semi-major axis of 1.84 AU and an eccentricity of 0.0963. What is the perihelion distance of the new planet in AU? 

The perihelion distance (\(q\)) of a planet is the closest distance between the planet and the Sun. It can be calculated using the formula:

\[
q = a(1 - e)
\]

Where:
- \(a\) is the semi-major axis of the planet's orbit (in AU),
- \(e\) is the eccentricity of the orbit.

For this planet:
- \(a = 1.84 \, \text{AU}\),
- \(e = 0.0963\).

Substitute the values into the formula:

\[
q = 1.84 \times (1 - 0.0963) = 1.84 \times 0.9037
\]

Now, let's calculate:

\[
q = 1.6628 \, \text{AU}
\]

Thus, the perihelion distance of the new planet is approximately **1.6628 AU**.

Would you like further details or have any other questions?

---

Here are 5 related questions:
1. What is the aphelion distance of the planet?
2. How does the eccentricity affect the planet's orbit?
3. How can we determine the orbital period of the planet?
4. What is the significance of the semi-major axis in Kepler's laws of planetary motion?
5. How does perihelion distance affect the climate of planets like Earth?

**Tip:** The perihelion distance decreases as the eccentricity increases, meaning the orbit becomes more elliptical.

A new planet in orbit about the Sun has a semi-major axis of 1.84 AU and an eccentricity of 0.0963. What is the perihelion distance of the new planet in AU?

Learn how to calculate the perihelion distance of a planet with a semi-major axis of 1.84 AU and an eccentricity of 0.0963. This problem demonstrates the application of Kepler's laws of planetary motion and the perihelion distance formula, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation