Math Problem Statement

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?

Solution

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

q=a(1e)q = a(1 - e)

Where:

  • aa is the semi-major axis of the planet's orbit (in AU),
  • ee is the eccentricity of the orbit.

For this planet:

  • a=1.84AUa = 1.84 \, \text{AU},
  • e=0.0963e = 0.0963.

Substitute the values into the formula:

q=1.84×(10.0963)=1.84×0.9037q = 1.84 \times (1 - 0.0963) = 1.84 \times 0.9037

Now, let's calculate:

q=1.6628AUq = 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Astronomy
Elliptical Orbits
Planetary Motion

Formulas

Perihelion distance formula: q = a(1 - e)

Theorems

Kepler's First Law of Planetary Motion

Suitable Grade Level

Grades 9-12