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 () of a planet is the closest distance between the planet and the Sun. It can be calculated using the formula:
Where:
- is the semi-major axis of the planet's orbit (in AU),
- is the eccentricity of the orbit.
For this planet:
- ,
- .
Substitute the values into the formula:
Now, let's calculate:
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:
- What is the aphelion distance of the planet?
- How does the eccentricity affect the planet's orbit?
- How can we determine the orbital period of the planet?
- What is the significance of the semi-major axis in Kepler's laws of planetary motion?
- 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.
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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
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