Calculate the maximum aphelion distance of a planet with an orbital period of 100 years.
Calculate the maximum aphelion distance of a planet with an orbital period of 100 years.
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![**Transcription:**
"Calculate the maximum aphelion distance of a planet with an orbital period of 100 years."
**Explanation:**
This text poses a problem related to celestial mechanics, specifically focusing on the aphelion distance of a planet. The aphelion is the point in the orbit of a planet, asteroid, or comet at which it is farthest from the sun. The goal is to calculate this distance given the planet's orbital period, which is the time it takes for the planet to complete one full orbit around the sun.
In celestial mechanics, this calculation can be approached using Kepler's third law, which relates the orbital period of a planet to its average distance from the sun. The law is usually stated as:
\[ P^2 = a^3 \]
where:
- \( P \) is the orbital period in years,
- \( a \) is the semi-major axis of the orbit in astronomical units (AU).
Given:
\[ P = 100 \text{ years} \]
You would need to solve for \( a \) and then determine the maximum aphelion distance considering the orbit's eccentricity, if provided. If the orbit is nearly circular, the aphelion distance would be approximately equal to the semi-major axis. For more eccentric orbits, additional information about the eccentricity would be necessary for precise calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fdfc26a-e6d8-4dfd-b2bf-654dccb4509d%2F692976a2-fc25-4c4b-9a5b-a9f792912c9d%2Ftfncreo_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription:**
"Calculate the maximum aphelion distance of a planet with an orbital period of 100 years."
**Explanation:**
This text poses a problem related to celestial mechanics, specifically focusing on the aphelion distance of a planet. The aphelion is the point in the orbit of a planet, asteroid, or comet at which it is farthest from the sun. The goal is to calculate this distance given the planet's orbital period, which is the time it takes for the planet to complete one full orbit around the sun.
In celestial mechanics, this calculation can be approached using Kepler's third law, which relates the orbital period of a planet to its average distance from the sun. The law is usually stated as:
\[ P^2 = a^3 \]
where:
- \( P \) is the orbital period in years,
- \( a \) is the semi-major axis of the orbit in astronomical units (AU).
Given:
\[ P = 100 \text{ years} \]
You would need to solve for \( a \) and then determine the maximum aphelion distance considering the orbit's eccentricity, if provided. If the orbit is nearly circular, the aphelion distance would be approximately equal to the semi-major axis. For more eccentric orbits, additional information about the eccentricity would be necessary for precise calculations.
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