The dwarf planet Pluto has an elliptical orbit with a semimajor axis of 5.91 × 10¹² m and eccentricity 0.249. During Pluto's orbit around the sun, what are its closest and farthest distances from the sun?

Verified step by step guidance

1. Understand that the closest distance from the sun in an elliptical orbit is called the perihelion, and the farthest distance is called the aphelion.
2. The formula for the perihelion distance \( r_{p} \) is given by \( r_{p} = a(1 - e) \), where \( a \) is the semimajor axis and \( e \) is the eccentricity.
3. Substitute the given values into the perihelion formula: \( r_{p} = 5.91 \times 10^{12} \text{ m} \times (1 - 0.249) \).
4. The formula for the aphelion distance \( r_{a} \) is given by \( r_{a} = a(1 + e) \).
5. Substitute the given values into the aphelion formula: \( r_{a} = 5.91 \times 10^{12} \text{ m} \times (1 + 0.249) \).

Key Concepts

Elliptical Orbits

Elliptical orbits are the paths followed by celestial bodies, like planets, around a star, characterized by an elongated circle or oval shape. The shape of an ellipse is defined by its semimajor axis, which is the longest diameter, and its eccentricity, which measures the deviation from a perfect circle. Understanding elliptical orbits is crucial for calculating distances at various points in the orbit.

Semimajor Axis

The semimajor axis is half of the longest diameter of an ellipse and is a fundamental parameter in describing the size of an orbit. In celestial mechanics, it represents the average distance of a planet from the star it orbits. For Pluto, the semimajor axis is 5.91 * 10^12 meters, which helps determine its orbital characteristics, including the closest and farthest points from the Sun.

Orbital Eccentricity

Orbital eccentricity quantifies how much an orbit deviates from being circular, with values ranging from 0 (a perfect circle) to 1 (a parabolic trajectory). An eccentricity of 0.249 for Pluto indicates a moderately elliptical orbit. This value is essential for calculating the perihelion (closest point) and aphelion (farthest point) distances from the Sun, using the semimajor axis and eccentricity.