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

Verified step by step guidance

1. Identify the given values: semimajor axis (a) = 5.91 \times 10^{12} \text{ m}, eccentricity (e) = 0.249.
2. Recall the formula for the closest distance (perihelion, r_{min}) from the sun in an elliptical orbit: r_{min} = a(1 - e).
3. Substitute the values of a and e into the formula for r_{min} to find the closest distance.
4. Recall the formula for the farthest distance (aphelion, r_{max}) from the sun in an elliptical orbit: r_{max} = a(1 + e).
5. Substitute the values of a and e into the formula for r_{max} to find the farthest distance.

Key Concepts

Elliptical Orbits

An elliptical orbit is a closed curve that describes the path of an object in space as it revolves around another object, such as a planet around the sun. The shape of the ellipse is defined by its semimajor axis and eccentricity, where the semimajor axis is the longest diameter of the ellipse, and eccentricity measures how much the orbit deviates from being circular.

Semimajor Axis

The semimajor axis is half of the longest diameter of an ellipse and is a crucial parameter in determining the size of the orbit. For Pluto, the semimajor axis of 5.91 * 10^12 m indicates the average distance from the sun over one complete orbit, serving as a reference point for calculating its closest and farthest distances.

Eccentricity

Eccentricity is a dimensionless parameter that quantifies the deviation of an orbit from a perfect circle. It ranges from 0 (circular orbit) to 1 (parabolic trajectory). For Pluto, an eccentricity of 0.249 indicates a moderately elongated orbit, which affects the variation in its distance from the sun throughout its orbit.