Predict/Calculate Halley's Comet Halley's comet, which...

Predict/Calculate Halley's Comet Halley's comet, which passes around the Sun every 76 years, has an elliptical orbit. When closest to the Sun (perihelion) it is at a distance of $8.823 \times 10^{10} \mathrm{m}$ and moves with a speed of 54.6 $\mathrm{km} / \mathrm{s}$ . The greatest distance between Halley's comet and the Sun (aphelion) is $6.152 \times 10^{12} \mathrm{m}$ . (a) Is the speed of Halley's comet greater than or less than 54.6 $\mathrm{km} / \mathrm{s}$ when it is at aphelion? Explain. (b) Calculate its speed at aphelion.

Predict/Calculate Halley's Comet Halley's comet, which passes around the Sun every 76 years, has an elliptical orbit. When closest to the Sun (perihelion) it is at a distance of $8.823 \times 10^{10} \mathrm{m}$ and moves with a speed of 54.6 $\mathrm{km} / \mathrm{s}$ . The greatest distance between Halley's comet and the Sun (aphelion) is $6.152 \times 10^{12} \mathrm{m}$ . (a) Is the
speed of Halley's comet greater than or less than 54.6 $\mathrm{km} / \mathrm{s}$ when it
is at aphelion? Explain. (b) Calculate its speed at aphelion.

Key Concepts

Elliptical Orbits

An elliptical orbit is a closed, oval-shaped trajectory followed by an object under the influence of a central gravitational force. Unlike circular orbits, the distance between the orbiting body and the central mass changes continuously, which leads to variations in speed along different parts of the orbit.

Perihelion and Aphelion

These are the two extreme points in an elliptical orbit. The perihelion is the point at which the orbiting object is closest to the central mass, while the aphelion is where it is farthest away. The differences in these distances are critical for understanding how the object's speed changes throughout its orbit.

Conservation of Angular Momentum

In an orbit where external torques are negligible, the angular momentum of the orbiting body remains constant. This principle means that when the orbiting object is closer to the central mass (at the perihelion), its speed is higher, and when it is farther away (at the aphelion), its speed is lower. The relation r*v = constant illustrates this dependency.

Vis-viva Equation

The vis-viva equation provides a direct relationship between the speed of an object in orbit, its current distance from the central body, and the semi-major axis of its orbit. Derived from energy conservation, it is particularly useful for calculating the orbital speed at any given point along an elliptical path.

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