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Chapter 12: Problem 17

Is the orbital speed of the Earth when it is closest to the Sun greater than, less than, or equal to the orbital speed when it is farthest from the Sun? Explain.

Short Answer

Expert verified
Answer: The orbital speed of Earth when it is closest to the Sun (perihelion) is greater than when it is farthest from the Sun (aphelion).

Step by step solution

01

Understand the concept of orbital speed

Orbital speed is the speed at which an object (in this case, the Earth) moves in its orbit around another object (the Sun). The primary factor affecting the orbital speed of an object is the gravitational force acting between the objects, which depends on their masses and the distance between their centers.
02

Apply Kepler's second law

Kepler's second law, also known as the Law of Equal Areas, states that a line joining a planet and its star sweeps out equal areas in equal periods of time. This law implies that when the distance between the planet and the star is reduced, the planet moves faster to cover the same area in the same time.
03

Determine the orbital speed at perihelion and aphelion

We need to find the Earth's orbital speed when it is closest to the Sun (perihelion) and when it is farthest from the Sun (aphelion). According to Kepler's second law, Earth moves faster at perihelion than at aphelion because of the different distances between Earth and Sun.
04

Compare the orbital speeds at perihelion and aphelion

Since Earth moves faster when it is closer to the Sun (perihelion), we can conclude that the orbital speed of Earth when it is closest to the Sun is greater than when it is farthest from the Sun.

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Most popular questions from this chapter

Eris, the largest dwarf planet known in the Solar System, has a radius \(R=1200 \mathrm{~km}\) and an acceleration due to gravity on its surface of magnitude \(g=0.77 \mathrm{~m} / \mathrm{s}^{2}\) a) Use these numbers to calculate the escape speed from the surface of Eris. b) If an object is fired directly upward from the surface of Eris with half of this escape speed, to what maximum height above the surface will the object rise? (Assume that Eris has no atmosphere and negligible rotation.

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Two 30.0 -kg masses are held at opposite corners of a square of sides \(20.0 \mathrm{~cm} .\) If one of the masses is released and allowed to fall toward the other mass, what is the acceleration of the first mass just as it is released? Assume that the only force acting on the mass is the gravitational force of the other mass. a) \(1.5 \cdot 10^{-8} \mathrm{~m} / \mathrm{s}^{2}\) b) \(2.5 \cdot 10^{-8} \mathrm{~m} / \mathrm{s}^{2}\) c) \(7.5 \cdot 10^{-8} \mathrm{~m} / \mathrm{s}^{2}\) d) \(3.7 \cdot 10^{-8} \mathrm{~m} / \mathrm{s}^{2}\)
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