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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

A planet with a mass of \(7.00 \cdot 10^{21} \mathrm{~kg}\) is in a circular orbit around a star with a mass of \(2.00 \cdot 10^{30} \mathrm{~kg} .\) The planet has an orbital radius of \(3.00 \cdot 10^{10} \mathrm{~m}\). a) What is the linear orbital velocity of the planet? b) What is the period of the planet's orbit? c) What is the total mechanical energy of the planet?

The distances from the Sun at perihelion and aphelion for Pluto are \(4410 \cdot 10^{6} \mathrm{~km}\) and \(7360 \cdot 10^{6} \mathrm{~km},\) respectively. What is the ratio of Pluto's orbital speed around the Sun at perihelion to that at aphelion?

Where the International Space Station orbits, the gravitational acceleration is just \(11.4 \%\) less than its value on the surface of the Earth. Nevertheless, astronauts in the space station float. Why is this so?

For the satellite in Solved Problem 12.2, orbiting the Earth at a distance of \(3.75 R_{\mathrm{E}}\) with a speed of \(4.08 \mathrm{~km} / \mathrm{s}\) with what speed would the satellite hit the Earth's surface if somehow it suddenly stopped and fell to Earth? Ignore air resistance.

What is the magnitude of the free-fall acceleration of a ball (mass \(m\) ) due to the Earth's gravity at an altitude of \(2 R\), where \(R\) is the radius of the Earth?
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