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Chapter 4: Problem 14

What are the foci of an ellipse? If the Sun is at one focus of a planet's orbit, what is at the other focus?

Short Answer

Expert verified
The foci of an ellipse are two fixed points such that the sum of the distances from any point on the ellipse to the foci is constant. In a planet's orbit, the Sun is located at one of these foci. There is nothing significantly massive or notable at the other focus -- it is an empty spot in space.

Step by step solution

01

Definition of an ellipse

The first part of the solution is about the definition of an ellipse. An ellipse is a shape that is defined as the set of all points such that the sum of the distances from two fixed points (the foci) is constant for every point on the ellipse.
02

Identification of foci in a planetary orbit

Next, the Sun is at one of the foci of a planet's elliptical orbit. This is a given fact in the problem statement, which arises from Johann Kepler's first law of planetary motion.
03

Identification of the second focus

Finally, the other focus of a planet's elliptical orbit is an empty spot in space. There is nothing significantly massive or notable located at the other focus of a planet's orbit. The statement of the problem concludes from the fact that the center of mass of the planet-Sun system is nearer to the Sun, which results in the Sun being at one of the foci of the elliptical orbit, while the other focus does not contain any significant celestial body.

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Most popular questions from this chapter

Figure 4-21 shows the lunar module Eagle in orbit around the Moon after completing the first successful lunar landing in July 1969. (The photograph was taken from the command module Columbia, in which the astronauts returned to Earth.) The spacecraft orbited \(111 \mathrm{~km}\) above the surface of the Moon. Calculate the period of the spacecraft's orbit. See Appendix 3 for relevant data about the Moon.

How did the ancient Greeks explain why the Sun and Moon slowly change their positions relative to the background stars?

What is an epicycle? How is it important in Ptolemy's explanation of the retrograde motions of the planets?

What is the difference between the synodic period and the sidereal period of a planet?

What are Newton's three laws? Give an everyday example of each law.
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