Introduction

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Searching for Exoplanets

In 1992 the first planet outside our solar system was discovered by astronomers. Such planets, called extrasolar planets or exoplanets, are of great interest to astronomers in the search for potential extraterrestrial life forms. The first exoplanets discovered were large planets similar in size to Jupiter and Neptune. Larger planets are easier to detect but less likely to have an atmosphere hospitable for life. Since the light reflected by a planet is much fainter than the light emitted from the star it revolves around, most exoplanets cannot be observed directly. Instead, exoplanets are discovered through the use of indirect methods such as radial velocity or the Doppler method. A star with a planet will move in a small orbit in response to the planet’s gravity. This creates a slight fluctuation in the radial velocity, the speed at which the star moves toward or away from earth. Due to the Doppler effect, these fluctuations can be measured, indicating the existence of an exoplanet.

In certain cases the exoplanet passes between Earth and the star once every orbit. This is called a transit. Since the planet is cooler than the star, the transit causes the star’s brightness to decrease slightly while it is in front of the star. With very careful observations, this decrease in brightness can be recorded, even by amateur astronomers. The transit method has also been used from space by NASA’s Kepler satellite to identify more than 3000 candidate exoplanets.

CHAPTER 12 PROJECT

In the Chapter Project on p. 861, we examine the transit method for discovering exoplanets and investigate the main source of error when it is used with telescopes on the ground.

In Chapter 1, we discussed finding the limit of a function \(y=f(x) \), a function of one variable, and investigated where such a function is continuous. In Chapters 2 and 3, we defined the derivative of a function \(y=f(x) ,\) investigated properties of derivatives, and developed methods for finding derivatives that eliminated the need to actively use the definition. In this chapter, we extend these concepts to functions of more than one variable. Instead of a derivative, we define partial derivatives of such functions. And instead of a single chain rule, we discover functions of more than one variable have a variety of chain rules.