Chapter 7, Problem 101A

To determine

To Explore: The discovery of planets around other stars, the method used by Astronomers, the measurements taken by the Astronomers, and the way the Astronomers used the Kepler’s third law.

Explanation of Solution

Introduction:

Planets are visible in the solar system because they reflect the sunlight and are nearby. But,whenone inspects the other stars, it can be found that the quantity of light a planet reflects is a very minute fraction of the light emitted by its star.Therefore it is very difficult to detect the planets outside the solar system. Astronomers used the Kepler’s third law to detect the planets around other stars. In astronomy, Kepler’s laws of planetary motion are the empirical laws which describes the motion of planets around the star.

Kepler’s third law gives the relationship among the distances of planets from the star and their orbital periods. The square of the period is directly related to the cube of the distance.

Astronomers calculated the velocity of stars by assessing the Doppler shift of the stars light which is caused by their motion. They found that the velocity of the stars are extremely small because of the force of gravitation exerted by a massive planet on the stars. As the planets orbit the star, their velocity oscillates back and forth which allowed the astronomers to calculate the period of planets. The planets distance and mass were calculated from their velocity. By comparing the distances and periods of planets in the solar system with multiple planets and by using the Kepler’s third law of planetary motion astronomers measured the masses and distances of planets and stars.