Question

In recent years, astronomers have found planets orbiting nearby stars that are quite different from planets in our solar system. Kepler-39b has a diameter that is 1.2 times that of Jupiter (rJupiter = 6.99 × 10⁷ m), but a mass that is 18 times that of Jupiter (mJupiter = 1.90 × 10²⁷ kg). What is the diameter of Kepler-39b?

Answer 1

To find the diameter of Kepler-39b, use the relationship between the diameter and mass of a planet. The diameter of Kepler-39b is approximately 2.3 × 10⁸ meters.

Step-by-step explanation:

To find the diameter of Kepler-39b, we can use the relationship between the diameter and the mass of a planet. The density of a planet is approximately the same as the density of water, so we can assume that the volume of Kepler-39b is the same as its mass. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. Since the diameter is twice the radius, the formula can be rewritten as V = (4/3)π(d/2)³, where d is the diameter. We can equate this to the mass of Kepler-39b, which is 18 times that of Jupiter. Setting up and solving the equation, we have: (4/3)π(d/2)³ = 18 * (4/3)π(6.99 × 10⁷)³. Simplifying and solving for d, we find that the diameter of Kepler-39b is approximately 2.3 × 10⁸ meters.