Question

An Extrasolar Planet In July of 1999 a planet was reported to be orbiting the Sun-like star lota Horologii with a period of 320 days. Find the radius of the planet's orbit, assuming that lota Horologii has the same mass as the Sun. (This planet is presumably similar to Jupiter, but it may have large, rocky moons that enjoy a relatively pleasant climate.)

Name: Problem 27, Chapter 12: Physics
Uploaded: 2020-03-17T01:07:12-08:00
Duration: 2 min 47 s
Channel: Andy Chen
Description: An Extrasolar Planet In July of 1999 a planet was reported to be orbiting the Sun-like star lota Horologii with a period of 320 days. Find the radius of the planet's orbit, assuming that lota Horologii has the same mass as the Sun. (This planet is presumably similar to Jupiter, but it may have large, rocky moons that enjoy a relatively pleasant climate.)

   An Extrasolar Planet In July of 1999 a planet was reported to be orbiting the Sun-like star lota Horologii with a period of 320 days. Find the radius of the planet's orbit, assuming that lota Horologii has the same mass as the Sun. (This planet is presumably similar to Jupiter, but it may have large, rocky moons that enjoy a relatively pleasant climate.)

Physics

James S. Walker 5th Edition

Chapter 12, Problem 27

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Solved by Expert Andy Chen

03/17/2020

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Mathematically, this can be written as: \[T = \sqrt{\frac{2\pi}{GM}} r^{3/2}\] Show more…

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An Extrasolar Planet In July of 1999 a planet was reported to be orbiting the Sun-like star lota Horologii with a period of 320 days. Find the radius of the planet's orbit, assuming that lota Horologii has the same mass as the Sun. (This planet is presumably similar to Jupiter, but it may have large, rocky moons that enjoy a relatively pleasant climate.)

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Key Concepts

Kepler's Third Law

Kepler's Third Law establishes a proportional relationship between the orbital period of a body and the size of its orbit, specifically stating that the square of the period is proportional to the cube of the semi?major axis. This law is critical in astrophysics for determining the orbital radius of a planet when its period is known, especially when the central star has a mass similar to that of the Sun, allowing the use of simplified units such as years and astronomical units.

Orbital Mechanics and Gravitational Dynamics

Orbital mechanics, built upon Newton’s laws of motion and universal gravitation, describes how celestial bodies move under the influence of gravitational forces. By balancing gravitational attraction with the motion of the orbiting body, one can derive relationships such as the one in Kepler’s Third Law, which is essential for calculating orbital parameters in planetary systems, including extrasolar systems.

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