Skip to ContentGo to accessibility page
OpenStax Logo
Astronomy

Figuring for Yourself

AstronomyFiguring for Yourself

Figuring for Yourself

22.

When astronomers found the first giant planets with orbits of only a few days, they did not know whether those planets were gaseous and liquid like Jupiter or rocky like Mercury. The observations of HD 209458 settled this question because observations of the transit of the star by this planet made it possible to determine the radius of the planet. Use the data given in the text to estimate the density of this planet, and then use that information to explain why it must be a gas giant.

23.

An exoplanetary system has two known planets. Planet X orbits in 290 days and Planet Y orbits in 145 days. Which planet is closest to its host star? If the star has the same mass as the Sun, what is the semi-major axis of the orbits for Planets X and Y?

24.

Kepler’s third law says that the orbital period (in years) is proportional to the square root of the cube of the mean distance (in AU) from the Sun (P ∝ a1.5). For mean distances from 0.1 to 32 AU, calculate and plot a curve showing the expected Keplerian period. For each planet in our solar system, look up the mean distance from the Sun in AU and the orbital period in years and overplot these data on the theoretical Keplerian curve.

25.

Calculate the transit depth for an M dwarf star that is 0.3 times the radius of the Sun with a gas giant planet the size of Jupiter.

26.

If a transit depth of 0.00001 can be detected with the Kepler spacecraft, what is the smallest planet that could be detected around a 0.3 Rsun M dwarf star?

27.

What fraction of gas giant planets seems to have inflated radii?

PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/astronomy/pages/1-introduction

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/astronomy/pages/1-introduction

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Jan 28, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.