One way to determine the mass of a distant star (or planet) is to observe the motion of its planets (or moons). If exoplanet CSN-2021 is found to have a small moon orbiting at a radius of 7.77 x 10* m with a period of 23.1 days, what is the mass of CSN-2021? (a) 1.90 x 1033 kg (b) 6.97 x 1025 kg (c) 2.54 x 1023 kg (d) 4.49 x 1010 kg 9. If the radius of exoplanet CSN-2021 is 2.97 × 107 m, find the acceleration due to gravity near its surface.
One way to determine the mass of a distant star (or planet) is to observe the motion of its planets (or moons). If exoplanet CSN-2021 is found to have a small moon orbiting at a radius of 7.77 x 10* m with a period of 23.1 days, what is the mass of CSN-2021? (a) 1.90 x 1033 kg (b) 6.97 x 1025 kg (c) 2.54 x 1023 kg (d) 4.49 x 1010 kg 9. If the radius of exoplanet CSN-2021 is 2.97 × 107 m, find the acceleration due to gravity near its surface.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
Hello, I need help with this question, along with the statement below it, hat goes along with the question.
![---
### Problem 9:
One way to determine the mass of a distant star (or planet) is to observe the motion of its planets (or moons). If exoplanet CSN-2021 is found to have a small moon orbiting at a radius of \(7.77 \times 10^8\) m with a period of 23.1 days, what is the mass of CSN-2021?
#### Options:
- (a) \(1.90 \times 10^{33}\) kg
- (b) \(6.97 \times 10^{25}\) kg
- (c) \(2.54 \times 10^{23}\) kg
- (d) \(4.49 \times 10^{10}\) kg
If the radius of exoplanet CSN-2021 is \(2.97 \times 10^7\) m, find the acceleration due to gravity near its surface.
### Explanation:
This problem involves using the gravitational properties and orbital dynamics to estimate the mass of a celestial body. Students need to apply their knowledge of orbital mechanics, specifically the use of Kepler's laws and the gravitational formula, to solve for the exoplanet's mass.
To find the mass of the exoplanet, they might need to use the formula:
\[ M = \frac{4\pi^2r^3}{GT^2} \]
where:
- \( M \) is the mass of the exoplanet,
- \( r \) is the orbital radius,
- \( T \) is the orbital period, and
- \( G \) is the gravitational constant.
Additionally, to find the acceleration due to gravity at the surface of the exoplanet, students can use the formula:
\[ g = \frac{GM}{r^2} \]
where:
- \( g \) is the acceleration due to gravity,
- \( M \) is the mass of the exoplanet,
- \( r \) is the radius of the exoplanet, and
- \( G \) is the gravitational constant.
These calculations help in understanding the gravitational influence of celestial objects and are essential for astrophysical studies and space missions planning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3524539-73d7-4b1e-9607-006acd5ee568%2F32436496-7907-402e-8fa5-6882590ceb8b%2F9l7gy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Problem 9:
One way to determine the mass of a distant star (or planet) is to observe the motion of its planets (or moons). If exoplanet CSN-2021 is found to have a small moon orbiting at a radius of \(7.77 \times 10^8\) m with a period of 23.1 days, what is the mass of CSN-2021?
#### Options:
- (a) \(1.90 \times 10^{33}\) kg
- (b) \(6.97 \times 10^{25}\) kg
- (c) \(2.54 \times 10^{23}\) kg
- (d) \(4.49 \times 10^{10}\) kg
If the radius of exoplanet CSN-2021 is \(2.97 \times 10^7\) m, find the acceleration due to gravity near its surface.
### Explanation:
This problem involves using the gravitational properties and orbital dynamics to estimate the mass of a celestial body. Students need to apply their knowledge of orbital mechanics, specifically the use of Kepler's laws and the gravitational formula, to solve for the exoplanet's mass.
To find the mass of the exoplanet, they might need to use the formula:
\[ M = \frac{4\pi^2r^3}{GT^2} \]
where:
- \( M \) is the mass of the exoplanet,
- \( r \) is the orbital radius,
- \( T \) is the orbital period, and
- \( G \) is the gravitational constant.
Additionally, to find the acceleration due to gravity at the surface of the exoplanet, students can use the formula:
\[ g = \frac{GM}{r^2} \]
where:
- \( g \) is the acceleration due to gravity,
- \( M \) is the mass of the exoplanet,
- \( r \) is the radius of the exoplanet, and
- \( G \) is the gravitational constant.
These calculations help in understanding the gravitational influence of celestial objects and are essential for astrophysical studies and space missions planning.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![Physics for Scientists and Engineers](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Lecture- Tutorials for Introductory Astronomy](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
![College Physics: A Strategic Approach (4th Editio…](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON