A far away planet orbits its sun. If the planet has a mass of 5 x 1020 kg and the sun has a mass of 4 x 101 kg and they are 2 x 1012 meters away from each other, what is the gravitational force due to gravity between them?
A far away planet orbits its sun. If the planet has a mass of 5 x 1020 kg and the sun has a mass of 4 x 101 kg and they are 2 x 1012 meters away from each other, what is the gravitational force due to gravity between them?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Problem Statement:**
A far-away planet orbits its sun. If the planet has a mass of \( 5 \times 10^{20} \) kg and the sun has a mass of \( 4 \times 10^{31} \) kg and they are \( 2 \times 10^{12} \) meters away from each other, what is the gravitational force due to gravity between them?
---
**Explanation:**
To find the gravitational force between the planet and its sun, we use Newton's Law of Universal Gravitation, which states that the force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( G \) is the gravitational constant, \( G \approx 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \).
- \( m_1 \) and \( m_2 \) are the masses of the two objects.
- \( r \) is the distance between the centers of the two masses.
Given:
- \( m_1 = 5 \times 10^{20} \) kg (mass of the planet)
- \( m_2 = 4 \times 10^{31} \) kg (mass of the sun)
- \( r = 2 \times 10^{12} \) meters
Substitute these values into the formula:
\[ F = \frac{ (6.67430 \times 10^{-11}) \times (5 \times 10^{20}) \times (4 \times 10^{31})}{(2 \times 10^{12})^2} \]
Perform the calculations step-by-step:
1. Calculate the multiplication of the masses:
\[ 5 \times 10^{20} \times 4 \times 10^{31} = 20 \times 10^{51} \]
2. Calculate the square of the distance:
\[ (2 \times 10^{12})^2 = 4 \times 10^{24} \]
3. Compute the gravitational force:
\[ F = \frac{ (6.67430 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9fb32d1-3317-4767-a0fa-42a0fecf2dcd%2Fcec5b8f4-0973-4aa0-a808-0ec45dfea009%2F6ym9i73_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A far-away planet orbits its sun. If the planet has a mass of \( 5 \times 10^{20} \) kg and the sun has a mass of \( 4 \times 10^{31} \) kg and they are \( 2 \times 10^{12} \) meters away from each other, what is the gravitational force due to gravity between them?
---
**Explanation:**
To find the gravitational force between the planet and its sun, we use Newton's Law of Universal Gravitation, which states that the force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( G \) is the gravitational constant, \( G \approx 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \).
- \( m_1 \) and \( m_2 \) are the masses of the two objects.
- \( r \) is the distance between the centers of the two masses.
Given:
- \( m_1 = 5 \times 10^{20} \) kg (mass of the planet)
- \( m_2 = 4 \times 10^{31} \) kg (mass of the sun)
- \( r = 2 \times 10^{12} \) meters
Substitute these values into the formula:
\[ F = \frac{ (6.67430 \times 10^{-11}) \times (5 \times 10^{20}) \times (4 \times 10^{31})}{(2 \times 10^{12})^2} \]
Perform the calculations step-by-step:
1. Calculate the multiplication of the masses:
\[ 5 \times 10^{20} \times 4 \times 10^{31} = 20 \times 10^{51} \]
2. Calculate the square of the distance:
\[ (2 \times 10^{12})^2 = 4 \times 10^{24} \]
3. Compute the gravitational force:
\[ F = \frac{ (6.67430 \times
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