Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine which statement is most likely correct about the gravitational interaction between Star 1 and Star 2, we need to consider their masses.
Given:
- Mass of Star 1 = 3.61 million solar masses
- Mass of Star 2 = 11.73 million solar masses
According to Newton's law of universal gravitation, the gravitational force [tex]\( F \)[/tex] between two objects is given by:
[tex]\[ F = G \frac{{m_1 \cdot m_2}}{{r^2}} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant,
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects,
- [tex]\( r \)[/tex] is the distance between their centers.
Since the distance [tex]\( r \)[/tex] between Star 1 and Star 2 is assumed to be equal in both directions and is a common factor, we can compare the forces solely based on their masses.
### Analysis:
Let's analyze the statements one by one:
1. Earth exerts a greater gravitational force on Star 1 than on Star 2.
- This statement suggests that the gravitational force between Earth and Star 1 is greater than between Earth and Star 2.
- Given that the mass of Star 2 is significantly greater than the mass of Star 1, Earth would exert a greater gravitational force on Star 2 due to its larger mass.
- Thus, this statement is incorrect.
2. Earth exerts a greater gravitational force on Star 2 than on Star 1.
- Since the Earth exerts gravitational force proportional to the mass of the star, and Star 2 has a greater mass than Star 1, Earth would indeed exert a greater gravitational force on Star 2.
- This statement is plausible but not the focus of our comparison between Star 1 and Star 2 themselves.
3. Star 1 attracts Star 2 with a greater gravitational force than Star 2 attracts Star 1.
- This statement suggests that Star 1, despite its smaller mass, attracts Star 2 more strongly.
- Based on Newton's third law of motion, forces between two objects are equal and opposite.
- However, in comparing masses directly, since the mass of Star 1 is smaller, it cannot exert more force than Star 2.
- Therefore, this statement is incorrect.
4. Star 2 attracts Star 1 with a greater gravitational force than Star 1 attracts Star 2
- Given that Star 2 has a much larger mass (11.73 million solar masses) compared to Star 1 (3.61 million solar masses), Star 2 would exert a significantly larger gravitational force compared to Star 1.
- Thus, Star 2 exerts a greater gravitational force on Star 1 than vice versa.
- Therefore, this statement is correct.
### Conclusion:
The correct statement is:
Star 2 attracts Star 1 with a greater gravitational force than Star 1 attracts Star 2.
Given:
- Mass of Star 1 = 3.61 million solar masses
- Mass of Star 2 = 11.73 million solar masses
According to Newton's law of universal gravitation, the gravitational force [tex]\( F \)[/tex] between two objects is given by:
[tex]\[ F = G \frac{{m_1 \cdot m_2}}{{r^2}} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant,
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two objects,
- [tex]\( r \)[/tex] is the distance between their centers.
Since the distance [tex]\( r \)[/tex] between Star 1 and Star 2 is assumed to be equal in both directions and is a common factor, we can compare the forces solely based on their masses.
### Analysis:
Let's analyze the statements one by one:
1. Earth exerts a greater gravitational force on Star 1 than on Star 2.
- This statement suggests that the gravitational force between Earth and Star 1 is greater than between Earth and Star 2.
- Given that the mass of Star 2 is significantly greater than the mass of Star 1, Earth would exert a greater gravitational force on Star 2 due to its larger mass.
- Thus, this statement is incorrect.
2. Earth exerts a greater gravitational force on Star 2 than on Star 1.
- Since the Earth exerts gravitational force proportional to the mass of the star, and Star 2 has a greater mass than Star 1, Earth would indeed exert a greater gravitational force on Star 2.
- This statement is plausible but not the focus of our comparison between Star 1 and Star 2 themselves.
3. Star 1 attracts Star 2 with a greater gravitational force than Star 2 attracts Star 1.
- This statement suggests that Star 1, despite its smaller mass, attracts Star 2 more strongly.
- Based on Newton's third law of motion, forces between two objects are equal and opposite.
- However, in comparing masses directly, since the mass of Star 1 is smaller, it cannot exert more force than Star 2.
- Therefore, this statement is incorrect.
4. Star 2 attracts Star 1 with a greater gravitational force than Star 1 attracts Star 2
- Given that Star 2 has a much larger mass (11.73 million solar masses) compared to Star 1 (3.61 million solar masses), Star 2 would exert a significantly larger gravitational force compared to Star 1.
- Thus, Star 2 exerts a greater gravitational force on Star 1 than vice versa.
- Therefore, this statement is correct.
### Conclusion:
The correct statement is:
Star 2 attracts Star 1 with a greater gravitational force than Star 1 attracts Star 2.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
