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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.
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