Question

question 18 (multiple choice worth 3 points) ou 04two stars, star 1 and star 2, are at almost equal distances from earth. the table below shows the masses of the two stars.

name of star	mass of star (in million solar masses)
star 2	3.59

which of these statements is most likely correct about the stars?

• earth exerts almost equal gravitation force on both the stars.
• earth exerts greater gravitation force on star 2 than on star 1.
• star 1 attracts star 2 with a greater gravitational force than star 2 attracts star 1.
• star 2 attracts star 1 with a greater gravitational force than star 1 attracts star 2.

Explanation:

1. For the gravitational force between Earth and the stars: The formula for gravitational force is \( F = G\frac{Mm}{r^{2}} \). Since the two stars are at almost equal distances from Earth (\( r \) is almost equal), and \( G \) is a constant, the force depends on the mass of the star (\( m \)) and Earth's mass (\( M \)). Star 1 has a mass of 3.61 million solar masses, Star 2 has 3.59 million solar masses. The masses are almost equal, so Earth exerts almost equal gravitational force on both stars.
2. For the gravitational force between the two stars: By Newton's third law, the gravitational force that Star 1 exerts on Star 2 is equal in magnitude and opposite in direction to the force that Star 2 exerts on Star 1. So the statements about one star attracting the other with a greater force are incorrect. Also, Earth's mass is much smaller than the stars' masses, and the distance between the stars is not given, but the key here is the comparison of Earth's force on the stars (due to similar distances and similar star masses) and the mutual force between stars (action - reaction). So the correct statement is "Earth exerts almost equal gravitational force on both the stars."

Answer:

A. Earth exerts almost equal gravitational force on both the stars.