Answer :
To determine the force of gravity between the two spaceships, we can use Newton's law of universal gravitation, which is given by:
[tex]\[ F = G \frac{m_1 \cdot m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between the two masses.
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2\)[/tex]).
- [tex]\( m_1 \)[/tex] is the mass of the first spaceship ([tex]\(300,000 \, \text{kg}\)[/tex]).
- [tex]\( m_2 \)[/tex] is the mass of the second spaceship ([tex]\(300,000 \, \text{kg}\)[/tex]).
- [tex]\( r \)[/tex] is the distance between the centers of the two masses ([tex]\(250 \, \text{m}\)[/tex]).
Now, substitute the given values into the equation:
[tex]\[ F = (6.67 \times 10^{-11}) \frac{300,000 \times 300,000}{250^2} \][/tex]
First, calculate the product of the masses:
[tex]\[ 300,000 \times 300,000 = 90,000,000,000 \, (\text{kg}^2) \][/tex]
Next, calculate the square of the distance:
[tex]\[ 250^2 = 62,500 \, (\text{m}^2) \][/tex]
Now, divide the product of the masses by the square of the distance:
[tex]\[ \frac{90,000,000,000}{62,500} = 1,440,000 \, (\text{kg}^2 / \text{m}^2) \][/tex]
Finally, multiply by the gravitational constant [tex]\( G \)[/tex]:
[tex]\[ F = 6.67 \times 10^{-11} \times 1,440,000 \][/tex]
This results in:
[tex]\[ F = 9.6048 \times 10^{-5} \, \text{N} \][/tex]
Therefore, the force of gravity between them is:
[tex]\[ \boxed{9.6 \times 10^{-5} \, \text{N}} \][/tex]
So the correct answer is:
C. [tex]\( 9.6 \times 10^{-5} \, \text{N} \)[/tex]
[tex]\[ F = G \frac{m_1 \cdot m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force between the two masses.
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2\)[/tex]).
- [tex]\( m_1 \)[/tex] is the mass of the first spaceship ([tex]\(300,000 \, \text{kg}\)[/tex]).
- [tex]\( m_2 \)[/tex] is the mass of the second spaceship ([tex]\(300,000 \, \text{kg}\)[/tex]).
- [tex]\( r \)[/tex] is the distance between the centers of the two masses ([tex]\(250 \, \text{m}\)[/tex]).
Now, substitute the given values into the equation:
[tex]\[ F = (6.67 \times 10^{-11}) \frac{300,000 \times 300,000}{250^2} \][/tex]
First, calculate the product of the masses:
[tex]\[ 300,000 \times 300,000 = 90,000,000,000 \, (\text{kg}^2) \][/tex]
Next, calculate the square of the distance:
[tex]\[ 250^2 = 62,500 \, (\text{m}^2) \][/tex]
Now, divide the product of the masses by the square of the distance:
[tex]\[ \frac{90,000,000,000}{62,500} = 1,440,000 \, (\text{kg}^2 / \text{m}^2) \][/tex]
Finally, multiply by the gravitational constant [tex]\( G \)[/tex]:
[tex]\[ F = 6.67 \times 10^{-11} \times 1,440,000 \][/tex]
This results in:
[tex]\[ F = 9.6048 \times 10^{-5} \, \text{N} \][/tex]
Therefore, the force of gravity between them is:
[tex]\[ \boxed{9.6 \times 10^{-5} \, \text{N}} \][/tex]
So the correct answer is:
C. [tex]\( 9.6 \times 10^{-5} \, \text{N} \)[/tex]
