To determine the gravitational force between Earth and Venus, we need to use Newton's Law of Universal Gravitation, which is defined by the equation:
[tex]\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the force of gravity,
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.673 \times 10^{-11} \)[/tex] N m[tex]\(^2\)[/tex] / kg[tex]\(^2\)[/tex]),
- [tex]\( m_1 \)[/tex] is the mass of the first object (Earth, [tex]\(6.0 \times 10^{24}\)[/tex] kg),
- [tex]\( m_2 \)[/tex] is the mass of the second object (Venus, [tex]\(4.88 \times 10^{24}\)[/tex] kg),
- [tex]\( r \)[/tex] is the distance between the centers of the two objects ([tex]\(3.8 \times 10^{10}\)[/tex] meters).
Plugging the values into the equation, we get:
[tex]\[ F = \frac{(6.673 \times 10^{-11}) \cdot (6.0 \times 10^{24}) \cdot (4.88 \times 10^{24})}{(3.8 \times 10^{10})^2} \][/tex]
Performing the calculations step-by-step:
1. Multiply the masses of Earth and Venus:
[tex]\[ 6.0 \times 10^{24} \times 4.88 \times 10^{24} = 2.928 \times 10^{49} \][/tex]
2. Multiply this result by the gravitational constant:
[tex]\[ 6.673 \times 10^{-11} \times 2.928 \times 10^{49} = 1.953624 \times 10^{39} \][/tex]
3. Square the distance between Earth and Venus:
[tex]\[ (3.8 \times 10^{10})^2 = 1.444 \times 10^{21} \][/tex]
4. Finally, divide the product from step 2 by the result from step 3:
[tex]\[ \frac{1.953624 \times 10^{39}}{1.444 \times 10^{21}} = 1.3530847645429363 \times 10^{18} \][/tex]
So, the gravitational force between Earth and Venus is:
[tex]\[ F = 1.353 \times 10^{18} \text{ newtons} \][/tex]
Therefore, the correct answer is:
C. [tex]\( 13.52 \times 10^{17} \)[/tex] newtons
