Question

Select the correct answer.
What is the force of gravity between Earth (mass = 6.0 × 1024 kilograms) and Jupiter (mass = 1.901 × 1027 kilograms)? The distance between the two planets is about 7.5 × 1011 meters.
A.
2.027 × 1017 newtons
B.
7.10 × 1017 newtons
C.
1.352 × 1018 newtons
D.
1.014 × 1019 newtons
E.
1.54 × 1019 newtons

Answer 1

To calculate the gravitational force between two objects, we use Newton's law of universal gravitation, which is given by the formula:

\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]

where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant \((6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2)\),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two objects.

Plugging in the values:

- \( m_1 = 6.0 \times 10^{24} \, \text{kg} \) (mass of Earth),
- \( m_2 = 1.901 \times 10^{27} \, \text{kg} \) (mass of Jupiter),
- \( r = 7.5 \times 10^{11} \, \text{m} \) (distance between Earth and Jupiter).

Now substituting these values into the formula:

\[
F = \frac{(6.674 \times 10^{-11}) \cdot (6.0 \times 10^{24}) \cdot (1.901 \times 10^{27})}{(7.5 \times 10^{11})^2}
\]

Calculating \( (7.5 \times 10^{11})^2 \):

\[
(7.5 \times 10^{11})^2 = 56.25 \times 10^{22} = 5.625 \times 10^{23}
\]

Now, calculate the numerator:

\[
(6.674 \times 10^{-11}) \cdot (6.0 \times 10^{24}) \cdot (1.901 \times 10^{27}) = 6.674 \cdot 6.0 \cdot 1.901 \times 10^{(-11 + 24 + 27)}
\]

Calculating \( 6.674 \cdot 6.0 \cdot 1.901 \):

\[
= 6.674 \cdot 6.0 = 40.044
\]
\[
40.044 \cdot 1.901 \approx 76.072
\]

So, the numerator becomes:

\[
76.072 \times 10^{40}
\]

Now, substituting these back into the force equation:

\[
F = \frac{76.072 \times 10^{40}}{5.625 \times 10^{23}} \approx 13.53 \times 10^{17}
\]
\[
F \approx 1.353 \times 10^{18} \text{ newtons}
\]

This rounds to approximately \( 1.352 \times 10^{18} \, \text{newtons} \).

Thus, the correct answer is:

**C. 1.352 × 10^18 newtons**