To determine the gravitational force between the two asteroids using Newton's law of gravitation, we will follow these steps:
1. Identify the given values:
- Mass of the first asteroid, \( m_1 = 3.45 \times 10^3 \, \text{kg} \)
- Mass of the second asteroid, \( m_2 = 6.06 \times 10^4 \, \text{kg} \)
- Distance between the asteroids, \( r = 7200 \, \text{m} \)
- Gravitational constant, \( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)
2. Write down Newton's law of gravitation formula:
[tex]\[
F_{\text{gravity}} = \frac{G m_1 m_2}{r^2}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
F_{\text{gravity}} = \frac{(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2) \times (3.45 \times 10^3 \, \text{kg}) \times (6.06 \times 10^4 \, \text{kg})}{(7200 \, \text{m})^2}
\][/tex]
4. Calculations step-by-step:
a. Calculate the product of \( G \) and the masses:
[tex]\[
(6.67 \times 10^{-11}) \times (3.45 \times 10^3) \times (6.06 \times 10^4)
\][/tex]
After calculating this, you will get an intermediate result.
b. Calculate the square of the distance:
[tex]\[
(7200)^2 = 51840000
\][/tex]
5. Divide the product from step 4a by the result from step 4b to find \( F_{\text{gravity}} \):
After performing the division, the result is:
[tex]\[
F_{\text{gravity}} \approx 2.690001736111111 \times 10^{-10} \, \text{N}
\][/tex]
6. Compare this result with the given choices:
- A. \( 4.03 \, \text{N} \)
- B. \( 2.69 \times 10^{-10} \, \text{N} \)
- C. \( 3.38 \times 10^{32} \, \text{N} \)
- D. \( 1.93 \times 10^{-6} \, \text{N} \)
The closest and correct answer is:
B. \( 2.69 \times 10^{-10} \, \text{N} \)
Hence, the gravitational force between the two asteroids is [tex]\( 2.69 \times 10^{-10} \, \text{N} \)[/tex].
