Let's solve the problem using the given gravitational force formula:

$F = \frac{GMm}{r^2}$

Step 1: Write down the given values

• $G = 6.67 \times 10^{-11} \, \text{m}^3 \cdot \text{kg}^{-1} \cdot \text{s}^{-2}$
• $M = 3 \times 10^{30} \, \text{kg}$
• $m = 18 \times 10^{27} \, \text{kg}$
• $r = 1 \times 10^{11} \, \text{m}$

Step 2: Plug the values into the formula

$F = \frac{(6.67 \times 10^{-11})(3 \times 10^{30})(18 \times 10^{27})}{(1 \times 10^{11})^2}$

Step 3: Simplify the calculation

1. Multiply $G$, $M$, and $m$: $(6.67 \times 10^{-11}) \cdot (3 \times 10^{30}) \cdot (18 \times 10^{27}) = 6.67 \cdot 3 \cdot 18 \cdot 10^{-11 + 30 + 27}$ $= 360.18 \times 10^{46}$

2. Compute $r^2$: $r^2 = (1 \times 10^{11})^2 = 1^2 \times 10^{22} = 10^{22}$

3. Divide the results: $F = \frac{360.18 \times 10^{46}}{10^{22}} = 360.18 \times 10^{46 - 22} = 360.18 \times 10^{24}$

Step 4: Write the final answer in scientific notation

$F = 3.6018 \times 10^{26} \, \text{N}$

Final Answer:

The gravitational force between the two objects is approximately:

$\boxed{3.60 \times 10^{26} \, \text{N}}$

Would you like me to go over any step in more detail?

Related Questions:

1. What is the significance of the gravitational constant $G$ in physics?
2. How does the distance between two objects affect the gravitational force between them?
3. How would the force change if $r$ were doubled?
4. What are some real-life examples where this formula is applied?
5. How does gravitational force compare to other fundamental forces in nature?

Tip:

Always pay attention to units when solving physics problems—they ensure the calculations are correct!