On earth, two parts of a space probe weigh 11 000 N and 3400 N. These parts are separated by a center-to-center distance of 12 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space, far from any other objects.

Options

A. `1.7xx10^(-6)` N
B. `3.4xx10^(-7)N`
C. `1.8xx10^(-7)` N
D. `3.6xx10^(-5)` N

Answer

To find the gravitational force that each part of the space probe exerts on the other, we can follow these steps:

### Step 1: Calculate the masses of the two parts
The weight of an object (W) is related to its mass (m) by the equation:
\[ W = m \cdot g \]
where \( g \) is the acceleration due to gravity. On Earth, \( g \approx 9.8 \, \text{m/s}^2 \).

For the first part (weight = 11,000 N):
\[ m_1 = \frac{W_1}{g} = \frac{11000 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 1122.45 \, \text{kg} \]

For the second part (weight = 3,400 N):
\[ m_2 = \frac{W_2}{g} = \frac{3400 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 346.94 \, \text{kg} \]

### Step 2: Use the gravitational force formula
The gravitational force (F) between two masses is given by Newton's law of universal gravitation:
\[ F = G \frac{m_1 \cdot m_2}{r^2} \]
where:
- \( G \) is the gravitational constant, \( G \approx 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)
- \( r \) is the distance between the centers of the two masses, which is given as 12 m.

### Step 3: Substitute the values into the formula
Now, substituting the values we have:
\[ F = 6.67 \times 10^{-11} \frac{(1122.45 \, \text{kg}) \cdot (346.94 \, \text{kg})}{(12 \, \text{m})^2} \]

### Step 4: Calculate the force
Calculating the product of the masses:
\[ m_1 \cdot m_2 = 1122.45 \cdot 346.94 \approx 389,040.53 \, \text{kg}^2 \]

Calculating \( r^2 \):
\[ r^2 = 12^2 = 144 \, \text{m}^2 \]

Now substituting these values back into the force equation:
\[ F = 6.67 \times 10^{-11} \frac{389040.53}{144} \]
\[ F \approx 6.67 \times 10^{-11} \cdot 2705.28 \approx 1.80 \times 10^{-7} \, \text{N} \]

### Final Answer
The magnitude of the gravitational force that each part exerts on the other is approximately:
\[ F \approx 1.80 \times 10^{-7} \, \text{N} \]

---