Which of these pairs of bodies would have the strongest gravitational force between them?

Options

A. The earth and the sun
B. The earth and a human
C. The earth and a mouse
D. The earth and an elephant

Answer

To determine which pair of bodies would have the strongest gravitational force between them, we can follow these steps:

### Step 1: Understand Newton's Law of Gravitation
Newton's law of gravitation states that the gravitational force (F) between two bodies 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,
- \( m_1 \) and \( m_2 \) are the masses of the two bodies,
- \( r \) is the distance between the centers of the two bodies.

### Step 2: Identify the Masses in Each Option
We have four options to consider:
1. Earth and Sun
2. Earth and Human
3. Earth and Mouse
4. Earth and Elephant

In each case, the mass of the Earth (m1) is constant. The mass of the second body (m2) differs in each option:
- Sun has a significantly larger mass compared to Earth.
- Human, mouse, and elephant have much smaller masses compared to Earth.

### Step 3: Analyze the Masses
- **Earth and Sun**: The mass of the Sun is approximately \( 1.989 \times 10^{30} \) kg.
- **Earth and Human**: The mass of an average human is about \( 70 \) kg.
- **Earth and Mouse**: The mass of a mouse is about \( 0.025 \) kg.
- **Earth and Elephant**: The mass of an elephant is about \( 6000 \) kg.

### Step 4: Compare the Gravitational Forces
According to the formula, the gravitational force is directly proportional to the product of the masses. Therefore, the pair with the largest mass (m2) will produce the strongest gravitational force:
- The Sun (mass ~ \( 1.989 \times 10^{30} \) kg) will exert a much stronger gravitational force on Earth than the human, mouse, or elephant.

### Step 5: Conclusion
Thus, the pair of bodies that would have the strongest gravitational force between them is:
**Option 1: Earth and Sun.**