Show that at infinity, gravitational potential energy becomes zero.

Explanation

To show that at infinity, gravitational potential energy becomes zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Gravitational Potential Energy**:
The gravitational potential energy (U) between two masses is given by the formula:
\[ U = -\frac{G M m}{r} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth (or the larger body),
- \( m \) is the mass of the smaller body,
- \( r \) is the distance from the center of the Earth to the smaller body.

2. **Consider the Scenario at Infinity**:
We need to evaluate the gravitational potential energy as the distance \( r \) approaches infinity.

3. **Substituting \( r \) with Infinity**:
Substitute \( r \) with infinity in the formula:
\[ U = -\frac{G M m}{\infty} \]

4. **Evaluate the Expression**:
We know that any finite number divided by infinity approaches zero:
\[ U = -\frac{G M m}{\infty} = 0 \]

5. **Conclusion**:
Therefore, we conclude that at infinity, the gravitational potential energy becomes zero:
\[ U = 0 \]