The acceleration due to gravity _____ with an increases in height and depth.

Answer

To answer the question regarding how the acceleration due to gravity changes with an increase in height and depth, we can break down the solution into clear steps:

### Step-by-Step Solution:

1. **Understanding Acceleration due to Gravity**:
The acceleration due to gravity, denoted as \( g \), is the gravitational force experienced by an object per unit mass at a given point in a gravitational field, particularly near the Earth's surface.

2. **Effect of Height on Gravity**:
- When an object is raised to a height \( h \) above the Earth's surface, the distance from the center of the Earth becomes \( r + h \), where \( r \) is the radius of the Earth.
- The formula for gravitational acceleration at height \( h \) is given by:
\[ g' = \frac{GM}{(r+h)^2} \]
- Since \( (r+h)^2 > r^2 \), it follows that \( g' < g \). Therefore, as height increases, the acceleration due to gravity decreases.

3. **Effect of Depth on Gravity**:
- When an object is taken to a depth \( h \) below the Earth's surface, the distance from the center of the Earth becomes \( r - h \).
- The gravitational acceleration at depth \( h \) is given by:
\[ g' = \frac{GM(r-h)}{r^3} \]
- Here, \( r - h < r \), which means that \( g' < g \). Thus, as depth increases, the acceleration due to gravity also decreases.

4. **Conclusion**:
- From both analyses, we conclude that the acceleration due to gravity decreases with an increase in height and depth.

### Final Answer:
The acceleration due to gravity **decreases** with an increase in height and depth.