1. Gravity's Dependence on Distance:
* Newton's Law of Universal Gravitation: The force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
* As you move further from Earth's center: The gravitational force (and hence acceleration) decreases.
2. Why We Can Usually Treat it as Constant:
* Small Distances: Within a few hundred miles of the Earth's surface, the change in distance from the Earth's center is relatively small compared to the Earth's radius (around 4000 miles).
* Negligible Change in Acceleration: The decrease in gravitational acceleration is so slight over these distances that it's often considered negligible for most practical purposes.
3. Example:
* If you drop an object from a height of 100 miles, the gravitational acceleration at the top will be slightly less than at the surface. However, the difference is small enough that it won't significantly affect the object's descent time or final velocity.
4. When it Matters:
* High Altitude Objects: For objects falling from very high altitudes (like satellites), the change in gravitational acceleration becomes significant and cannot be ignored.
* Precise Measurements: In highly precise scientific measurements, the variation in gravitational acceleration needs to be considered.
In Summary:
While free fall acceleration is not perfectly constant, the variation is small enough over short distances near the Earth's surface that we can often treat it as constant. It's important to remember this is an approximation, and the variation becomes more significant as the distance from Earth increases.
