The Short Answer:

Yes, in a vacuum, all objects in free fall experience the same acceleration due to gravity, regardless of their mass or shape.

The Explanation:

* Newton's Law of Universal Gravitation: This law states that every object in the universe attracts every other object with a force that is:

* Directly proportional to the product of their masses: The more massive the objects, the stronger the gravitational attraction.

* Inversely proportional to the square of the distance between their centers: The farther apart the objects, the weaker the attraction.

* Free Fall: Free fall means an object is moving solely under the influence of gravity. Air resistance is ignored in this scenario.

* The Key Insight: While the force of gravity between the Earth and an object depends on the object's mass, the acceleration due to that force does not. Here's why:

* Force = Mass x Acceleration (F = ma)

* The force of gravity on an object is directly proportional to its mass.

* Acceleration is equal to the force divided by the mass.

* This means the mass cancels out when calculating acceleration, leaving a constant value for all objects in free fall.

In Summary:

The acceleration due to gravity near the Earth's surface is approximately 9.8 m/s², and this value holds true for all objects in free fall, regardless of their mass or shape (in a vacuum).

Important Note:

* In reality, air resistance plays a role in free fall. Heavier objects tend to be less affected by air resistance than lighter objects, which is why a feather and a hammer will fall at different rates in air.

* The acceleration due to gravity is not exactly the same everywhere on Earth. It varies slightly depending on factors like latitude and altitude.