Why Does Gravity Decrease When We Go Inside the Earth?

In this detailed exploration, we will uncover why gravity decreases as we travel deeper into the Earth. Gravity, a fundamental force that affects everything on Earth, changes its nature as we delve beneath its surface. This article will not only explain the underlying principles but also delve into the mathematical models that support these concepts.

Gravitational Force Inside the Earth

To understand why gravity decreases as we move from the Earth's surface to its core, we must first comprehend how gravity behaves with respect to mass distribution. Gravity is undeniably a fascinating force, and its variations at different depths offer us a profound insight into the nature of our planet.

Shell Theorem

The Shell Theorem is a crucial principle in understanding gravitational forces within a spherical mass. According to this theorem, a uniform spherical shell of mass exerts a net gravitational force of zero on an object located inside it. This means that as you descend into the Earth, the mass of the Earth above you does not contribute to the gravitational attraction you feel.

Effective Mass

When you are at a distance r from the center of the Earth, only the mass of the Earth that is within this radius contributes to the gravitational force you experience. The mass outside this radius exerts no net force on you, a principle known as the shell theorem.

Decreasing Gravitational Force

As you go deeper into the Earth, the amount of mass pulling you down decreases. This is because the mass above you does not contribute to the gravitational force. Consequently, the gravitational force you feel reduces as you move closer to the center of the Earth. This is a key concept that underpins the behavior of gravity within the Earth's layers.

Mathematical Explanation

The gravitational force F at a distance r from the center of a spherical mass M is given by:

[ F frac{G cdot M_{r} cdot m}{r^2} ]

In this equation:

G is the gravitational constant Mr is the mass of the Earth enclosed within radius r m is the mass of the object experiencing the gravitational force

As you go deeper, Mr decreases because the mass above you does not contribute to the gravitational force. Consequently, the gravitational force you feel decreases.

At the Center of the Earth

At the very center of the Earth, the gravitational force would be zero because there is no mass beneath you to exert a pull. The center of the Earth is theoretically a point where there is equal attraction in all directions, with the vector sum of these forces being zero.

Conclusion

In summary, gravity decreases inside the Earth because the shell theorem explains why the mass above you does not exert gravitational force, and only the mass beneath you contributes to the gravitational pull, which decreases as you go deeper. This results in a reduction of gravitational force as you move toward the center of the Earth.

Note that it is a common misconception that you would be pulled apart. In reality, half of the Earth would not pull on your left arm and ignore the right one. The forces are directional and balanced.