What Happens If You Fall Through Earth

This lesson explores how gravity changes beneath Earth's surface. This covers why it decreases as you move towards the center and how this leads to a phenomenon known as gravity train motion.

What We Will Cover

1. Why gravitational force becomes zero inside a hollow spherical shell
2. How Newton's Shell Theorem applies to Earth's interior
3. How gravity changes as you travel from the Earth's surface to the core
4. The derivation of gravitational force inside a uniformly dense Earth
5. How simple harmonic motion emerges in a gravity tunnel
6. Why a trip through the Earth would take about 42 minutes

Key Concepts Explained

• Gravity inside Earth
• Shell Theorem
• Simple harmonic motion in gravity
• Uniform density model
• Gravity train motion
• Gravitational force inside Earth
• Mass distribution in Earth
• Restoring force and SHM

Understanding how gravity behaves inside Earth is crucial not only for conceptual physics but also for mastering gravitation topics in AP, IB, JEE, and NEET exams. The lesson connects Newtonian gravitation with real-world applications and idealized models, revealing elegant insights into motion under gravity.

Prerequisite or Follow-Up Lessons

• Newton’s Law of Gravitation
• Gravitational Potential Energy and Fields

Why every straight tunnel gives the same 42-minute trip

• Uniform-density + Shell Theorem → linear force
  For a constant-density Earth, only the mass inside radius r matters.
  Mᵢ(r) = 4 π ρ r³ / 3 ⇒ g(r) = G Mᵢ / r² = 4 π G ρ r / 3.
  Thus F = –m (4 π G ρ / 3) r = –k r, identical to a spring force.
• Simple Harmonic Motion with fixed clock-rate
  The “spring constant” k = 4 π G ρ / 3 is a property of Earth alone, so the natural angular frequency ω = √(k/m) = √(4 π G ρ / 3) is the same no matter how far you fall.
  Period of one full oscillation: T = 2 π/ω ≈ 84.5 min ⇒ surface-to-surface time = T / 2 ≈ 42 min.
• Any tunnel = a tilted SHO track
  Draw a chord tunnel that misses the center by angle θ.
  • Radial distance: r.
  • Distance along tunnel: s = r sin θ.
  • Component of gravity along tunnel: aₛ = g(r) sin θ = –(4 π G ρ / 3) r sin θ.
  Replace r sin θ by s → aₛ = –(4 π G ρ / 3) s = –ω² s.
  The same ω appears, so motion along any chord is still simple harmonic with the identical period.
• Path length cancels out
  A longer tunnel (diameter) gives a larger amplitude sₘₐₓ, but the object also accelerates harder.
  A shorter tunnel (shallow chord) has a smaller sₘₐₓ and weaker component of gravity.
  Both effects adjust so that T stays unchanged—exactly like different-length pendulums swinging with the same frequency if g were proportional to length.
• Bottom line
  Restore force ∝ distance to center, not to track length.
  Therefore every straight tunnel through a uniform Earth behaves like the same spring, giving the universal 42-minute one-way trip

FAQs About Gravitational Force Inside the Earth

Q1. Does gravity increase or decrease as you get closer to the core?
A1. Gravity first increases slightly but then decreases linearly as you go deeper toward Earth’s core. That’s because only the mass within your radius pulls you inward, and that mass gets smaller as you move in. Eventually, gravity becomes zero at the center.

Q2. What is the pressure and gravity at the center of the earth
A2. At the very center of Earth, gravitational force is zero due to perfect spherical symmetry — all pulls cancel. But pressure is maximum because the weight of all overlying layers compresses the inner core.

Q3. What kind of force is there in exact middle of earth?
A3. There is no net gravitational force at the center of Earth. All surrounding mass pulls equally in all directions, so the forces cancel completely.

Q4. Why does gravity 'increase' as you go deeper into the Earth?
A4. It increases at first because you're getting closer to Earth's mass. But as you go deeper, outer layers no longer pull you (Shell Theorem), and the remaining mass inside your radius decreases — so gravity falls, reaching zero at the core.

Q5. If you went closer toward the center of the earth, would there be less gravity
A5. Yes — gravity would gradually become weaker as you moved inward. The force is proportional to the distance from the center, assuming Earth has uniform density.

Q6. Gravity inside a planet
A6. Inside a uniform sphere (like an ideal planet), gravitational force is not constant — it increases with distance from the center up to the surface, then decreases with height above it. This is due to the Shell Theorem, which says only mass enclosed within your position matters.

Q7. What would be the magnitude of the gravitational field anywhere inside a hollow sphere?
A7. Zero. According to Newton’s Shell Theorem, a uniform hollow spherical shell exerts no net gravitational force anywhere inside it.

Q8. What happens to gravity in the center of the earth?
A8. Gravity is strongest near the surface, then drops to zero at the center. Forces from all directions cancel each other at the center point. So, you wouldn't float, but rather oscillate back and forth if dropped into a tunnel.

Q10. Is there less gravity the higher up you go?
A10. Yes — gravity decreases with altitude, following the inverse-square law. But going deeper inside Earth, it decreases linearly, assuming constant density. Both directions move you away from the zone of maximum gravitational pull — the surface.