What If an Object Plowed Straight Through the Earth?
So you’re wondering what it would take for a projectile to smash into Earth’s surface, tunnel right through the planet’s core, and pop out the other side like a slightly bruised but still‑spherical billiard ball. Let’s break it down—because science is fun, but also because someone might actually try this someday and we want them to be prepared.
1. Speed: More Than Just “Really Fast”
To shove your object all the way through 12,700 km of rock, metal, and molten iron, you first have to outrun gravity, air resistance, and the rock’s sheer compressive strength.
- Escape Velocity (~11 km/s): That’s just to leave Earth—not enough.
- Straight‑through Requirement: You need enough energy so that
\(\frac12 m v^2 \;\gtrsim\; \int_{0}^{R} \sigma_{\mathrm{eff}}(r)\,A(r)\,\mathrm{d}r\)
where:
- (m) is the projectile’s mass
- (v) is its entry speed
- $(\sigma_{\mathrm{eff}}(r))$ is the local “smash‑through” stress of rock/metal at depth (r)
- (A(r)) is your object’s cross‑sectional area at that depth
- Rough Number:
Assuming an average resistive stress of $(\sigma \approx 10^9)$ Pa (a gigapascal; typical for rock under extreme strain) and a constant cross‑section (A = 1) m² over a path (d = R = 6.37\times10^6) m,
\(d = \frac{m v^2}{2 A \sigma}
\quad\Longrightarrow\quad
v \sim \sqrt{\frac{2 A \sigma d}{m}}.\)
For (m=1) kg and (A=1) m²,
\(v \approx \sqrt{\frac{2\cdot1\cdot10^9\ \mathrm{Pa}\cdot6.37\times10^6\ \mathrm{m}}{1\ \mathrm{kg}}}
\approx 1.1\times10^8\ \mathrm{m/s},\)
which is over a third the speed of light: so we are squarely in relativistic territory.
2. Heating: Not Your Friendly Glow
At tens of millions of meters per second, you will be blasting through rock like a bullet through air. The shock‑heated material around you will reach tens of thousands of kelvin—turning rock into plasma and creating a mini‑supernova ahead of you.
- Radiation Losses: You’ll bleed energy as X‑rays and high‑energy particles; by the time you’re halfway through, your projectile might have lost most of its mass to vaporization.
- Self‑Shielding: A solid tungsten core might survive a bit longer than steel or rock—but not much.
3. Gravity & Trajectory: The Curvy Tunnel Problem
Even if you could maintain your shape, Earth’s gravity would tug you off‑axis. A truly straight shot needs:
- Perfect Aim. Any deviation and you spiral into the mantle.
- Infinite Stiffness of Path. You’d need something akin to a frictionless, gravity‑compensating rail from one side to the other.
Otherwise you just end up in a very eccentric orbit, “tunneling” partly but ultimately slingshotting around the core and then hitting the surface again somewhere else.
4. The Other Side: Pop Goes the Weasel
Assuming you somehow manage the above, emerging on the opposite hemisphere at cosmic speed, you’d:
- Exit Velocity ≈ Entry Velocity. (Energy in, energy out, minus losses.)
- Airblast. At Mach > 1000, you’d create a supersonic shock wave that sterilizes half a continent in seconds.
- Impact Crater. Behind you, a trough half‑molten from the frictional heat.
And then, because physics loves symmetry, you’d fall back toward Earth again—unless you’re past escape velocity (which you’re not, since you lost energy smashing rocks).
5. The TL;DR “What You’d Need”
- Speed: ∼0.3 c (tens of millions of km/s).
- Material: Something denser and stronger than anything we know—maybe neutron‑star debris?
- Energy Source: Roughly the kinetic energy of a small asteroid (∼10¹⁷ J for a 1 kg object at 0.3 c).
- Infrastructure: A vacuum‑sealed, gravity‑nullifying tunnel, 12,700 km long.
- Plan C: Build a tunnel, then take the train.
Conclusion:
In practice, colliding with Earth and exiting the other side as an intact object is firmly in the realm of science fiction (or very advanced alien tech). You’d either vaporize yourself and the planet’s core long before getting through, or you’d need to cheat the laws of physics. But hey—now you know exactly how outlandish your tunnel‑through‑Earth scheme really is. Enjoy your hypothetical deep‑Earth commute!