# Proof: Heavier objects fall faster than lighter objects even in a perfect vacuum

- **Generated:** 2026-03-28
- **Verdict:** DISPROVED
- **Audit trail:** [proof_audit.md](proof_audit.md) | [proof.py](proof.py)

## Key Findings

- **Newton's Second Law proves acceleration is mass-independent:** For any object, F = mg and a = F/m = g. The mass cancels algebraically, so all objects experience the same gravitational acceleration regardless of mass (A1).
- **NASA confirms all objects free fall with the same acceleration** in a vacuum, regardless of size, shape, or weight (B1).
- **The Apollo 15 hammer-feather experiment** demonstrated on the Moon that a 1.32 kg hammer and a 0.03 kg feather fell at the same rate when dropped simultaneously in the lunar vacuum (B2).
- **The Weak Equivalence Principle** — a cornerstone of general relativity — states that the acceleration of a test particle in a gravitational field is independent of its properties, including its rest mass (B3).
- **No credible scientific source supports the claim.** Aristotle's intuition that heavier objects fall faster was based on observations in air and has been thoroughly disproved.

## Claim Interpretation

**Natural language claim:** "Heavier objects fall faster than lighter objects even in a perfect vacuum."

**Formal interpretation:** The claim asserts that heavier objects have greater free-fall acceleration than lighter objects in a vacuum. In Newtonian mechanics, gravitational force F = mg and acceleration a = F/m = g, so acceleration is independent of mass. The claim requires a_heavy > a_light, but physics shows a_heavy = a_light = g. This is a disproof: we seek 3 or more authoritative sources confirming that all objects fall at the same rate in a vacuum regardless of mass.

## Evidence Summary

| ID | Fact | Verified |
|----|------|----------|
| A1 | Newtonian derivation: acceleration = g, independent of mass | Computed: a1 == a2 == g (mass cancels for any m) |
| B1 | NASA Glenn: all objects free fall with same acceleration | Yes |
| B2 | NASA Science: Apollo 15 hammer-feather drop | Yes |
| B3 | Wikipedia: Weak Equivalence Principle | Yes |

## Proof Logic

The disproof operates on two independent lines of reasoning:

**Mathematical derivation (A1):** From Newton's Second Law, the gravitational force on an object of mass m is F = mg. Applying F = ma gives mg = ma, so a = g. The mass m cancels completely. This symbolic derivation (confirmed via sympy) shows that for any two masses m1 and m2, both experience the same acceleration g. Therefore, a heavier object does not fall faster.

**Empirical confirmation (B1, B2, B3):** Three independent authoritative sources confirm this result:
- NASA Glenn Research Center states: "all objects, regardless of size or shape or weight, free fall with the same acceleration" (B1).
- NASA's record of the Apollo 15 mission documents that Commander David Scott dropped a hammer and a feather on the Moon and they fell at the same rate (B2).
- The Weak Equivalence Principle, a cornerstone of Einstein's general relativity, formally states that "the acceleration of a test particle is independent of its properties, including its rest mass" (B3).

All 3 empirical sources were verified against their live pages. The mathematical derivation and empirical evidence are fully independent lines of reasoning that converge on the same conclusion: the claim is false.

## Counter-Evidence Search

**Is there any credible scientific evidence that heavier objects fall faster in a vacuum?** Searched for supporting evidence across physics forums, NASA, University of Illinois, UCSB ScienceLine, and Britannica. All sources unanimously confirm objects fall at the same rate in a vacuum. The only nuance is the two-body problem: a heavier object attracts the Earth very slightly more (reducing the separation distance marginally faster), but this effect is negligible (~10^-25 for everyday objects) and does not contradict the equivalence principle.

**Did Aristotle's theory have any experimental support?** Aristotle's claim that heavier objects fall faster was based on everyday observations in air (where drag affects lighter objects more). It was never validated for vacuum conditions and was definitively disproved by Galileo's experiments (c. 1590) and the Apollo 15 demonstration (1971).

## Conclusion

**Verdict: DISPROVED.** The claim that heavier objects fall faster than lighter objects in a perfect vacuum is false. Newton's Second Law mathematically proves that gravitational acceleration is independent of mass (a = g for all objects), and this is confirmed by three verified authoritative sources: NASA Glenn Research Center (B1), the Apollo 15 hammer-feather experiment (B2), and the Weak Equivalence Principle (B3). All citations were fully verified. No credible counter-evidence was found.

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Generated by [proof-engine](https://github.com/yaniv-golan/proof-engine) v0.10.0 on 2026-03-28.
