A New Method to Derive an Empirical Lower Limit on the Mass Density of a UFO

Brief

The paper presents a single inequality, M > L/|v × a|, bounding an aerial object's minimum mass from three observables: infrared airglow luminosity (L), speed (v), and acceleration (a). When an object's radial velocity is negligible, the formula collapses further to M > 4πf/|(dθ/dt × d²θ/dt²)|, eliminating distance as a required input, a significant practical advantage for ground-based observatories. The Galileo Project's first Harvard observatory captures ~10⁵ objects per month using an all-sky 'Dalek' array of eight uncooled infrared cameras; triangulation with multiple Daleks separated by miles was planned within one month of submission to provide distance measurements. The proposed falsifiability criterion is concrete: any object with volume-averaged mass density exceeding Osmium (22.6 g/cm³, the densest terrestrial metal) would require exotic material and would be classified as anomalous.

Metadata

Category

Phenomenon

Venue

preprint (arXiv astro-ph)

Type

Preprint

Year

2024

Authors

Abraham Loeb

arXiv

2412.12142

Access

Open access

Length

65.4 K

Programs

Galileo Project

Instruments

Dalek all-sky infrared camera array (8 uncooled cameras, half-sphere mount)

Tags

UAP-physics, technosignature, infrared-detection, mass-density, observational-method

Key points

• Core inequality: M > L/|v × a|, object mass must exceed IR airglow luminosity divided by the product of speed and acceleration, bounding mass from measurable aerodynamic quantities alone.p.2
• Distance-independent special case: when radial velocity is negligible, M > 4πf/|(dθ/dt × d²θ/dt²)|, derived from angular velocity and angular acceleration of the sky-plane track and the measured IR flux.p.3
• Galileo Project Observatory 1 at Harvard collects data on ~10⁵ objects per month using eight uncooled all-sky infrared cameras arranged on a half-sphere ('Dalek' array).p.2
• Density anomaly threshold set at 22.6 g/cm³ (Osmium density); all human-made aircraft are described as orders of magnitude below this benchmark.p.3
• Objects exceeding Osmium density would require 'exotic material, not found on Earth,' making the threshold a hard, falsifiable filter for anomalous classification.p.3
• By summer 2025, three Galileo Project observatories across three U.S. states were projected to collect data on a few million objects per year, enabling statistical population-level application of the method.p.3
• A confounding factor is intrinsic IR emission from the object itself; resolving the object spatially is required to separate object emission from heated-air airglow.p.3

Verbatim

• “The object's mass must be larger than the infrared luminosity from heated air around it, divided by the product of the object's acceleration and speed.”

  p.2

• “A UFO with a higher mass density than Osmium would have to carry exotic material, not found on Earth.”

  p.3

• “With new quantitative data on infrared luminosities, velocities and accelerations of technological objects, it would be possible to check whether there are any UFOs denser than Osmium.”

  p.3

Most interesting

• The mass lower bound becomes fully distance-independent when an object's motion is primarily transverse to the line of sight, meaning existing single-station IR observatories can apply the filter without ranging hardware.
• Osmium at 22.6 g/cm³ is used as the falsifiability ceiling: every known human aircraft, including solid-metal components, sits orders of magnitude below it, making the threshold practically uncrossable by conventional technology.
• The Galileo Project's 'Dalek' camera array is described as eight uncooled infrared cameras on a half-sphere, the use of uncooled sensors makes large-scale deployment tractable but sets sensitivity limits that the paper does not quantify.
• The method requires the object to be spatially resolved in IR to separate self-emission from airglow; unresolved point sources would conflate the two and inflate the inferred luminosity, producing an artificially high mass lower bound.
• Loeb cites Zel'dovich & Raizer (1967), a Soviet-era shock-wave hydrodynamics text, as the foundational reference for the radiative efficiency of air friction, anchoring a 2024 UAP analysis in Cold War hypersonics literature.