A New Method to Derive an Empirical Lower Limit on the Mass Density of a UFO
Any object moving through air radiates excess heat in the form of infrared air luminosity, L. The air luminosity is a fraction of the total power dissipated by the object’s speed, v, times the frictional force of air acting on the object. If the object accelerates, then this friction force must be smaller than the force provided by the engine which propels the object. The net force equals the object’s mass, M, times its acceleration, a.
In conclusion, one gets an unavoidable lower limit on the mass of an accelerating object. 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. In other words:
M > L/|v*a|.
This limit provides an elegant way to constrain the minimum mass of Unidentified Flying Objects (UFOs), also labeled as Unidentified Anomalous Phenomena (UAPs). To turn the inequality into an equality, one needs to know the detailed object shape and atmospheric conditions around the object.
The first Galileo Project Observatory at Harvard University collects data on 100,000 objects in the sky every month. A comprehensive description of its commissioning data on 500,000 objects was recently posted online. The data includes infrared images captured by an all-sky Dalek array of eight uncooled infrared cameras placed on half a sphere, resembling the head of the fictional robot character R2-D2 in the film Star Wars.
Within the coming month, the Galileo Project’s research team plans to employ multiple Daleks separated by a few miles, in order to measure distances to objects through the method of triangulation.
The heated air’s infrared flux, f, and distance, R, can be combined to infer the luminosity, L, through the relation:
L= 4*pi*f*R².
The angular velocity, (dq/dt), times the distance, R, provide the transverse component of the velocity vector, v, which can be combined with the time derivative of the distance, (dR/dt), to get the square of the total speed,
v²= [R(dq/dt)]² + (dR/dt)².
The time derivative of the velocity vector provides the acceleration vector, a=(dv/dt).
Remarkably, in the special case where the radial speed is negligible, |dR/dt| << R|dq/dt|, we find that the lower limit on the object’s mass is independent of distance,
M> 4*pi* f /|(dq/dt)*(d²q/dt²)| .
The physical size of the object can be derived as the product of its angular size times its distance, (Dq)*R. The minimum mass could then be used to derive the minimum mass per unit volume, or mass density, of the object.
If the measured velocity and acceleration of a technological object are outside the flight characteristics and performance envelopes of drones or airplanes, then the object would be classified by the Galileo Project’s research team as an outlier. In such a case, it would be interesting to calculate the minimum mass density of the object. If the result exceeds normal solid densities, then the object would qualify as anomalous, a UAP. Infrared emission by the object would be a source of confusion unless the object is resolved and the emission from it can be separated from the heated air around it.
All flying objects made by humans have a volume-averaged mass density which is orders of magnitude below 22.6 grams per cubic centimeter, the density of Osmium — which is the densest metal known on Earth. A UFO with a higher mass density than Osmium would have to carry exotic material, not found on Earth.
By summer 2025, there will be three Galileo Project observatories operating in three different states within the U.S., collecting data on a few million objects per year. With new quantitative data on infrared luminosities, velocities and accelerations, it would be possible to check whether there are any UFOs denser than Osmium.
Yesterday, I announced the launch of the Galileo Project Foundation, founded on the bold belief that humanity can no longer ignore the potential existence of extraterrestrial technological civilizations. Our extensive collection of data relies on donations, which can be processed through the new Galileo Foundation link. In reciprocity, The Galileo Project will share its data with the public.
Are there any UFOs denser than Osmium? If they exist, we might know it by summer 2025.
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For the related scientific paper, click here.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. The paperback edition of his new book, titled “Interstellar”, was published in August 2024.
