What was the first astronomical measurement which demonstrated that "the Earth is surrounded by vacuum"?

Question

The question Who was the first to realize that the Earth is surrounded by vacuum? was closed because some users felt it was answered by answers to a different question in an different SE site: Who was the first to postulate that space was a vacuum?

To me the distance between realize and postulate is astronomical!

That aside, I've asked a new question: What was the first astronomical measurement which demonstrated that "the Earth is surrounded by vacuum"?

By demonstrated I'm talking about a measurement that shows it is, or at least is likely to be the case that Earth is surrounded by vacuum. It should be something such that it could be presented as scientifically convincing evidence to other scientists of the time, unencumbered by non-scientific predispositions (e.g. religion, rivalry, philosophy...)

Answer 1

Torricelli, the inventor of the Mercury Barometer (~1644) argued that the height of the column of mercury was governed by atmospheric pressure (the "weight of the atmosphere" as he would have put it). He asserted that the space above the mercury in his tube was a vacuum, a totally anti-Aristotlean concept at that time.
To test this he enlisted the help of Blaise Pascal and Florin Perier in carrying one of two barometers up a mountain, the Puy de Dome in central France. His prediction was that the pressure at the top of the mountain would be less than at the base because of a lesser weight of air.
The experiment showed a drop in height (ie of pressure) and Torriceli himself concluded that the height of the atmosphere would be about 20km, above which there would be vacuum - the same vacuum as in the top of the barometer tube. The experiment was IMHO one of the greatest experiments in the history of physics. See for example https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3768090/

Answer 2

I would argue the famous Michelson-Morley experiment.

Luminiferous Aether

A bit of background first before getting into the experiment itself. It is quite easy to surmise, via Newton's laws of motion, that Earth should be in a vacuum, otherwise the constant drag of traveling through some medium must eventually cause us to crash into the Sun. Despite this Isaac Newton himself proposed the concept of a Luminiferous Aether which pervaded all of space and was the medium through which light propagated. Before this point there were various concepts of an "Aether" pervading space, but this, I believe, was the first truly scientific approach to the concept as a way of explaining physical phenomenon rather than a simple supposition of existence (such as the Greeks had done). The Luminiferous Aether was proposed as an almost magical concept to avoid numerous physical issues. I think Wikipedia describes it best.

The mechanical qualities of the aether had become more and more magical: it had to be a fluid in order to fill space, but one that was millions of times more rigid than steel in order to support the high frequencies of light waves. It also had to be massless and without viscosity, otherwise it would visibly affect the orbits of planets. Additionally it appeared it had to be completely transparent, non-dispersive, incompressible, and continuous at a very small scale.

The concept of the Luminiferous Aether was accepted on the authority of Newton and inability to explain the propogation of light otherwise.

Michelson-Morley Experiment (1887)

It wasn't until the Michelson-Morley Experiment that the Luminiferous Aether was seriously shot down. The goal of the Michelson-Morley Experiment was to find evidence of this Luminiferous Aether and the null result was very strong evidence that this Aether did not exist.

The experiment itself was set up to measure the speed of light through this Aether. The idea was that as the Earth moved through the Aether, it would cause a sort of "Aether wind" that would slow down the speed of light. Thus if one measured the speed of light in the direction of the wind and perpendicular to it, one should get different speeds. The Michelson-Morley experiment set up exactly this scenario and used increasingly accurate measurements to try and find this difference in speed. Ultimate no difference was found and the Aether was ruled out as a material which existed.

From that point onwards it was assumed that space was a vacuum, completely devoid of anything. Oddly enough, this assumption was so strong, that people didn't even really believe in the concept of the Solar Wind at first and were quite perplexed initially when they sent the first rockets into space with particle detectors that ended up detecting all sorts of charged particles in space. Regardless, I would say the Michelson-Morley experiment is the first time scientists had scientific evidence that space was a vacuum.