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I'm trying to figure out what are the different paths to indirect measurement of things that are out of experimenter reach; for instance, the age of the observable universe, or an estimation of the number of atoms in it.

I'd like to have something like a hypergraph, whose nodes are measurements, and whose hyperedges are physical laws within an accepted model; initial nodes are measurements that can be done on Earth, like the speed of light in vacuum, or the Cavendish experiment.

For this purpose, i'd be happy to assume prior knowledge of the theoretical models; i'm only interested in verifying these models, not discovering them from scratch. Because of this, the graph may not necessarily match the timeline of their respective discoveries; cycles in the hypergraph would serve as evidence in favor of the model.

Here's a couple of things I can think of, that may or may not be correct, so please do correct me if I'm wrong:

  • Theodolite measurements => radius of Earth
  • Foucault or Michelson experiments => speed of light in vacuum
  • Cavendish experiment => gravitational constant
  • Timing of free fall in vacuum => Earth gravity
  • gravitational constant + Earth gravity => mass of Earth (via Newton's universal gravitation law)
  • diurnal parallax (venus transit) => Earth-Sun distance
  • Earth-Sun distance + earth revolution time => mass of Sun (via Kepler's third law)
  • Earth-Sun distance => close stars distance (via stellar parallax)
  • Spectrography => frequency shift of a star
  • frequency shift of a star + speed of light => relative velocity of star (via Doppler effect)

From there, how do I get to the size and age of the universe?

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    $\begingroup$ It seems that you are interested in mapping out logical interconnections between various laws and surmises from experiments within the current system of physical theories. I do not see how this is about history though. It might be a project for Physics SE if they want to take it up. $\endgroup$
    – Conifold
    Nov 20 '21 at 1:54
  • $\begingroup$ @Conifold I initially considered posting it to Physics, but in the end, I thought it was more closely related to history of science, no? $\endgroup$
    – b0fh
    Nov 20 '21 at 9:10
  • $\begingroup$ I guess there are two aspects: (1) which experiment(s) historically lead to a particular conclusion about the universe, and (2) which measurements are currently our best evidence for it. (2) is physics, (1) is history of science. At first sight I'm not sure if (1) and (2) are often the same or often different for each aspect. Anyway, I'd say this question has a strong hsm angle. $\endgroup$ Nov 20 '21 at 10:43

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