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Sometimes controlled experiments are prohibitively difficult, so researchers resort to natural experiments. Natural experiments take advantage of predictable natural changes in simple systems to measure the effect of that change on some phenomenon.
Much of astronomy relies on experiments of this type. It is clearly impractical, when trying to prove the hypothesis "suns are collapsed clouds of hydrogen", to start out with a giant cloud of hydrogen, and then perform the experiment of waiting a few billion years for it to form a sun. However, by observing various clouds of hydrogen in various states of collapse, and other implications of the hypothesis (for example, the presence of various spectral emissions from the light of stars), we can collect the experimental data we require to support the hypothesis.
An early example of this type of experiment was the first verification in the 1600s that light does not travel from place to place instantaneously, but instead has a measurable speed. Observation of the appearance of the moons of Jupiter were slightly delayed when Jupiter was far from Earth, as opposed to when Jupiter was closer to Earth; and this phenomenon was used to demonstrate that the time delays were consistent with a measurable speed of light.
Quasi-experiments are very much like controlled experiments except that they lack probabilistic equivalency between groups. These types of experiments often arise in the area of medicine where, for ethical reasons, it is not possible to create a truly controlled group. For example, one would not want to deny all forms of treatment for a life-threatening disease from one group of patients to evaluate the effectiveness of another treatment on a different group of patients. Researchers compensate for this with complicated statistical methods. See also quasi-empirical methods.
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