Forgive me for the naive question. Besides taking pictures of tons of objects in space, what kinds of revolutionary discoveries were made as a result of data from Hubble? Did Hubble shed light on any open problems or did it lead astronomers to conclude the existence of something that they had not known to have existed before?
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1$\begingroup$ The American Astronomical Society had a press conference about the 25 year history of the Hubble Space Telescope January this year. They use a very very bad media player, you have to click "Seminar for Science Writers: HST @ 25", you cannot download it, it loads very slowly and if you happen to click anywhere it will immediately reset. But the talks are very informative. $\endgroup$– LocalFluffJan 27, 2015 at 16:59
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Wikipedia has some handy-dandy discoveries. I don't know if they're "revolutionary" per se, but they're pretty interesting.
Hubble measured the distance to some Cepheid variables with very good accuracy. Cepheids are variable stars that periodically oscillate between larger and more luminous states and smaller and more dimmer states. They are used as "standard candles" in astronomy because their luminosity and periods can be used to easily calculate how far away they are. In fact, Edwin Hubble used Cepheids to establish Hubble's law, $v=H_0D$. It states how fast objects are moving away from us ($v$) as a function of distance ($D$). $H_0$ is Hubble's constant. It was originally written as $H$, but it was determined that it isn't actually a constant at all! $H_0$ is used as the value in the present era.
Anyway, the measurements from Hubble were used to establish the distance to the Cepheid variables and their recessional velocities. With that, $H_0$ could be determined more accurately than ever. Freedman et al. published a paper detailing the results. The team found that $H_0 = 72 \pm 8 \text{ kms}^{-1}\text{ Mpc}^{-1}$.
Hubble had a tiny role in the Supernova Cosmology Project, as described by Gerson Goldhaber in this paper. Under Saul Perlmutter's leadership, the team gathered more evidence that the universe is expanding at an accelerating rate, which earned Perlmutter a Nobel Prize in 2011. Two members of the High-Z Supernova Search Team shared the prize with Perlmutter, and they, too, briefly used the telescope. Hubble played a minor role, as Goldhaber explains, but it was still important: looking at supernovae to determine their light curves, data which was then used in the final results.
I'm not sure I'd describe any of Hubble's other achievements as "revolutionary", though it has an amazing track record. NASA discusses some of Hubble's successes here, including the discovery of black holes and supermassive black holes in other galaxies; see this paper and this paper. There's also a decent page here that discusses those discoveries.
One last field is planet formation, one area of study that's been hot recently. This is one of the better links from that NASA page.
answered Jan 27, 2015 at 17:41