Graviton Technology is the pinnacle of technological research in the game. Due to its unusual cost (0 metal, 0 crystal, and 0 deuterium; 300,000 energy), its construction time is 1 second. It is a required technology for the construction of Deathstars.
The only realistic way to get the energy needed is from a very large number of Solar Satellites, which makes you an extremely desirable target (due to the potential debris field rich in crystal). Ideally, you want to research it at a (remote) location where you are unlikely to be attacked. Be wary of other players watching your fleet score increase, monitoring your solar satellite numbers on the scoreboard, or stumbling across your research location.
To calculate how many satellites, you need:
Planets closer to the sun will require fewer satellites because they produce more power. Make sure you have enough resources available to build all the satelites at once. You can reduce the time needed to produce these satellites with Nanite Factories and having higher levels of Shipyards.
Once you have carried out the research, you will want to have an alliance member or friend attack you and destroy the satellites so that you can recycle the debris field. Before doing so, consider first utilizing the excess energy left from Graviton Research to build the Terraformer to its highest possible level, which will result in a number of additional fields for building.