I very dislike, that the planets stands still in their solar system, they should move in an orbit around their star and not just rotating on one place. : /
The phasejumps would be abit hard to code i guess....but my idea is that the lines only connect planets who are reachable to eachothers without complications (means no other planets or stars in the way). To make it easier for the player it should be also a tab for planets in the menu between the diplomacy, science, blackmarket... tabs in which the player can see details about his planets orbit. e.g. the next planets it will be connected with, with a countdown. The menu could look like this if opened:
[Star 1]
Planet 1
- Current Phaseconnections: Planet 2 (**: ** (Countdown)) Planet 3 (**: **)
- Upcomming Phaseconnections: Planet 4 (**: **) Planet 5 (**: **)
Planet 2
- Current Phaseconnections: Planet 1 (**: **) Planet 3 (**: **) Planet 4 (**: **)
- Upcomming phaseconnections: Planet 5 (**: **) ..........
And so on....
[Star 2]
Planet 1
- Current Phaseconnections: ........
- Upcomming Phaseconnections: ..........
And so on....
Every species should also have an independent phase connector (like the phase stabilizer of the Vasari). The Vasari should get that research earlier due to the fact that they are phase masters.
And if you click on the planet in that menu, more details pops up in another window, like detailed diplomacy and loyality informations, additional planet upgrades,....
this extra menu could also be reached if you click on the planet in the galactic map (just as if you want to place a space station), then you'll see a button in the upper menu which opens the detailed menu for the planet.
Proportions of space objects (stars, planets,..) and technical devices (ships, bases,..) could be abit more realistic. Means planets and stars have to be bigger.
But also limited units or bases that are bigger would be awesome. Like units with the ability to hardly demage or even destroy a planet (like the Death Star from Star Wars). This units should be limited to one for each player and should move veeeery slow, also the ability of destroying planets should have a veeery long cooldown time. Those super units also should take alot of fleetspace, so you would have to chose between big fleets with alot of ships and cruisers or a few super units and less big fleets, because the superunit needs a big crew (like 100 fleetpoints and 5 captains). To balance this hyper unit, counterunits, who are specialised to destroy that big bad units, should be included.
Also moons would be great! And more types of spaces objects...our real solar system has more planet types than the whole game 
Moons could be used as extra mines or moonbases to improve credit, ressource and diplomacy rate or such....
The research tree should be enhanced to 10 for each species, just adding two new research steps to get the superunits and the planet destroyer ones (for ALOT of credits and ressources).
....just a few ideas which would make the game epicly perfect.
a big shame that i have no clue about programming 
