vasari experimental weapon

Yes, each faction has a super weapon they can research at tier 8. They fire at planets and you can build no more than 4 of them. They have the following effects.

TEC: Novalith Cannon - Fires a powerful nuclear warhead that inflicts 3500 damage to a planet. If it destroys the planet it will be uncolonizeable for some time, and in either case it has an extremely powerful half and hour long debuff to maximum planet population and trade. You can protect your planets from the damage with the axillary government upgrade or equivalent though.

Advent: Deliverance Engine - Easily the weakest one, but it spreads culture from the planet it hits, assuming your culture is weak enough for it to overpower it. It also give a +25% damage bonus to all allied ships at that planet, so if an hostile fleet is at where it hits they'll get a lot stronger.

Vasari: Kostura Cannon - This is what you got hit by. It can do moderate damage to all structures in a hostile gravity well, and disable them for a period of time. What probably happened is your labs got disabled, temporarily making it so you didn't have the research for Kodiaks and Orgrovs. When the effect wears off they should come back online. It also makes a phase gate at the planet it targets, allowing enemy ships to use the Vasari phase network to directly jump to your planet, making this weapon excellent for surprise attacks behind enemy lines. The AI rarely uses it this way though.

GoaFan77: Thanks for your useful info. I get annoyed when the game introduces conditions of play in the late game that cannot be anticipated, as you might try to do in a 'strategy' game. According to the Trinity manual I am unlikely to survive with the Kostura Cannon in play? I also noticed it has disabled planetary shield production on the target planet. Is there any counter to this enormous threat, apart from trying to take out the weapon on the planet? It is unlikely the latter can happen as I am sure the Kostura will continue to hit my planets and disable what might have allowed that. 

If you have ships with abilities that remove the disabled debuff, such as the Domina Subjugator's Perseverance, you could keep a couple in orbit around important planets to reactivate important structures after being hit by the Kosturas, such as your shield generator, factories, etc...

There isn't a whole lot that can be done to defend against it, no. However, the disable only lasts 3 minutes, which isn't a huge amount of time by Sins standards. Assuming they don't fire several rounds in a row, once the disable expires the damage is usually quickly repaired with repair bays. Also it does not disable starbases, so if you really need some sort of planet defense active at all times they're the one to go to.

That said, you don't necessarily need to destroy the cannon to keep it from firing. Like your ship production, if at any time a player has view labs that required to research the superweapon (8 military for Novalith/Kostura, 8 civic for Deliverance engine). So if you destroy enough military labs to bring their total down to 7 they won't be able to use any of their super weapons until they're rebuilt. This is especially useful if they're using several different cannons or if its in a hard to reach planet.

I am not really sure what the Domina Subjugator is. I have not seen something similar in the TEC arsenal.

It is an Advent support cruiser. It can heal targets a bit like the rebotics cruiser while preventing them from being disabled, but its not as efficient, so its best used on a few valuable targets like capital ships and titans.