In today's game, my opponent used the Death Star on Coruscant, destroying the planet as he knew froma previous mission that I had the Heart of the Empire objective card.
If Coruscant is destroyed, can I still claim the 2 victory points with that objective if there is no imperial units and only rebel units there, even if the planet is gone?

There is no direct refference to objectives, but given that for action cards and missions it works even if the system is destroyed, I'd say that you can use Heart of the Empire even if Coruscant is destroyed.

QQ: Can missions and action cards be attempted or resolved in destroyed systems?
AA: Yes. For example the “Seek Yoda” mission card be resolved in the Dagobah system even if Dagobah has been destroyed.

From the Official Rules Responses :

Quote

Destroyed systems retain their names. Missions and action cards can still be attempted and resolved in Destroyed systems. This includes the Seek Yoda mission card.

I hope this answers your question!

-Corey Konieczka

VP of Research & Design

Fantasy Flight Games

Corey didn't specifically spell out objective cards, but the intent (at least to me) seems clear that the system should still be valid for objectives, despite not having the pictured planet there.

Destroying Corescaunt actually makes it easier to score Heart of the Empire because you only need to hold space and not the space and the ground.

On 17.7.2017 at 7:39 AM, grisix said:

In today's game, my opponent used the Death Star on Coruscant, destroying the planet as he knew froma previous mission that I had the Heart of the Empire objective card.
If Coruscant is destroyed, can I still claim the 2 victory points with that objective if there is no imperial units and only rebel units there, even if the planet is gone?

"So you threaten to invade my home planet. What if i destroy the planet first? Joke is on you!" #SuperiorTactics, #JustDeathstarThings

That might be the Palpatinest thing I've ever heard. Dang...

19 hours ago, subtrendy2 said:

That might be the Palpatinest thing I've ever heard. Dang...

Sounds more like a Trump move.