Starfleet Jedi

I wonder what happen if Federation space station or even Federation base on a planet try to us a holographic ship to block Death Star super weapon

Assuming the DS crew doesn't detect it's a hologram they're fireing at, in all likelyhood the beam will go right through the hologram.

Wether or not the hologram will still be there is anyone's guess, ST canon is inconclusive in this regard (for example, in ST:Voyager, some holograms shot against them and vanished, some apperantly took (as in absorbed) the hit but nothing happened to them and some where damaged by weapons hits, but didn't stop the projectile)*

*) Ref: the doctor in space being hit by a Kazon weapon - he's still there but the beam was stopped. In the same episode, the fake ships actually vanished when hit (IIRC). Later, in season seven, the doctor destroyed a hologram using the mobile emitter by shooting it with his phaser (as far as I saw he did not hit the emitter itself). Which is interesting, because other holograms in the same episode could survive hits by similar weapons - the weapons just shot straight through them.

The simplest answer is that we don't know what would happen since the very nature of what the Death Stars' superlaser does is still a matter of debate in and of itself. If you believe the weapon is a 1e38 joule DET beam, then it would just blow right through the hologram, and the game would be up. If it is a chain-reaction weapon, then the effects might vary depending on how much actual energy is in the beam, and how the chain-reaction process works.
-Mike

If the DS can't detect that it's a hologram then we're in business (tm).

DS shows up?
Create 2 holograms:

1) Hiding the object (doable, holodecks do this all the time)
2) A copy of the object, just far enough away to be plausible

DS shoots copy, copy does a nifty explosion animation and your world is safe!

Naturally things might not go quite this smoothly, but it's a start ;)

The idea of hiding at least a starship-sized object is nothing new. In ST:ENT's "Babel" trilogy, the Romulans of the 2150's had sufficently advanced holographic technology that they were able to disguise a remotely controlled drone ship so that it looked like other powers' starships such that no one could immediately tell them apart. I suppose it's possible, in theory, that an entire planet could be hidden that way, but how do you protect that world from the secondary effects of the Death Star superlaser? Would the Death Star crew figure out it by realizing that the holo-planet is not in the proper orbit for the target world?
-Mike

Surely the holo disguise would only be a temporary fix anyways. If it's enough to have the DS fire it's superlaser, it still has a large number of turbolasers to bombard it's target with.

It shouldn't be hard for the crew to figure out that there is a planet there either (assuming they use to holo to "cloak" it so it's invisible, based on the orbits of the other planets.

Well, yes. The key word here is "temporary" as you say since the DS crew might actually notice that there is still a substantial gravitational field, even after having supposedly blown up the target planet. On the other hand, luck might hold out and the Imperials are over-confident and leave, thinking they've actually destroyed the target. It all would hinge on how much time the Imperials have post target destruction to sit around until they can spin up the hyperdrive and be on their merry way. The recharge time for the superlaser is also critical here as they may attempt a second shot at where they see the gravity distortion.

So tactics-wise, those attempting to hide behind a holo-cloak would probably also have to do something to hide the planet's gravitational effects and possibly have a plan of counterattack and evacuation ready to go once the superlaser has fired off at the holographic decoy.
-Mike

Of course, there are problems with the strategy. As you've outlined rather well.

Not the least of which is the assumption that they fall for this trick to begin with. I've made that assumption in my earlier post ;)

Anyway, I'm thinking having something beats having nothing. The question then becomes if they could accurately determine the position of the actual world after their failure to do so initially. At the very least it buys you some time. At best it could even have the Imperials give up to save them from being embarassed.

A lot of this also hinges on Star Trek holographic technology being up to the task of creating holograms on a planetary scale and with the necessary fidelity.
-Mike

Quite true.

I'll admit it's a bit of a stretch, I can see a ship-sized hologram easy. But I'm not so sure about a planet sized one myself.

Still, it's a fun thing to think about :)