Star Trek: Asterisk "Final Mission"

Vital Information
Series: The Next Generation
Episode: S04E09
Air Date: November 19, 1990
Written by: Kacey Arnold-Ince and Jeri Taylor
Directed by: Corey Allen

After being informed that he's going to Starfleet Academy, Wesley decides the last thing he needs to do before leaving is save Picard's life. Riker takes out the trash.

Wesley huffs and puffs onto the bridge and apologizes for being late when Picard called for him ten minutes ago. Picard tells him that kind of tardiness will not go over well in the academy. It takes a few seconds for Wesley to process that that means he's going to the academy! At last! All of Wesley's dreams are coming true! But first, Picard has one final mission for him: accompany his captain on a trip to Pentarus III where Picard will arbitrate a mining dispute. Before they can leave, however, a distress signal comes in from Gamelan V. Radiation is being pumped into their atmosphere from a space barge. Picard assigns Riker to take care of that while he and Wesley meet Captain Dirgo and take his shuttle to Pentarus III. His shuttle is a rust bucket... absolutely nothing could go wrong!

After bragging about the efficiency of his engines, Dirgo's engines are the first things to go out. When they encounter space turbulence, they have to make a landing on the nearest planet... which happens to be a moon. A desert moon that is just barely habitable. After landing, Picard identifies what should be their main objectives: food and shelter. The shuttle will act like an oven in the hot sun, so they head toward a mountain. Unfortunately, the only food they had was a replicator unit that was destroyed in the crash. In a sweltering desert, they have no water. They have to hurry to the mountain and find a cave with a spring.
At least they have fancy headgear.
So they get to the cave and it doesn't take a long time at all for them to find a spring. There's only one problem: there's a force field around it. Dirgo tries to fire his phaser at it, but when he does that a wispy, ghost-like sentinel flies down and knocks the phaser out of his hand. And while it's doing that, it goes ahead and knocks some rocks off of the wall. The rocks are about to fall on Wesley, but Picard pushes him away and takes the brunt of the collision. As a result, he is fatally wounded. It is now more important than ever to get to the water. And to keep headstrong Dirgo under control.

If you're wondering what the Enterprise is up to during all this, don't worry, they know that Picard and Wesley are missing. They just don't know how bad it is. And, to be fair, their mission, should they complete it, will save millions of lives. The barge, it turns out, is a garbage scow that wandered through space and ended up there coincidentally. It's just their bad luck that the garbage is highly radioactive. The Enterprise is doing their best to quickly fling it into the sun and then go look for Picard and Wesley.  Dirgo they don't care so much about.
Riker's new job as the garbageman.
Speaking of Dirgo, he has a marvelous idea. While Wesley is studying and scientifically evaluating a way past the force field, Dirgo decides he's just going to use more force. He figures if both he and Wesley fire phasers at the force field, they'll overload it somehow. Before Wesley has a chance to react, he tells him to fire, but the sentinel comes down and, instead of taking his phaser, takes Dirgo completely and encases him in a shell of plastic and spaghetti. He's either dead or well-preserved. With Picard already down for the count, it's now up to Wesley to deactivate the shield on his own.

Before he does that, he has a nice chat with Picard. He informs Picard that Dirgo is dead. Picard encourages Wesley and tells him to have fun at the Academy. Picard envies him this opportunity to start a Starfleet career anew, but laments the idea that he'll probably be too dead to watch him do it. But Wesley perks up and is more motivated than ever to keep Picard alive. He goes to the fountain, fires on it again, but this time when the sentinel comes, he pokes some buttons his tricorder and fights back at it. Eventually, the sentinel submits to the superior mind and flies away, lowering the force field on his way out. Wesley examines the water, rejoices, and then brings the water directly to Picard.
Eventually, he passes out from tiredness. But the next sight he sees as he opens his eyes is that of his mother, Beverly Crusher, assuring him that everything is going to be fine. The Enterprise followed the shuttle's flight path to the moon and a search team found the arrow that Picard had laid to direct them toward the cave. (Although, why they couldn't just pick up on their comm signatures, I don't know.) As Picard is being carried away on a stretcher, he grabs Wesley's arm. He jokes that Wesley's uniform is dirty, and Wesley jokes back saying "You don't exactly look ship shape yourself." And in a moment of fatherly love, Picard informs Wesley that he "will be missed." And that's the end of Wesley's journey! ...Or is it?

Overall Thoughts
For an episode that was specifically written to take Wil Wheaton off of the Enterprise, this is a surprisingly good story. Although, it was a little obvious that the B plot was only there to keep the Enterprise out of range for a while while still allowing the rest of the cast to have a part. So Wesley goes off to the academy after this. But don't worry, there are a few Wesley stories still ahead. It's just good to know that he has finally achieved his dream of going to the Academy. It was getting to the point where all the excuses for him not to go were getting silly.