Lost in Space

In the year 2058, Earth will soon be uninhabitable due to irreversible effects of pollution. The United Global Space Force prepares the first launch for the colonization of a distant planet much like our own. Meanwhile, a terrorist group called the Global Sedition wants to interrupt the colonization to be able to take over the same planet themselves. Professor John Robinson, lead scientist of the Jupiter Mission, prepares to take his wife Maureen, daughters Judy and Penny and son Will on a 10-year mission in suspended animation to the nearby planet Alpha Prime, where they will build a companion "hypergate" to the one orbiting Earth. The project is accelerated after Sedition terrorists attack Earth's hypergate, but are stopped by fighter pilots, one of whom is Major Don West. When the pilot for the Jupiter Mission is murdered, West is assigned as his replacement.
Dr. Zachary Smith, a spy employed by the Sedition, reprograms the mission's robot to destroy the ship. He is betrayed, though, by his employers and left as an unwilling stowaway when the Jupiter II blasts off. A few hours after launch, the robot activates and starts destroying vital ship and navigation controls. The Robinsons, awakened from their cryosleep by Dr. Smith, stop the robot, but not before it causes the ship to become trapped in the gravitational pull of the Sun. Their only option to escape the gravity well would be to use the hyperdrive and end up anywhere in the galaxy. Now lost, the ship eventually comes across a "hole in space" and, after entering, finds a planet with two abandoned ships in orbit; the Proteus, an Earth ship somehow from decades in the future, and another ship that is clearly not human. When they investigate the Proteus they find navigational data that can be used to get to Alpha Prime (suggesting that humanity has somehow settled on Alpha Prime without the Robinsons) and a young alien primate that they adopt as a pet. They also find the aging ship is infested with carnivorous spider-like lifeforms, with the leg of one accidentally scratching Dr. Smith during an attack. To escape the spiders' attack, Don reactivates and overloads the Proteus' engine, with the shock wave from the resulting explosion damaging the Jupiter II and forcing it to crash on the planet below.
Professor Robinson and Major West go out onto the surface in search of radioactive material to replace the burnt-out part of the ship's core. They find a strange, growing bubble of unknown origin, which they must enter. They learn that the "holes" and "bubbles" are distortions of time and space, caused by future versions of Will and Dr. Smith constructing a time machine. The future Will Robinson wants to travel back in time to prevent the Robinsons from ever taking off. Robinson and West find out the bubble is actually a small schism in time on the same planet. They are all betrayed by the future Smith, who has mutated due to the spider scratch going untreated. He plans to unleash an army of spiders on the Earth. Robinson battles with Spider Smith while Major West returns to the stranded Jupiter II to evacuate everyone. Robinson stops Spider Smith by tearing open his eggsac, freeing the baby spiders, who then attack the injured Spider Smith. John pushes the mutated Smith into the uncompleted time portal, where he is torn apart by the gravitational field.
The others attempt to escape the planet in the Jupiter II, as the time machine's warping tears everything apart. They are unable to reach escape velocity and the ship is destroyed by flying debris. Future Will finally recognizes his father's deep love for his family and allows him to travel back through the time portal to before the Jupiter II attempts to escape. Knowing that the escape velocity won't be enough, John commands West to pilot the ship through the planet's core as it breaks up, using the planet's gravity to propel the ship out the other side. They escape, but the collapsed planet forms a small black hole that begins to suck the Jupiter II back in. To escape, the Robinsons once again activate the hyperdrive, using the Alpha Prime navigational data from the Proteus to blast off again, into potentially unknown space.

Question: Who find out that the schism actually takes place on the same planet?
Answer: Robinson and West