Head down to the Brain Machine and take note of the book titles being displayed on the screen.
In the Archive of Orbis, turn the statues in the room as many times as the book names show up on the screen.
Turn only the statue on the same level and wall as the book.
For instance, if a bookshelf contains a book from the screen, turn the statue once. If a bookshelf contains two books from the screen, turn the statue twice.
Once all statues are turned properly, head up the ladder and grab the model of Neptune.
Head back into the dome room and above the brain machine, place the Neptune model in the solar system hanging from the ceiling.
Then, you'll need to align each planet by shooting them and putting them in a specific quadrant around the sun hanging from the ceiling. The direction for the three required can be found on three notes around the map:
Activate the brain machine to cause the portal to start opening in the center of the room.
Shoot the drones coming off of the O.S.C.A.R. so they don't attack the portal until the portal is done and you'll be teleported to Mars.
Pick up the brain in the center of the area and place it in the Electricity Machine.
Interact with the machine and look outside the map to the east to see four coils on top of pillars.
Shoot the coils in a specific order:
Far Right
Far Left
Close Right
Close Left
Then, shoot the coil above the electricity machine.
A flying eye will enter the area. Jump up and grab the eye out of the sky and place it in the Eye Machine.
Next, head back to the Harmonic Oculus and interact with the organ.
Four symbols will be displayed with a fifth one hidden.
Around the arena, shoot the five antennas on top of the pillars with the LGM-1 in order that it appeared on the screen, with the hidden one being whichever pillar symbol you didn't see.
