Factual error: Although it's already been mentioned that the scene of the shuttle being stolen from the back of the 747 is impossible because the shuttle wouldn't be fueled while being transported, it should also be noted that even if the shuttle was fueled, it would still be just as impossible: During the getaway, the thieves ignited the shuttle's 3 main engines to get free of the 747 and escape: the thing is, the shuttle's main engines are fueled entirely by the large external tank the shuttle and the solid fuel boosters are attached to during liftoff, and once the tank is jettisoned, these engines cannot be used. The only engines the shuttle's internal fuel feeds are the reaction control thrusters, and the Orbital Maneuvering System (which are the two smaller engines located in the bulges just above the main engines). Both the RCS thrusters and OMS engines are almost totally useless within the atmosphere, so even if the thieves managed to get the shuttle free of the 747, they could only get it as far as it would glide unpowered: In fact, they could probably get it farther if it wasn't fueled.
Factual error: The space station rotates for pseudo-gravity, but everyone falls along the rotational axis towards the bottom of the screen instead of falling outward from the axis as they actually would. Admittedly this would be difficult to film (Stanley Kubrick's astronaut jogging in a giant hamster-wheel in Space Odyssey - nuff respect) so I guess they just hoped the audience wouldn't know the difference.
Factual error: Two pilot/astronauts steal a space shuttle by firing it up and launching it off the back of the Boeing 747 transporter. This cannot happen : the 747 can't lift the shuttle with a full fuel load - it only just lifts it empty. (Why would they carry a fully fuelled shuttle anyway?)
Factual error: When a real shuttle is launched (or any other large rocket) the exhaust must be deflected sideways and guided through massive tunnels or trenches so that it does not bounce back into the base of the vehicle and destroy it. The Moonrakers lift off from inside an enclosed structure with no means of guiding the massive exhaust plume safely away. The tiny tunnel through which Bond and Holly escape would have been utterly useless to vent the exhaust of a real shuttle. In common with other movies, the noise and violence of a real launch simply cannot be portrayed accurately.
Factual error: Moonraker 6 with Holly and James on board jettisons its booster rockets after reaching space. The solid fuel boosters are jettisoned after they burn out at about 50 km height, far below orbit. Their empty weight is considerable, it is highly doubtful if the shuttle would even be able to carry them into orbit.
Factual error: When Bond and Goodhead's space shuttle enters space, it still has the main fuel tank attached. However, when Bond releases the fuel tank it falls downward. It should maintain its momentum in orbit around the Earth until atmospheric drag (which extends out to high orbit) causes the orbit to decay over many years.
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