In the movie Star Wars: Episode V – The Empire Strikes Back (1980) Luke Skywalker goes to train with the Jedi Master Yoda on the planet Dagobah. During his training his T-65 X-Wing fighter sinks into a bog which dismays Luke, but Yoda tells him he has to have more faith in the force.

How much force must Yoda exert to lift the X-Wing fighter?

Solution: In order for the X-wing fighter to move up  Yoda’s upward ‘force’ must be greater than the downward force of gravity. The mass of an X-wing fighter is not known, following xkcd we can guess at its mass assuming it isn’t that different than a modern fighter jet. On the internet we can find that an X-wing fighter is 12.5 meters long. The most advanced fighter jet in the world is the Lockheed Martin F-35 Lightening II, which has a length of 15.67m and a mass of 13,199kg when empty. If we scale this to the X-wing fighters length then we would get a mass of

m = {12.5m\over{15.67m}}(13,199kg) = 10,529kg.

If the local gravitational acceleration on Dagobah is the same as that on Earth then weight of the X-wing fighter would be

F = mg = (10,529kg)(9.8m/s^2) = 103,183 N %s=2

which shows that Yoda can exert a considerable amount of force with the ‘force’. Of course the scene takes place on Dagobah, not Earth, so the value of g need not be the same. However, from watching Luke’s movements we can see that the gravity on the surface of Dagobah must be pretty close to Earth gravity