The Answer...

Using the x-position values from the video along with the mass values from my estimations, I get a Yoda-mass of -43.7 kg. Yes, that is a negative mass. But what does that mean? It means that in order for Luke to balance in that position, Yoda would have to pull UP on his leg rather than push down. One way to pull up would be to have a negative mass (which we don’t see). The other way for Yoda to pull up on Luke would be with The Force.

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The short snip of a very long (with pictures, mathematical equations, charts and more) post

Everyone knows Luke Skywalker travels to Dagobah to learn the ways of The Force (like his father before him). He trains with Jedi master Yoda. Perhaps you recall the scene where Luke does a one-armed handstand while balancing Yoda on one foot. Yes, for a real person this is pretty much impossible—but not for a Jedi.

Ok, so here is the plan: I am going to use Luke’s pose to estimate the mass of Yoda. This will be all about the center of mass. If the Luke-Yoda system is in equilibrium, then the center of mass for the entire system must be directly above Luke’s one hand on the ground. (If you want a more detailed explanation of center of mass and balance, check this post where I use center of mass to estimate the mass of Darth Vader.) To do this, I will make the following assumptions:

The planet Dagobah is just like Earth—the gravitational field on the surface of the planet doesn’t really matter, but still I am going to assume this.

Luke’s mass and mass distribution is just like any normal human. I guess Luke is a human. Now that I think of it, he should be an alien, right?

Luke has a height of 5 feet 9 inches and a weight of 150 pounds (1.75 m and 68 kg).

There are only two external forces on the Luke-Yoda system: the gravitational force and the force of the ground pushing up. For this calculation, there is no The Force force.

What is the mass distribution for a human? I am going to use some values from this very interesting survey of different measurements of the human body (pdf).

The paper I listed has multiple representations of the human body. Just to be clear, I am going to use the values based on Dempster. I am going to represent my human (or alien that looks like a human) as a five-point mass. Here are the locations and values of these masses:

link below for you math freaks :-)