I get so excited about new movies when I see the trailers. Take the Interstellar trailer for example. I don't even know what's going on, but I want to see this movie. When I have to wait for something, my only outlet is to write about it. So here we go.

The one thing I want to look at is the spinning spacecraft (or space station - I have no idea) that you can see in the trailer.

Why Do Spacecraft Spin? ———————–

This isn't such a simple question. Let me start with the statement that astronauts are "weightless" when traveling in space. I won't go into a full explanation - but you can find one here (I think it's fairly complete).

Here are the key points:

There is still gravity in space.

Astronauts feel weightless when both they and their spacecraft are accelerated only by gravity.

To the astronauts, it feels just like there is no gravity.

Humans don't even really feel the gravitational force since it pulls on all parts of our body. Instead, we associate weight with the external contact forces such as that of the ground pushing up on us. We call this force the "apparent weight".

The main point is that if I say there is no gravity where this spacecraft is located, it's the same problem as if it's in orbit around the Earth. In both cases astronauts are "weightless". The solution to weightlessness (I left off the quotes this time) is to provide some type of force on the body such that there will be an apparent weight.

Here are two astronauts. On the left, an astronaut standing on Earth and on the right one in a spaceship. If the astronaut is in a location with very little gravity (like in deep space), then the only way to "feel weight" would be to have a force from the floor pushing up. In this case, both astronauts would feel the same.

So how do you make this force on the astronaut in space? It all depends on the nature of force. Perhaps you are familiar with this equation:

This says that the total (net) force on an object makes it accelerate. Both force and acceleration are vectors - this will be important in a little bit. But for now, let's say that I look at some short time interval. Over this time interval, the average acceleration would be:

If you change the velocity of the spacecraft, you will have an acceleration. If this acceleration is in the direction from the feet to head of the astronaut, there will also be a force from the floor pushing up and the astronaut will feel an apparent weight. Of course it would be quite difficult to continue to accelerate by speeding up for a significant time (but not impossible).

There is another way to have an acceleration for an astronaut and it has to do with the vector nature of velocity. The acceleration depends on the change in velocity. Since velocity is a vector, changing either the magnitude or the direction of the velocity will result in an acceleration. Boom. There's your answer. If you just move in a circle (at a constant speed), you will change direction all the time and be accelerating. Here is a diagram.

Moving in a circle means you have to accelerate. But you already knew this. Every time you turn your car, you can feel the forces on you that go along with this circular acceleration. A spinning spacecraft does essentially the same thing. If you want a more complete derivation of the acceleration of an object moving in a circle, might I suggest Chapter 9 in my ebook on introductory physics - Just Enough Physics.

The apparent weight an astronaut feels depends on just two things (in a spinning spacecraft): the radius of the circle and the rotation speed (traditionally represented by ω). The following is an expression for the apparent weight (in g's) in a spinning spaceship.

Here you can see that bigger spaceships (larger r) don't have to spin as fast. If you have a smaller spacecraft, you have to spin faster. Oh, the angular speed in this expression must be in units of radians per second.

How Big Is the Spacecraft in Interstellar? ——————————————

Now that we have a relationship for the apparent weight, we can use this on the spinning spacecraft in the Interstellar movie. Remember, I am going to use a good dose of speculation here (since I haven't seen the movie) - but this Entertainment Weekly article states that the spacecraft spins "to generate 1g of gravity". Yes, that is the actual quote and of course it's wrong because you don't actually generate gravity. I guess I am being picky there.

If the spacecraft has an apparent weight of 1 g and I know how fast it spins, then I can calculate the radius. Simple, right?

Step 1 is to figure out the rotational speed of the spacecraft. This isn't too difficult since just about every version of the Interstellar trailer shows the spinning spacecraft. Now I can use video analysis software (I like Tracker Video Analysis) to plot the motion of one part of the spaceship. If I make the origin the center of the ship, then I get the following for the angular position of one of those "pods" or whatever they are.

It's rather difficult to mark positions on that spacecraft since it's so tiny in the video. However, you can see the trend that shows it is actually rotating with a constant angular speed. From the slope of this line, I get an angular speed of 0.59 radians per second. With an assumption 1 g apparent weight, this would put the spacecraft radius at 28.2 meters or a diameter of 56.4 m (185 feet). I guess that's not too big. The International Space Station is about 100 meters long (with the solar panels).

What About Other Spinning Spacecraft? ————————————-

You might not be too surprised, but I have already done this exact same thing with the Discovery One (from 2001: A Space Odyssey) and the space station in Elysium. But there are other spacecraft (in science fiction) that spin. Here are some that I can think of.

The big space station in 2001: A Space Odyssey.

The Russian spacecraft in 2010: The Year We Make Contact.

The alien spacecraft in Rendezvous with Rama (Arthur C. Clarke).

The Russian space station in the movie Armageddon (maybe it is the Mir). Yes, I know the real Mir didn't spin.

For your homework assignment, find video clips of all of these rotating spacecraft (except for the Rama - it's a book). Measure the rotational speed and use that to calculate the size by assuming they all produce 1 g of apparent weight. Now you can make a cool graphic with all of these space vehicles next to each other in the correct scale. That would be cool.