Ascension: How Far Do They Go?

I just discovered the SyFy Channel’s mini-series Ascension.  In it, a spaceship (pictured above), the size of the Empire State Building, carries 600 people from Earth to another star in order to colonize a new world.  The premise of the show holds that the ship must travel 100 years to its destination.  Neat!

Now, on the ship, people are operating as though there is Earth-like gravity.  Look! In the photo below, from the first episode, they’re standing around, talking about a dead person, as though they were on Earth, standing around, talking about a dead person.

As you watch the show, you soon understand that the living quarters are arranged so that people perceive “up” to be the top of the ship, and “down” to be the bottom, as though they were standing in a skyscraper.  In the photo at the top of the blog, people would be standing, and their heads would be pointing left, their feet pointing right.

This gives us a clue how the show designers imagine creating gravity. TASK 1: Read about general relativity, and describe: what should be the motion of the spaceship?  Should it move at constant speed, or some acceleration? What speed, or acceleration?

TASK 2: Once you have answered the above, use one of the kinematics equations to determine – how far do they go? You’ll need to list assumptions that you make, but keep this first calculation simple, just assuming a single value for the velocity or acceleration you determined.

To help out, here are the kinematics equations:

Remember that the kinematics equations assume something about the acceleration.

If you make the same assumptions as me, then you will determine that the ship went a distance of somewhere around 4.9 x 1019 meters, assuming that we know the time of the travel to the nearest 1 year, giving the number 100 years 3 significant digits.  (We might say 100. years)

TASK 3: If the spaceship actually went that distance, then how many light years is that?   How does that compare to some of the closest stars to our own?

TASK 4:  Uh oh.  You know what happens when you make assumptions, don’t you?  There’s a problem.  Well, there are several, but let’s address just one in this task.  Use an equation of motion to determine the final speed of the space ship after 100 years.   Then compare that to the speed of light.  Then look up special relativity, and discuss: what is the problem here?

TASK 5:  Ok – here’s another problem: how does the spaceship stop? Many space-travel theorists suggest that an interstellar trip should have two halves.  The first half is an acceleration to a top speed, at which point the spaceship turns itself around, while its momentum continues to carry it in the original direction of travel.  Once it is turned around, it fires its engines directly at its (far away) target, to slow it down.  So let’s say that the Ascension turns around at 50 years.  Does this resolve the problem in Task 4?  Explain.

TASK 6: Use the relativistic rocket equations to determine how far the spaceship ACTUALLY  would go in that 50 years.  Ha ha!  Not really.  It’s already been done by someone much more knowledgeable than me.  But reading might lead to some insight about the issue.

The real TASK 6: Discuss how realistic it is for the show’s creators to generate gravity in the way they seem to in the show.

Ok, my physics-teaching or physics-knowing peeps, here are my questions about the problem:
1) What do you think of breaking it up into tasks like the above?
2) Questions too vague? I intended to be fairly cagey about particularly task 1, because I want them to relate the motion of the ship to their reading of the relativity.
3) Anyone have some particular favorite online explanations of special and general relativity that would support students in this problem?
4) Anything I should add?  Did I get anything wrong?

EDIT – 6/25/15
As I re-read this, there are a couple of items to point out:

1) I can see this being used to introduce relativity to high school Physics 1 students who have already done some work with 1-dimensional motion. It could also be done in a typical kinematics project (as an embedded problem) or unit.

2) I like the idea of rolling this out with just the introduction that ends with the sentence, “In the photo at the top of the blog, people would be standing, and their heads would be pointing left, their feet pointing right,” and no tasks enumerated.  Rather, give small groups of students the opportunity to inquire.   Perhaps a prompt of,

“What questions does this raise for you?  As a practitioner of physics, what kinds of information might you be able to calculate from the given information?”

That would create a bit more of an organic start, but you could still hold a list of tasks for students who seem to flounder.


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