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AICN's Astrophysicist calculates STAR WARS ANTHOLOGY ROGUE ONE's DEATH STAR distance!!!

Man, it is a great time to be a Star Wars fan!  I am so jealous of Quint and his adventures at Star Wars Celebration in Anaheim.  I couldn’t get away, because I was giving a midterm in my Astro 2 class at UCSB.  I felt bad for the students, having to take an exam on the day the STAR WARS: THE FORCE AWAKENS trailer was released.  As a consolation, I showed the trailer in class before the exam on the big screen.  Here I am before that, watching it in my office.



STAR WARS is the biggest reason I became a professional astronomer.   It is my favorite movie of all time, by a wide margin.  My brother and I had tons of the toys as a kid and played with them constantly.  In those days there was no home video, and no internet, so between films you’d just have to use your imagination to speculate on what might be coming in the next film.   I used to subscribe to Bantha Tracks, the newsletter of the Star Wars Fan Club, and occasionally they’d dribble out a new nugget of information, which would of course send me and all my friends into a frenzy.

Things haven’t changed!  We know almost nothing about STAR WARS ANTHOLOGY: ROGUE ONE, and yet that hasn’t stopped us from speculating.  And when Lucasfilm gives us the tiniest dose of information, it still causes us to lose our damn fool minds.  It is 1978 all over again, and I love it.

As I’m sure you know by now, the first teaser for ROGUE ONE dropped at Celebration on Sunday, and cell phone footage of it was online for a few hours before Disney shut it down.  It had voiceover and music showing a tie fighter above a canyon on a jungle planet or moon.  Eventually the Death Star came into view, taking up a huge fraction of the sky above the planet.  Here’s a screenshot I grabbed off the web.  

This just sent me into a fit of joy.  Can you imagine sitting on a planet, looking up and seeing *that* in the sky? 

There is some confusion over whether or not the Death Star is being built on the planet or in space.  Trust me, it is being built in space.  That’s the way celestial bodies look when viewed through an atmosphere.  And there is no way to build something round and the size of a small moon on a planet.  Tidal forces, atmospheric drag, and the impossibility of launching the thing are just a few of the problem’s you’d face.

But this still brings up so many questions!  Are we on a planet or a moon?  We know from RETURN OF THE JEDI that the Empire likes to build Death Stars near planets or moons and then use a shield generator to protect them.  Might the plans be there at the base with the shield generator?  I don’t think they’d go that route since we’ve already had a third of a film dedicated to infiltrating the shield generator of a jungle planet and it was the worst part of the entire original trilogy.  Still, ROGUE ONE could take place partly on that celestial body.  It also could be that this was just a throw-away image for teasing purposes.  

One place we can be sure the plans exist is on the Death Star itself.  I’d bet serious money that the rebels end up there.  Yes, we’ve already had another third of a movie about rebels sneaking into and out of a Death Star.  But for my money, that was the best third of a movie in all STAR WARS history.  I’d give a kidney to see 70’s era bad-ass chokin’-a-bitch Vader prowling the place one more time. Yes, that would make the Empire seem even more incompetent to have two sets of rebels breaking into and out of their fortress months apart.  So what.  It would be worth it!

Here’s another thing my money’s on:  Carrie Fisher’s daughter, Billie Lourd playing Princess Leia in the film.  Carrie Fisher said long ago that she wanted a part for her daughter in the new films.  And indeed there were rumors of her casting, but for EPISODE VII.  Maybe she’s in an EPISODE VII flashback (and maybe that will help set up ROGUE ONE), but I think it makes much more sense that we see Leia in ROGUE ONE.  At the very least, the rebels have to give her the plans at the end.  She might well be one of the rebels stealing the plans in the first place.

Fans of the site know that I occasionally write about the science in movies, and in fact, I’ve already written about Science of STAR WARS.  But today, I want to do a few calculations and see if we can deduce anything at all about ROGUE ONE from it.

In the image above, the Death Star looks huge on the sky.  As the teaser played on, it didn’t look quite as big as it does in that still.  It is pretty hard to estimate the angular size of something from such limited info, but we can at least get it approximately right.  

To give you a sense of scale, our moon is half a degree wide in the sky.  The moon looks larger when it is close to the horizon, which is called the moon illusion.  The reasons for this are not completely understood, but it at least partly has to do with buildings and trees on the horizon providing reference points for our brains.  That’s why the canyon in the teaser was brilliant — it provides a natural “reveal” and it makes the Death Star look huge at the same time.

The whole sky is 180 degrees across, so a quarter of it is 45 degrees.  As a first approximation, let’s say the Death Star was about that big — say 40 degrees.  If we know the angular size, and the linear size, we can just use a bit of trigonometry to calculate the distance to it!  From various sources, the Death Star is said to be either 140 km in diameter or 160 km.  Let’s call it 150 km (the 10 km uncertainty doesn’t matter given our larger angular uncertainty).  Now we just have to remember a bit of trigonometry.  The tangent of an angle is the ratio of the opposite side of the triangle to the adjacent side.  To keep everything in right angles, I’m going to use the radius (not diameter) of the Death Star, and the half-angle it subtends, so 20 degrees instead of 40.  Here’s the math…

When we do the calculation, it seems that the Death Star is about 200 km away.  But maybe we’re wrong about the angle.  Let’s say it is half what we thought, so 20 degrees for the full diameter of the Death Star, and only 10 degrees for the half-angle.  In that case, the Death Star is about 400 km away.  On Earth, low-Earth orbit (LEO) starts at about 160 km and goes up to 2000 km above the Earth’s surface.  At 160 km you get a lot of drag from the atmosphere, so I’d hope the Empire’s engineers would have put the Death Star would be higher. So let’s say the Death Star is closer to 400 km high.  Interestingly enough, that’s about the same altitude as our very own International Space Station! It orbits at 360 km!  You can see a sense of the scale of this in the below image I cropped from a larger one on Wikipedia.  That’s really close to the planet!

So immediately we know one thing.  If the celestial body we see in the ROGUE ONE teaser is a planet that the Death Star is orbiting, there is almost certainly no shield generator!  For that to work, the Death Star would have to be in geosynchronous orbit.  In such an orbit, a satellite orbits Earth once in 24 hours, so that it always stays above the same place on the planet.  Compare this to something orbits once every 90 minutes in LEO.  On Earth, geosynchronous orbit is at an altitude of about 36,000 km — much, much farther than what we calculated.  Of course, we don’t know that the planet in the teaser is like Earth, but it would have to be pretty wildly different to have a geosynchronous orbit so low.  For example, it could have such a low geosynchronous orbit if the day were only 45 minutes long.  That would actually be pretty cool.

If there is no shield generator, there are still reasons to build the Death Star near a planet.  You have to launch the materials from somewhere.

There is one other freaky thing about having the Death Star that close, and large in the sky.  Nights would be weird.  While the sun was down, but the Death Star is still reflecting the sun (like our moon does), it would be bright as hell at night — it wouldn’t get totally dark.  How long per night (or how many times this happens) depends on the orbital configuration — it could stay like that all night, or the Death Star could be in the shadow of the planet some of the time.  It could be that every 45 minutes the Death Star catches the sunlight and turns night nearly into day.  That would make for some tense situations for any rebels sneaking around in the dark.

Incidentally, if our heroes go running around this planet, you can bet it is fairly similar to Earth in properties.  If you go much larger or smaller, gravity would be different.  

There is one problem with the Death Star only being 400 km or so away.  That could make sense if that it the distance it is overhead.  But we know it isn’t overhead — it is low on the horizon (see the right-hand side of my hand-drawn figure above).  Earth has a radius of about 6000 km, so to get something low on the horizon, you’d have to be more like 1000 km or more away.  The problem wouldn’t be as bad if the planet were much smaller than Earth.  Maybe it isn’t a planet at all — it could be a moon.

If we’re on a moon, that means we’re orbiting something bigger — possibly a gas giant.  It could be that this moon and the Death Star share the same orbit.  In fact, this happens in lots of different places in our Solar System.  The rings of Saturn are rocks sharing orbits.  And Epimetheus and Janus are two moons of Saturn that share *almost* the same orbit.  In fact, they trade orbits!  

If the thing we see in the trailer is a moon, it could also solve our geosynchronous problem. Most moons are tidally locked, meaning they always present the same face to their parent body.  Earth’s moon is like this.  In that case, a shield generator would work.  However, if the Death Star were not in orbit around the moon, and instead was only in orbit alongside it, their mutual gravity would cause them to crash into each other.  But maybe the shield generator is keeping them apart.  After all, we know they have force fields, tractor beams, and artificial gravity in the Star Wars universe.

It is entirely possible some artists at ILM just came up with what we saw in the teaser for the “wow” factor, and didn’t put a lot of thought into it.  And of course STAR WARS has always been space fantasy.  But I hope the powers that be have thought it through.  There are so many implications that follow from what they showed, and thinking them through can take the story in many different fun directions.  AVATAR was fantasy too, but it was all the more special because Cameron thought through the incredible implications of the of worlds he built.

At any rate, I’m just happy we have not just one, but six new STAR WARS movies to endlessly speculate about.  And to top it off, they are being helmed by a new crop of directors, many of whom, like me, were inspired to get into their career because of STAR WARS in the first place.

Copernicus (aka Andy Howell).  Email me or follow me on Twitter.

And here’s me on Halloween last year.  I’m the one in the middle.


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