Scaling the Death Stars

Quick Reference: 
Page 1:    DS1 Scaling, Falcon Yardstick, DS2 Scaling, Shuttle Yardstick, Saxton vs. Sarli
Page 2:    Alternatives, The Endor Issues, Conclusion


Alternate Methods

1.  The Escape from DS2

We can estimate the size of DS2 based on the escape run of the Millennium Falcon.  After attacking the DS2 core, the Falcon races out of the superstructure in approximately 39 seconds of screen-time, and, based on the apparently-finished hull around the exit point, emerges from a portal on the exterior shell (as opposed to within the incomplete superstructure, which is in keeping with the Rebel hologram's depiction of the entrance).  If we assumed a distance of 135 kilometers (i.e. the radius of a 270km Death Star), the average velocity would be just under 3.5 kilometers per second.  If we assumed constant acceleration over the journey (and thus a final velocity of 6.923 km/sec), the acceleration would be 177.5m/s, well within the known capabilities of the Millennium Falcon.  

If we were to use Saxton's preferred size of ~900 kilometers for the station based on backstage materials, the run would've been 450 kilometers, requiring a constant acceleration of over 590m/s . . .  far exceeding the Falcon's capabilities.

However, at no point in the Falcon's run did she appear to reach a speed of 7km/s, and the assumption of constant acceleration would ignore the weaving and turning and slowing through the DS machinery which had to be done in order to reach the core.  As a result, station radii smaller than 135 kilometers (such as, for instance, 80 kilometers) would be very much preferred for the sake of Star Wars consistency, and consistency with the other scenes within the Death Star 2 in RoTJ.

2.  The Super-Trench

I am well aware of Saxton's conclusion of ~900km diameter for the DS2.   Saxton abandons his 270km value (based on a flawed interpretation of canon, but on canon at least) in favor of one more closely resembling backstage information, choosing to infer that there is an additional "super-trench" within which lies the one we see and that he scaled against.   In other words, the trench we see would just be a tiny trench in the midst of a larger one.   However, no such super-trench exists in the canon, or even in the non-canon that Saxton references.   If one were wanting to tempt Occam in such a fashion, one could just as easily assume a super-super-trench, and more supers beyond that.  

Saxton's super-trench would have to be very large, with walls of sufficient height (or distance from the existing trench) to obscure the existing trench from view when looking at the Death Star from many dozens of kilometers away.  No additional trenching is suggested by the silhouette of the trench against Endor, as seen through the Falcon's cockpit windows:

There is no additional visible structure to the left in the image below of Vader's docking, as one would expect of an additional trench layer in this view:

(Also, incidentally, the view above is the canon version of an unfinished matte painting Saxton points to has his one possible example of proof of a super-trench, based on an odd jutting box structure (completely unlike the curving trench rim we see above) at the top of the matte painting.  That box structure does not appear in the above canon image . . . instead, the finished matte has the odd girder structure.)

And finally, Saxton's upward-revised conclusion involves the idea that the assumed super-trenching would make the total super-trench height be at least three times the height of the trench we can in fact see.   Why does that matter?  Well, when the Emperor arrives at the Death Star, the image pans downward from looking well above the trench docking bays.   Combining those images together so that the areas of unfinished construction match yields this view:

The scene cuts away before we can see the bottom of the trench.  However, we could see it during Vader's landing earlier in the film.  Scaling and overlaying that image on the bottom of the image above yields this view:

The method (and thus the result) is a little rough, but the basic issue is clear.  As you can see, the trench has another trench-height worth of hull above it, plus some.   For the hull we see to be inside a super-trench, then it would either have to be a very shallow-walled super-trench (and thus useless to Saxton), or else its cavernously-deep walls would have to be very much more than three times taller than the actual trench, in order to avoid casting a shadow on what we can see above.   The angle of the shadow is the same in both docking bay views.  

The reason this is a problem for Saxton's assumption of a super-trench and the adjusted conclusion that comes from it is twofold.   First, as mentioned, he needs very high super-trench walls to totally obscure the existence of the visible trench . . . and the higher the walls are, the taller the super-trench must be.  Second, the taller his super-trench gets, the taller the Death Star must become to account for it, and thus the greater the Death Star's diameter must be.  The trench we can see and measure produces a 270km Death Star . . . a "super-trench" no less than four times that big (in keeping with the canon visuals above) would require a Death Star of almost 1100 kilometers diameter.  And, in reality, given that we cannot see the super-trench in the side-view of Vader's shuttle docking, and given that it must have high walls, the super-trench would have to be even taller . . . which would drive up the Death Star size ridiculously, and the size of Endor along with it.

Thus, the 270km Death Star idea has the virtue of canonical backing (even though, as Sarli has demonstrated, it's still wrong), unlike the fudge of the non-existent super-trench that expands the Death Star even beyond Saxton's estimate. 

The Endor Issues

There are some issues regarding such values for the second Death Star, and both revolve around the moon which it orbited.  

1.  The Hyperspace Exit Shot

Endor is commonly assumed to be Earth-sized or thereabouts.  As seen below, the Death Star is quite visible with Endor as its backdrop.

I scale Endor to be approximately 11.1 times the width of the Death Star in this image . . . Saxton's value is 11.5 times, and assuming his source was of higher quality than my own (in which the Death Star is only about 9 hazy pixels wide, and thus rather indistinct for this purpose), then 11.5 is the value I shall use, as well.  If Endor were the size of Earth (12,756km), the Death Star would have to be more than 1,100 kilometers in size. Since the scaling based on the film appears sound and the novel statement is virtually inviolable, either (1) the assumption of an Earth-sized Endor simply does not follow, or (2) there is some sort of visual distortion in effect in the image above (the fleet was moving out of hyperspace at the time).

Let's take a look at both options.

1.  A smaller Endor:

Even a 270km Death Star would result in Endor's diameter being only about 3105 kilometers, making it about 90% the size of Earth's moon.  Our own low-density moon only has one-sixth the gravity of Earth.  It is a curiosity, to say the least, that such a small world could have gravity visually indistinguishable from Earth-normal, as well as a similar atmosphere and rotation rate.  It would end up needing a very dense core in order to maintain its planetwide density, which would be around 22,000kg/m.   In effect, almost the entire planet would have to be made of osmium (~22,400kg/m), iridium (~22,500kg/m), or one of Trek's odd elements not found on the present periodic table.

But that is with a 270km Death Star.  At the true value of about 160 kilometers, not even the densest of cores composed of any known material could support the planet, for its diameter would be only 1,840 kilometers.  Some wonky Trek technobabble element would have to be what the planet was made of.

Alternately, one could almost imagine that the Imperials were responsible for artificially increasing the gravity, but the glaring problem with that idea is the fact that the plantlife, the Ewoks, and the Ewok technology all seem to be well-adapted to the gravity . . . there's no indication of everything having suddenly found itself several times heavier than normal.   That would imply that Earth-normal gravity is the natural state of affairs for Endor.

Of course, the circumstances of Endor are most peculiar in the first place.  We learn in the novelization that Endor is "a moon whose mother planet had long since died of unknown cataclysm and disappeared into unknown realms".   However, I see no way for that to justify such a tiny world being blessed with such an insane density.

2.  Visual distortion, presumably due to hyperspace exit:

The use of the hyperspace exit shot for scaling is questionable, since the representation of Endor's size versus that of the DS2 is not exactly consistent throughout the film.  The very first time we see the DS2 and Endor together,for instance, they look like this:

Even the tiny amount of visible Endor is over seven times broader than the Death Star . . . the moon as a whole would utterly dwarf the station.  As another example, take a look at the image below:

In the above image, the Death Star is 164 pixels in height, and is clearly in front of the horizon of the planet.  Using the scaling from the hyperspace exit scene, we would expect the planet as a whole to be some 11.5 times larger than the Death Star, or a total of 1886 pixels.

It is not.

Below I present the image above, but with the arc of an 1886px circle overlaid in red:

As you can see, the moon's actual curvature is inconsistent with the notion of Endor being 11.5 times larger than the second Death Star.  To be fair, of course, I have not accounted for any differences in appearance due to relative distance, but doing so would actually make the situation worse for the 11.5 argument.   After all, if we are very much closer to DS2 relative to the moon (as, of course, we would be in this case), then DS2 should appear even larger, or the red curve smaller (take your pick).

As example, consider the NASA images of astronauts engaged in spacewalks.   If the Death Star were an astronaut's helmet, then the astronaut coming closer would make the relative size difference seem smaller.  If he moved further, then the relative difference would be greater.   Alternately, we could adjust the orbit of the astronaut and get a similar effect . . . a more distant planet would be smaller, a closer planet larger.

Below, I present a different version of the above, this time with the red circle visible and a blue circle more in keeping with Endor's appearance in the shot.  (Image below is cropped quarter-scale of original.  Click pic for cropped half-scale.)

Based on the blue circle of the above image, Endor would be 33.54 times larger than the Death Star (5500px/164px).  That would mean that Endor was actually about 5,400 kilometers in width, ignoring distance issues.    This would give us an average Endor density of 'only' 13,000 kg/m, which is still absurdly high but far closer to the bounds of reason.

Alternately, we could scale by that first image . . . below is the result of overlaying an 8400 pixel circle, and as you can see it closely matches the surface.

The Death Star is 85 pixels tall in the image above, which would actually serve to drive up the size of the moon to some 15,800 kilometers.  Such a value would mean it would have an average density much less than that of Earth.

Alas, it isn't clear in this shot what the relative distances of Endor and the Death Star might be.  If, for instance, the Death Star was positioned above a point well over the horizon, then 15,800 kilometers would be an upper limit of distance.  If she were quite close, however, it would serve as a lower limit.  What we do know is that the planet is also visible beneath the Star Destroyers in one of the two shots of them . . . but, then, planets are hardly small things, so this doesn't prove much insofar as on which side of the horizon the Death Star's orbit has carried her. 

One thing seems pretty clear . . . she's not directly above the horizon (though that is, by necessity, how I scaled her), since otherwise she'd basically  have to be skimming atmosphere. 

As a result of the above, our options have become to (1) stretch the bounds of credibility in reference to Endor's composition, or (2) to dismiss the peculiar hyperspace exit picture as suffering from a visual distortion of some type, or simply as an inconsistency.

The second option is obviously the better of the two.  Thus, we can conclude that Endor has a diameter of somewhere between 5,400 and 15,800 kilometers in all but the hyperspace exit shot.   The average of the two values is 10,600 kilometers . . . we can comfortably assume that the moon's true size is somewhere on the order of Earth's diameter of 12,700 kilometers.

2.  The Rebel Holo

There is one remaining inconsistency, this one in regards to the orbit of the Death Star.   The novelization makes it clear in the prologue that the Death Star was hanging in a "stationary orbit" over Endor, and the many references to the Death Star simply hanging, floating, and so on strongly suggest that it was not engaging in powered flight to maintain the position.

Contrary to such a view would be shots like the one below.

The image shows the Rebel hologram representation of the Death Star and Endor, and suggests that the DS2 was orbiting Endor at an altitude of perhaps 200 kilometers.  Earth geostationary orbit is better than 42,000 kilometers distant from the center of the planet, or over 35,000 kilometers from the surface.  The orbit shown above is rather less than that.  Even if Endor were only 9,000 kilometers wide, some 75% of Earth's diameter, geostationary orbit should still fall somewhere in the range of 30,000 kilometers above the surface.  In order for the above to be a simple geostationary orbit, we would either have to accelerate the Endor days to about 80 minutes in length (which is absurd and contrary to the film), or drop Endor's mass (and hence gravity) down to virtually nil (which is worse).

There are three possibilities which come to mind.

1.  Co-Orbit:

The only normal-physics hope I can think of that might not conflict with the canon would be that the Death Star, the mass of which works out in scientific notation to "way the hell too damn heavy", is able to maintain the low orbit (or more precisely in this case, "co-orbit") naturally.  The problem there, even assuming that's right, would be that the Death Star's mass changes as it is being constructed, which would mean that over the period of construction, the DS2 would be all over the place, orbitally speaking.

2.  Tractor/Pressor Beams:

It's conceivable that the shield projector on Endor had a tractor beam dragging the Death Star around the planet.   However, one can readily imagine several problems with this.   First and most obviously, that the power cost for such a thing would've been absurd.   Second, that Newton would freak out not only during the process, but also as soon as this beam disengaged.    Having that 'cord' between the moon and the Death Star would've wrought havoc on Endor's orbit and rotation over time, and as soon as the beam was released the two objects would've spun away from one another like tops gone mad. 

3.  It's another damn Rebel display:

Let's face it . . . historically, Rebel displays have been on the inexact side of the spectrum, to say the least.    

- Dodonna's ANH briefing screen showed a Death Star I with a superlaser dish on the equator.
- The Rebel version of the Yavin orbit of the Death Star showed that, scaling from the Death Star size on the screen, that the Yavin "gas giant" would've been 1,500 kilometers wide, with the Yavin moon itself being some 400 kilometers in diameter.   And, ah yes, all of this orbiting would've been occurring within just a few thousand kilometers.
- The Rebel holodisplay showed different orbital heights for the Death Star, as Greg M. Sarli pointed out recently on his page.  The image I showed above gives us an altitude of around 1.5 Death Star diameters.  

The image above, meanwhile, shows the Death Star at an orbit of more than three Death Star diameters.  (And, as long as we're here anyway, it also suggests an Endor size of only 2,050 kilometers.)

It seems clear that the Rebel hologram is not only inconsistent with the other scenes and the novel, but is also inconsistent with itself.  As a result, this issue is a non-issue.


Conclusions

Death Star I diameter:   ~120km
 Death Star II
diameter:  ~160km

 

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