The Death Star battle stations could perform controlled rotation on at least one axis. This capability was vital to each station's role as a weapon. The composite "superlaser" beam could be fired off-axis within some limits, but the whole station must rotate to face targets sitting outside that arc. The first Death Star rotated towards its targets after arriving in the Alderaan and Yavin systems facing off-target. The second Death Star turned several times to face parts of the rebel fleet near Endor, and finally rotated almost 180° to face the moon.
Rotation about the polar axis was much less necessary for manoeuvring, since the station's sublight drives were equally spaced around the equator. Rotation about the other two axes may have helped the performance of manoeuvres involving accelerations above or below the equatorial plane.
When the first Death Star arrived in the Alderaan system the main weapon was pointed at more than 45° away from the planet. Within a few minutes, the station had rotated until it had a direct facing to the target. The rotation then apparently slowed or stopped when the planet Alderaan was in aim.
The Death Star approaches Alderaan, facing slightly away from target.
During the final minutes of the Battle of Endor, rebel commandos destroyed the deflector shield protecting the Death Star II. In the chaos after the impact of the Imperial flagship Executor, Moff Jerjerrod stayed alone in the bridge of the battle station in order to implement Emperor Palpatine's contingency order: the destruction of the sanctuary moon. In an interval of less than a minute the Death Star II changed from an outward facing (firing on the rebel fleet) to an inward orientation, bringing the moon almost within the firing arc. Combatants on the moon's surface looked in the sky and recognised the superlaser dish aiming towards them, immediately before the station exploded.
Jerjerrod's discussion with an aide [in Return of the Jedi, p.206] enables us to infer the limits of the battle station's rotational abilities. Initially the station was almost spinless when it faced the rebel fleet. At that time the Death Star needed to accomplish slightly less than half a rotation before the Endor Moon was within the reach of the superlaser. At the initial rotation rate the projected firing time was two minutes. Moff Jerjerrod ordered that the rotation be accelerated. At this (presumably maximal) angular acceleration, the firing time was brought forward to sixty seconds. This implies an angular acceleration of the order of:
α = 0.0003 radians / s².
If we knew the mass density of a Death Star then we could estimate the power consumed by this opration. Unfortunately the density is not easy to determine. A lattice of metallic solid is visible through the gaps in the incomplete superstructure, but the void fraction is unknown. The power requirements of the prime weapon also imply the presence of a considerable amount of mass-energy fuel in some other exotic form, and the fuel mass may exceed the "dry" structural mass of the station. Using a fiducial density the same as water, and a diameter of approximately 900km, the power involved in the observed rotational acceleration is on the order of:
P = 1026 W = 1017 GW
This estimate should be adjusted in proportion to the actual density (relative to water). For any plausible density the rotational power is negligible compared to the power of recharging the superlaser.
Given Jerjerrod's urgency in destroying the moon, it seems likely that the acceleration he ordered was near the maximum physical tolerance of the incomplete structure. A robust, fully built Death Star — with a complete internal framework, a full set of inertial compensators and tensor field generators — might be able to accelerate its rotation faster.
The region within approximately six diameters from a habitable world is known as "antigrav range". Within this zone the use of repulsorlift against the planet's gravitational field is a more efficient means of support or outward propulsion than the ion-drive sublight thrusters which are most useful in deep space. The Death Star I fired upon the planet Alderaan shortly after reaching this proximity. The fact that a control room technician announced the station's passage through this threshold in the novel of A New Hope implies that the Death Star was able to support itself using immense repulsor fields. At this distance from Alderaan, if the battle station supported itself entirely by repulsorlift, without engaging in any orbital motion, then its repulsors would need to oppose the local gravitational field strength of about 0.07 m / s². This characterises the lower limits of the accelerative ability of Death Star I's repulsors.
This observation accords well with the physics of Return of the Jedi, and might be able to help solve a minor mystery.
As will be detailed below, the Death Star II required a significant repulsorlift force to sustain it in a low orbit about the sanctuary moon of Endor.
Naturally, the second battle station could not have provided its own repulsor support during the early stages of construction, but it is comforting to know that repulsors of sufficient magnitude to lift a Death Star were within the reach of Imperial military engineering.
at least during the earliest phases of the Endor construction, the ground installation which generated the security deflector shield would also have provided an upwards repulsorlift force.
Sublight drives
The sublight drives of the Death Stars were not conspicuous when the battle stations were viewed from afar. Various sources claim that the sublight engines were housed around the equatorial waistband, but the actual nozzles were too small to be seen from more than a few kilometres away. The Mandel blueprints indicate that there are 68 "antimatter engines", which presumably are the sublight drives.
The tiny size of the sublight drives in proportion to the whole vessel is an important hint to the nature of this technology: clearly the effectiveness of this propulsion mechanism does not increase greatly according to the aperture area.
Though not impotent, the sublight drives of the Death Star were not strong enough to move the battle station's immense bulk around the planet Yavin in less than half an hour. According to dimensions of the Yavin system calculable from data in Galaxy Guide 2: Yavin and Bespin, the average of the velocity of the Death Star in this trajectory must have been of the order of 400km/s. Of course a sustained acceleration would make any sublight velocity attainable after a sufficient time, but this was the maximum attainable within the constraints of time and the celestial mechanics of the Yavin system.
Rebel starfighters were capable of accelerating well enough to meet the Death Star within only a few minutes. Unsurprisingly, this is much better speed than the battle station could make.
The STAR WARS blueprints quote the maximum acceleration of the first Death Star as "0.0001 grav", which probably means a ten-thousandth of the surface gravity of a standard habitable planet. This would mean something like 0.001 m / s² in metric units. If the Death Star I emerged from hyperspace at rest with respect to Yavin then it would have taken over four and a half days to accelerate to its proper orbital velocity. Either the "0.0001 grav" is in error, has been misinterpreted by me or else vessels are able to emerge from hyperspace at whatever realspace velocity the pilots choose.
For the Death Star II to achieve mobility and firepower similar to its predecessor, its power systems must at least be scaled up in proportion to the overall volume of the station. However when a sphere is scaled up its surface area increases much more slowly than the total volume. Therefore the density of sublight thruster nozzles and heat dispersion ducts on the surface of the Death Star II must be much greater than on the original station. Otherwise these systems must be built for markedly greater efficiency.
The Death Star arrives in the Yavin system and heads towards the planet. In these frames the station is moving at a speed of a few tens of km/s relative to the camera. The camera's velocity relative to the planet is not measurable.
Death Star during its ill-fated orbit of the planet Yavin.
Blueprints stating maximum sublight acceleration of Death Star I. Unrealistically low figure considering the actual accelerations implied in the orbit around Yavin.
Suppose that a Death Star has a total mass M (including its hypermatter fuel), and a radius R. Suppose that the battle station can use its equatorial thrusters to change its spin, such as Jerjerrod's attempt to rotate and target the Endor moon in the last moments of the Battle of Endor.
If a single thruster on the surface exerts a force f at an angle θ to the local vertical direction then the torque it exerts on the Death Star is τ = f R sin θ. If the maximum possible deflection off vertical is δ and if all thrusters fire at maximum thrust towards the same side then the total torque exerted on the Death Star is τ = F R sin δ, where is the total output of all N thrusters, F = N f. The resulting angular acceleration of the Death Star (rate of change of the spin) is given by α = τ / I , where I is the moment of inertia about the polar axis.
The moment of inertia is related to the mass and radius of the object, I ∝ M R². The constant of proportionality, which we may label as X=I/M R², depends on how centrally concentrated the density is. If essentially all of the mass were concentrated at the exact centre then X=0. If all the mass were concentrated on the spherical surface then X=2/3. If all the mass were concentrated around the equator then X=1. If the mass is evenly distributed throughout the spherical volume then X=2/5. The possible values of X are realistically limited to the range 0<X<1, unless the outer radius has been misidentified and the Death Star really has a substantial halo of invisible mass far outside its visible surface (implausible).
Combining the definitions above, X M R α = F sin δ. Call this the equation of maximum torque.
Now consider the way the Death Star can direct its equatorial thrusters for maximum acceleration in a particular direction, but no torque (alteration of spin). Individual thrusters fall into one of three areas of usefulness:
The Death Star's total thrust force is (F / π) (δ + cos δ) = M a. Here a is the resulting acceleration, and M is the total mass of the battle station, its fuel and contents. Call this the equation of maximum acceleration.
Finally, we can eliminate F from the equation for maximum acceleration and the equation for maximum torque. Thereby we find that the maximum spin acceleration (α*) and the maximum linear acceleration (a*) of the Death Star are related via the mass concentration parameter X and the maximum deflection of an individual thruster (δ).
a* / R α* = X (δ+cos δ)/(π sin δ).
Example: We have deduced that the maximum angular acceleration of the Death Star II was about 0.0003 rad/s, and the radius was at least 400km. If the internal mass distribution is almost even, and if the thrusters can deflect by 10° in either direction then this particular (incomplete) battle station was capable of accelerating laterally by about 100 m / s², i.e. about ten G. If instead the thrusters can deflect by 30° then the maximum linear acceleration is 40 m / s², just over four G. If the thrusters can deflect as far as the local horizon, up to 90°, then the maximum sublight acceleration of the battle station is 24 m / s², over two G. Thus a Death Star appears to be much more sluggish than the 3000G accelerations that a star destroyer achieves in a straight line chase (e.g. chasing down the Millennium Falcon on several occasions).
Caveat: This relationship between maximum torque and maximum thrust only applies if the equatorial sublight drives are the only devices able to spin a Death Star. We could consider more fanciful alternatives, such as counter-rotating masses of hypermatter in the core acting as invisible, internal flywheels.
The hyperdrives were at least fast enough to allow Death Star I to arrive at Yavin from the Alderaan system within a day after the Millennium Falcon. (Lord Vader stated "This will be a day long remembered. It has seen the end of Kenobi; it will soon see the end of the Rebellion." This clearly indicates that only a few hours passed between the escape of Princess Leia and the Death Star's arrival at Yavin.)
When the battle station arrived in the Yavin it was on a heading towards the planet but at right angles to the sunlight. Thus the hyperspace course did not pass any point closer to the sun, nor did it point towards the sun. Is this kind of tangential course typical or necessary for hyperspace jumps?
The Death Star arrives in the Yavin system and heads towards the planet. The battle station is heading at right angles to the direction of the sun. Its hyperspace course into the system probably went in the same direction.
In terms of tides and celestial dynamics, the arrival of a Death Star is equivalent to the arrival of a new moon. The presence and motion of an object of this size has the potential to perturb the orbits of a planetary or satellite systems. The gravitational tug exerted on a nearby moon by the Death Star effects an exchange of orbital energy and angular momentum, and if an encounter is close enough and of the right duration then the size and eccentricity of the moon's orbit may be substantially permanently altered. A moon with a naturally short orbital period may suffer more severe perturbations, if it passes the Death Star multiple times. Less massive objects will tend to be more greatly affected. In extreme cases, a moon may be perturbed into collision with its planet, or unbound into interplanetary space.
In some planetary systems the orbits of the smallest moons and the planetary ring particles are a self-regulated by a delicate balance of orbital gravitational resonances. In such systems, the direct pertubation of one or more moons may eventually cause further perturbations, indirectly affecting other moons and planetary ring particles as well. The long-term dynamical effects may be chaotic.
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