Yes, it has been done, I think a few here on SFJN. But a lot of assumptions have to be made, like the size of Yavin Prime and the exact path the Death Star took while orbiting the gas giant, etc.Mr. Oragahn wrote:Has anyone calculated the energy needed to accelerate that big ball of doom though? (assuming the reactors provide the energy and not local fission/fusion thrusters or else)
A couple years ago, during the "Brian Young's new website is up!" I worked out the photometrics to show that Yavin 4 was not subtending a small enough width of the screen in one screencap to place it far enough away for Yavin Prime to be a Jupiter-sized gas giant, but rather a Neptune or Uranus-sized one. And although that was applied to the speed of the X-wing and Y-wing fighters, it can most certainly applied to the Death Star and its trip around Yavin Prime, and remember it was expected to take the Death Star at least 30 minutes to travel at most one-half the circumference.
Given a 60,000 km diameter, 188,495 km will be the circumference and half that is 94,247.7 km. So now that we have a distance and a time we can get a velocity of 30 minutes x 60 seconds = 1,800 seconds which is then divided into 94,247.7 km = 52.36 km/sec.
So then we need to figure out how big is the first Death Star is and what kind of mass it might have. Since the ICS and the rest of the EU are gone, we're back to good old fashioned scaling from the movie, and I opt for a sensible scaling like
this one.
And so a Death Star 1 of 120 km is quite reasonable, and a volume of 9.047E14 m2. Also to be extra fair, instead of assuming the thing is mostly made of steel as the novelizations have suggested, why don't we assume that it is made of Trek materials and has Trek ship densities. Call it 453 trillion metric tons.
Thus the following:
mass (m) =453000000000000 ton metric =4.53E+17kilogram
velocity (v)= 52 kilometer/second =52000 meter/second
Solution:
kinetic energy (K) = 6.12456E+26 joules
That's the maximum output of the Death Star, if you go by that, which is well short of the minimum 1e32 joules needed to blow an Earth-sized apart.
-Mike