The spectacle also probably broke the movie's illusion somewhat- because we all asked ourselves whether such a thing as this were possible in the real world? Is it scientifically possible to destroy a planet like the Death Star destroyed Alderaan?
In a word: yes.
And the method is actually fairly simple as well. For something to be capable of destroying a planet (or star, or other astronomical object that is a sphere with a roughly average density), it needs to generate enough energy (in joules) to overcome that object's gravitational binding energy. That is, the energy by which a planet's gravity binds its mass together as a single object. Equal or exceed that, and the planet's mass is scattered far enough so that its gravity will not pull it back together again. This means that the debris will equal or exceed a planet's escape velocity (more on escape velocity in another post).
The equation for figuring out gravitational binding energy is as follows:
The gravitational binding energy of a spherical astronomical object (like a planet or star) is U. G is the gravitational constant (6.67x10^-11), M is the mass of the object, and r is its radius in meters (keep that in mind, because if you put its radius in kilometers, as you may find preferable when dealing with objects this big, you will get nonsensical results).
Now let's use the Earth as an example of putting this equation in action.
The Earth's mass, as you may know, is 5.97219×10^24 kilograms. Its radius in meters is 6,378,100.
Now with my favored calculator, this is very easily solved:
5.97219×10^24 = 5972190000000000000000000
6.67x10^-11 = 0.0000000000667
3 x 0.0000000000667 x 5972190000000000000000000^2 / (6378100 x 5) = 223796346390292093256612470798513.66394380771703171790972.
There is your gravitational binding energy in joules. Obviously this is a large and very abstract number that is difficult for most people to make sense of. For this reason, I generally prefer to break the joules down into TNT equivalent, which is far easier to grasp.
Using a simple energy converter, you will find that the answer in terms of TNT equivalent is 5.3488610514e+22 tons of TNT. That's 53.488 sextillion tons, which you can verbalize using this numbers to words converter. In metric prefixes, the number sextillion is denoted by the word "zetta." So the gravitational binding energy of Earth is 53.488 zettatons of TNT.
This is obviously, again, a staggering amount of energy (though not as much as the kinetic energy of the planet's orbit). For some perspective, the Tsar Bomba, the most destructive weapon ever constructed by man, at around 50-60 megatons (the word "mega" denotes the number million in metrix prefixes), was a quadrillion times less powerful.
This equation isn't perfect, of course. It assumes both uniform density (which astronomical objects do not possess), and a perfect sphere (which again, the Earth and other bodies are not), but this is a good estimate of the Earth's gravitational binding energy and is more than usable in a scientific context.
And if you're lazy and don't want to use the equation, you can try the SD.net Planetary Parameter Calculator, and look for the "Death Star yield LL." It will be second from bottom on the right. By inputting the parameters of your object to the left, the calculator will tell you the gravitational binding energy of your object, though the surface gravity requirement might be a hassle if you're looking for an answer for an exotic star, for instance.
So, summing up...
1. To destroy a planet, star, or other large spherical object in space, you must overcome its gravitational binding energy.
2. To solve for this you can do the equation given above.
3. This equation is only a (good) approximation most of the time however, because it assumes perfect spheres and uniform density, which most astronomical objects do not have.
As a final note, you can use the kinetic energy equation to get a more accurate measurement of the power of a planet destroyer like the Death Star. By taking the velocity of a planet's mass scattering beyond its original radius, you can find the energy behind the attack. This will often be far higher in entertainment media than the bare minimum gravitational binding energy. Such was the case with the Death Star. Planet Busters Death Star Destroyers Star Wars Binding Energy Astronomy
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