The gravitational binding energy of the Milky Way?

[Solifugae]

How much energy is there keeping all of the stars and material together in the Milky Way? Or in other words, if the Daleks wanted to destroy it with a giant interdimensional extinction bomb, how much yield would it have to be packing? (and we're ignoring the fact that the central blackhole would soak most of it up.)

I don't know "math language" so I couldn't use the GBE formula cited on wikipedia. I tried a simple layman terms approximation just using the known parameters...

Assumed stars with mass of the sun (1.98892e+30 kilograms). They need to be accelerated to greater than 1000km/s to escape (but this figure is for our solar system's distance from the center, so it doesn't account for the much greater velocities needed for objects near the center).
This requires 9.945E+41 joules of relativistic kinetic energy for the sun.
The sun has a cross sectional area of 3.04385e+18 meters (half its surface area), and the sphere area of the 100,000 light year Milky Way Galaxy is
31,415,926,535 light years.

Therefore, the energy applied per square light year is 3.12431389e+52 joules.

However we still need to apply enough energy per the area that stars would reside in, so we need the difference between the sun and the sphere, which is 97,643,203.5, and we times the previous figure showing the amount of joules to get the required amount of energy per every area of the sphere that equals the area of the sun.

Gravitational Binding Energy: >3.05068017e+60 joules

This is 76.2670042 times the visible total mass-energy, and 30.5068017 times the total mass-energy estimate which includes dark matter and dark energy (You can find this cited on wikipedia).


So, have I gone wrong anywhere? I sort of doubt this has ever been calculated before, due to impossibility of occurrence in nature.

 

[emperor_of_localgroup]

Even though SDC is getting boring, this thread is one example I keep coming back to find something new, something that makes you ask yourself "why not think this way also?"

I would n't make any comment on your calculation of GBE, I also think no one has tried this before, but I wonder why have you jumped to finding galaxy binding energy instead of our solar system's binding energy first?

I'll look at your calculation in more details whenever I get some free time. But this thread can also raise another question. Are the masses of the planets and the sun are exact? Or some of the masses are converted into energy to hold them together, similar to nuclear binding energy? Does gravity come from mass conversion? Will breakup of a solar system generate incredible amount of energy?

Very interesting idea, IMO.

 

[Solifugae]

I wouldn't make any comment on your calculation of GBE, I also think no one has tried this before, but I wonder why have you jumped to finding galaxy binding energy instead of our solar system's binding energy first?

I don't know what that would be either. Wikipedia has the sun's binding energy listed(6.87e+41), but I'm not sure that that's exactly the same.

I'll look at your calculation in more details whenever I get some free time. But this thread can also raise another question. Are the masses of the planets and the sun are exact? Or some of the masses are converted into energy to hold them together, similar to nuclear binding energy? Does gravity come from mass conversion? Will breakup of a solar system generate incredible amount of energy?

I don't think that's the case. The reason the gravitational binding energy exceeds the total mass-energy is because of the space/distance between all the stars that the energy would be spread over in order to supply enough energy to each star to liberate its mass from the pull of all the other stars. In something like the sun, which is one body (more or less since we are talking about separating particles from each others gravity), the total-mass energy is higher than the binding energy by about 260,000 times. I included the total mass-energy of the galaxy after my calculation as an example of scale.