GBE of a Quark Star

Introduction[]

Some astronomers are suggesting that black holes do not actually exist and that Quark Stars should take their place in preexisting models. However, Quark Stars are almost entirely hypothetical, and evidence for their existence is in very short supply aside from some small hints here and there, like certain supernovae with yields up to 200 times greater than that of the "standard model", suggesting a greater cause. First, to understand the concept of a Quark Star, one must understand Neutron Stars.

Neutron Stars are stars that form when a regular star goes supernova and collapses. The sheer gravitational pull is so strong that it crushes protons and electrons together, making the star into pure neutronic matter. This Neutron stars on average would have a mass 1.5x that of that sun, all condensed to around 20 kilometers; 19.3x smaller than the width of the state of Michigan in which I live. The gravitational pull at the surface of this star is 200 billion times that of earth's surface gravity, and possesses magnetic fields that range from 100 million to 1 quadrillion times as powerful as earth's. Even a teaspoon of this thing's volume can weigh 10 million tons.

Then comes the concept of a Quark Star. The existence of these kinds of stars is purely hypothetical and the evidence of such stars existing is in rather short supply, but the idea is that while a Neutron star is condensed into neutronic matter, Quark Stars are neutron stars condensed even further into pure quark matter. It's essentially the step between a Neutron Star and a black hole. These stars have a density of 10^17 g/cm^3 and a diameter of 10 kilometers.

For this blog, I will be attempting to calculate the gravitational binding energy that this kind of star yields.

The Calculation[]

Step 1: Finding the Mass[]

So I'll use the density and size stated in this picture.

First, I'll find the volume.

Volume of a sphere = 3/4 * pi * radius^3

So the diameter I'll be using here is 10 km, or 5 km for the radius.

Plugging 5 into that formula gives me 523.6 cubic kilometers, or 5.236e+17 cubic cm.

Next, the mass.

The density is 10^17 g/cm^3.

10^17 * 5.236e+17 = 5.236e+34 grams, or 5.236e+31 kg.

Step 2: Finding the Surface Gravity[]

Formula for surface gravity:

g = G * M / r^2

g = surface gravity

G = Gravitational Constant (6.67 * 10^-11)

M = Mass

r = radius

(6.67 * 10^-11) * 5.236e+31 / 5000 = 6.984824000000 × 10^17 m/s^2, or 7.12253828 × 10^16 g

I did this so I can use it in the planetary parameter calculator on stardestroyer.net.

Step 3: Finding the Gravitational Binding Energy[]

GBE formula:

U = 3GM^2 / 5r

U = Gravitational Binding Energy

G = Gravitational constant (6.67 * 10^-11)

M = Mass

r = radius

((3 * (6.67 * 10^-11)) * (5.236e+31)^2) / 5 * 5 = 5.4858808e+53 joules

5.4858808e+53 / 10^44 = 5485880800 Foe, or 5.48 GigaFoe - Solar System level

Next let's try the planetary parameter calculator on Stardestroyer.net.

http://www.stardestroyer.net/Empire/Tech/Beam/Calculator.html

Plugging in the surface gravity value from earlier in g's as 7.12253828e+16 and the planetary diameter as 10, that gets me...

Death Star Yield UL: 3.271E+44 joules, or 3.27 Foe - Solar System level

Death Star Yield LL: 5.483E+56 joules, or 5.48 TeraFoe - Solar System level

Results[]

GBE of a Quark Star = 5.48 GigaFoe - Solar System level

Death Star Yield UL: 3.271E+44 joules, or 3.27 Foe - Solar System level

Death Star Yield LL: 5.483E+56 joules, or 5.48 TeraFoe - Solar System level

GBE of a Quark Star

Contents

Introduction[]

The Calculation[]

Step 1: Finding the Mass[]

Step 2: Finding the Surface Gravity[]

Step 3: Finding the Gravitational Binding Energy[]

Results[]

Sources[]