# Constants/properties of a very small-scale and compact universe that is still recognisably like our own (and is it possible)

Is it possible to tweak the gravitational constant and the "starting amount" of matter so that:

• My universe has 1-5 galaxies
• There are a few thousand stars per galaxy (a solution with an order of magnitude more or less stars is fine)
• The orbit sizes relative to the sizes of the bodies of mass involved are at least 5 times smaller
• A planet like our own (preferably with tectonics aka. crust, mantle and core) that orbits a star and has 0.8 to 1.3G is 500-2000km (range is for a bit of flexibility although I don't mind going under 500km that much) in diameter and is able to be created by natural processes in the first place

I would prefer to keep the universe as tight, compact and generally small-scale as possible and any insights would be great to creating a more realistic vision of my universe before starting to actually design layout/properties of planets, stars, solar-systems, etc.

• I seem to recall that our universe wouldn't exist as we know it if the value of G were anything other than it is now (e.g., planets don't form, the Big Bang never happens, etc.). – Frostfyre Apr 27 '15 at 17:38
• @Frostfyre, it's not just G but a multitude of fundamental parameters, see en.wikipedia.org/wiki/Fine-tuned_Universe (But then again who knows if those parameters and the physics behind it were to be different what kind of an universe would be the result.) – Ghanima Apr 27 '15 at 18:03
• The transformation you describe is not well-defined. For example, the fine-structure constant $\alpha$ is equal to $k_\text{e}e^2/\hbar c$: so it should increase by 20... but $\alpha=c\mu_0/2R_\text{K}$, so it should decrease by 1/20? The answer is that the other constants need to change as well. You need to tell us the new values of exactly five constants to specify the new values of all the other physical constants. – 2012rcampion Apr 27 '15 at 18:40
• Now that this question is closed, I would ask the physics.se for help on choosing the new values of constants so that such a universe is possible. – 2012rcampion Apr 27 '15 at 19:10
• @Twelfth I've decided that changing the speed of light is too risky for trying to create a realistic semi-predictable universe because the energy produced from nuclear fusion would change which would in turn change how the stars in that universe would work (and if they're even possible with a stronger/weaker speed of light) so it's probably best to leave light alone so I've removed it from the original question. Also, I would think that raising the gravitational constant would solve both the 3rd and 4th requirement but I don't know what other side effects it has. – god of llamas Apr 29 '15 at 7:57

Not sure if you can get away with weakening gravity but leaving the other 3 forces the same...gravity at 95% weaker and magnetic attraction/repulsion at 100% may see your atoms fly apart at a molecular level.

Your universe is going to contain far less energy. Mass to energy conversion is based on the speed of light, so your stars that depend on these fusions as their heat source will have less energy to work with which may start to inhibit their ability to even become stars. Limiting gravity will also affect the pressure these stars are put under...you'll likely need far larger stars to support life on the planets surrounding it.

Also note that the generation of heavier elements is based on fusion occurring in extremely large stars. These extremely large stars will have to be much larger to get the pressures they require for large element fusion (a bit counter-intuitive to your idea). It's possible that the universe you describe here outright fails to generate oxygen and heavier elements out to iron.

Remember that a galaxy doesn't 'just form'...a single star creates heavier elements, goes supernova ejecting the newly formed elements, and then the resulting mass is there for the next systems to form from (repeat). A few thousand star systems is exceedingly tiny and I'm not sure if you are giving the room for large stars to create the elements we have in today's earth.

I think your biggest issue here is your stars need to be much larger to make up for the lower gravity, they emit far less energy, and it's doubtful heavy elements will form.

• Gravity isn't a meaningful force at the atomic level, weakening it has no effect on anything to do with chemistry. I do agree with the rest of your gripes--this micro-universe isn't going to have planets. – Loren Pechtel Apr 27 '15 at 18:40

In addition to Twelfth's objections I think you have an end-of-life problem with stars.

First, consider $E=mc^2$.

Assuming the periodic table is unchanged this means the energy output of fusion is only $1\%$ of what we see. You'll need a lot more mass to get the same energy output from a star--which is a good thing as you'll also need much of this extra mass just to hold the star together. (It would be $10\times$ if the star were the same size but the extra mass means the star will also be bigger. I'm not confident of my ability to figure out how much bigger.)

Second, consider the equation of the event horizon of a black hole: $$r_s=\frac{2GM}{c^2}$$

Both $G$ and $c$ have been cut to $1/10^\text{th}$ of our values, but note the $c$ term is squared. Thus $r_s$ is $10\times$ what it would be in our universe.

In our universe the smallest black hole that can form by simple compression is about 3 solar masses. Wikipedia says 2.95km per solar mass for the radius of a simple black hole, thus we are looking at 8.85km radius in our universe. In this universe that's 88.5km.

Now, lets look at neutron stars. Take, for example, one with mass $1.4~M_\text{Sun}$ and diameter $20~ \text{km}$. This is set by the degeneracy pressure and I don't think this will change in your universe. Note that the neutron star is considerably smaller than a black hole of the same mass--in other words, a neutron star can't exist because it's going to be crushed into a black hole.

Edit: I focused on the math too much and forgot to tie these two bits together:

The smallest stars are about .1 solar mass. However, in this universe they must be at least 10x this, 1 solar mass. At best we have a narrow band in which stars can become a white dwarf but that's a low bound, I don't think this band actually exists. Thus all dead stars become black holes.