Synthesizing gravity

Question

There are substances with such massive density that a relatively small volume, could contain an immense mass. Given a substance like neutronium, could you conceivably synthesize gravity for a space station by placing the substance at the core and then building a structure that places the "floor" at an appropriate distance from the core?

Force of Gravity equation

F_grav = (G m1 m2)/d²

I am asking specifically about whether there are other factor to consider or if this theoretically true. This is not proposing building it.

Answer 1

It's "theoretically true" in that mass is what creates a gravitational pull.

The fact is impossible to do anything useful with, because you need to hold the mass at a particular distance from the floor, and any structure you built to support the floor above the core mass would be subject to a much greater force (because of the inverse-square law), and so supports, floors, crew, and spacecraft would all pretty instantly turn into a thin plating on the surface of a neutronium sphere.

Furthermore, to get a significant gravitational force, you'd need so much mass that it would be impractical to try and move the ship.

You could consider a thin spherical shell around a massive core, but it would be positionally unstable; when one side moves towards the core even by a millimeter, it will be pulled more and more rapidly to the core. You'd need some sort of active thrust system to monitor and keep it stable -- and how would you assemble such a thing?

"Neutronium" as in real neutron star material wouldn't work for this, by the way; it doesn't remain stably dense at the smallish volumes you'd want for synthesizing gravity. Neutron stars can't exist below about 0.2 solar masses (~4e29 kg). To get 9.81 m/s² (Earth surface gravity) acceleration at the floor, with the floor 100m above the center of the massive core, you'd need about 1.5e15kg, a 19cm diameter sphere of the stuff, which would instantly explode, since it isn't heavy enough to hold itself together.

Answer 2

Hmmm, why do people always insist on a spherical mass and the $\frac{1}{r^2}$ law?

Gravity and electrostatics are very very similar. For electrostatics, Maxwell's first equation is

$$\frac{Q}{\varepsilon_0}=\int_A\vec{E}d\vec{A}$$

Which means: If you have a closed surface and sum up the product of surface times perpendicular E-field, you get the charge enclosed divided by $\varepsilon_0$. In case of a spherical charge distribution, you can put a sphere of radius r and surface $4\pi r^2$ around it. The field is constant and perpendicular at each point of the surface, so the equation becomes simple and gives a well known result:

$$\frac{Q}{\varepsilon_0}=4\pi r^2 E \quad \Rightarrow\quad E=\frac{Q}{4\pi\varepsilon_0 r^2}$$

Now, if there's an infinite plate with charge Q, you would place two planes on both sides of it as surface. This time, you get

$$\frac{Q}{\varepsilon_0}=2A E \quad \Rightarrow\quad E=\frac{Q}{2A \varepsilon_0}=\frac{\rho}{2 \varepsilon_0}$$

Here, $\rho$ ist the charge per surface.

The result is remarkable because first, the field is parallel everywhere and points to the plate and second, it does not depend on distance!

Back to gravity, we know a sphere gives

$$a=G\frac{M}{r^2}$$

Comparing this to the formula for a spherical charge gives $$G\equiv\frac{1}{4\pi\varepsilon_0} \quad\Rightarrow\quad2\pi G\equiv\frac{1}{2\varepsilon_0}$$

which can be used for the formula of the plate. So, a plate with given weight per surface $\rho$ generates a constant (!) gravitational field of

$$a=2\pi G\rho$$

For a=9.81m/s², one gets $\rho=23.4\cdot10^9kg/m^2$.

Osmium has a density of $22.6\cdot10^3kg/m^3$, so the plate would have a thickness of 1000km. Neutronium, having a density of $3\cdot10^{17}kg/m^3$ would only require a layer of 0.08µm.

BUT:

The command module of the apollo missions had a diameter of 3.9m, or a base area of 12m². This would require a "neutronium carpet" with a weight of 280,800,000t (For comparison: Entire Saturn V: 3,000t; cheops pyramid: 6,500,000t). So, no way to lift/move this, and even no way to support it while the rocket is on the ground.

Further more, the field of this plane can't be considered constant,since the dimension of the module is large compared to the diameter. A space ship shaped more like a flying saucer would be better.

And as said in the other answers: Neutronium only exists under high pressure. Under "normal" conditions, it would for sure expand (explode?)to a more common type of matter.

Answer 3

Lets calculate the necessary mass for a distance of 10 m and a "gravity" of 9.81 m/s*s. It is only 14.7E12 kg, that is many orders of magnitude too much.