Science fiction aspects concerning the Law of Gravitation

Recently I thought of an interesting problem regarding the Law of Gravitation and in relation to matter density.

The problem goes this way. If the problem of matter density, and subsequent containment systems were neglected and assuming that at minimum matter density of such system were neither collapsing to the a known Schwarzschild radius, what might a gravitational field look like even if it were fictitious?

The consideration of the Law of Gravitation isn’t merely that compactification of matter as one might ordinarily reason, but let’s say that an object eight times the mass of the moon were compacted into a sphere approximately 1 meter.

As it turns out the computed Schwarzchild radius of this object defining a black hole is 1.09 e^(-16) meters that is assuming that the mass of the object is around 5.88 e^(11) kg. Again this is a pretty big and dense object. One should wonder that this object is also quite hot like a star if not hotter?! Let’s assumed there is corresponding outward inflationary pressure in the interior of such object avoiding the problem of gravitational collapse likewise. We’ll neglect the possibility of incinerating nearby matter likewise.

But what are the interesting properties of this highly compact exotic mass object?

One notices that acceleration in this at the surface of such object is approximately similar to that of Earth! And at scale 10 factors of r (m) acceleration (g) falloff is considerably smaller relative to surface acceleration.

Now let’s look at acceleration falloff relative to height from the surface Earth as it relates to gravity

Here we can see a difference in altitude relation and a corresponding falloff in acceleration (g). Greatest field strength difference occurs at 1,000,000 m

or 1000 km but even so acceleration has not diminished by magnitude orders.

Perhaps the purpose of this thought exercise is mostly in pointing out that mass of an object and density could provides relation to gravitational acceleration at a point. Field intensity strength between these massive objects obviously varies comparatively in stark contrast, but an equivalence in acceleration per surface altitude is provided given density differences in such objects. As it turns out surface gravity is nearly identical between the two, but it is only when surface altitude is gained that the difference between such are noticeable.