Gravitational force of a neutron star

[OmegaOm]

Maybe I can make an analogy on the topic. Newtons formula speaks for itself, but to put it into another picture.

Imagine you are on the surface of the sun with mass 1 sun. The suns radius is about 700,000 km. You have the whole mass of the Sun pulling on you. Since gravity gets weaker with distance, you have half the mass of the Sun pulling on you from within that 700,000 km radius and the other half pulling on you from up to 1.4 million km away.
Now shrink that mass to about a couple of km. Now you have the whole Suns mass pulling on you from within a couple of km. Your more closer to it all!, so it is stronger.

 

[Hornbein]

Thank you, I think I'm now at the root of my problem here. Is it possible to answer why exactly the center of gravity determines the force instead of the total amount of mass beneath you without saying that it's just the way how nature works? I think I'm trying to understand the roots of how gravity works here.

It was all worked out by Isaac Newton in the 17th century. Europe was most impressed. The idea is that you sum up the gravitational attraction of every tiny piece of each body. The result is surprisingly simple.