Why is the attraction of a black hole stronger than that of a star with the same mass?

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Black holes come in a variety of sizes and masses. There are known, for example, supermassive black holes, the mass of which is equal to millions of masses of our Sun, and there are black holes of stellar masses, the mass of which usually ranges between 5 and 10 masses of our Sun.

It is also well known that there are stars of similar masses. A reasonable question arises, why, then, the surface gravity of stars is less than the surface gravity of black holes of similar masses?

The question is quite reasonable and requires an explanation. In general, to give a really correct explanation, you will have to go into the jungle of general relativity and torment readers with a rather complicated matan, which I don’t want to do, so I’ll explain what is called “on the fingers”.

At school, we all learned Newton’s laws, including the law of gravitation. However, for some reason it so happened that many forget that, according to the law of universal gravitation, the attraction between bodies depends not only on the mass, but also on the distance between them.

Let’s take a look at a simple example. Let’s say we have our Earth. Let us denote its mass as

Let’s say on the surface of each of the planets there is an ordinary person with a mass

It is easy to make sure that on Earth the force of gravity will be equal to:

And on another planet:

Those. the force of gravity on a planet half the radius of the Earth will be 4 times greater! If this planet was 4 times smaller, then the force of gravity would be 16 times more, if it was 10 times less, then the force of gravity would generally exceed the Earth’s by 100 times !.

The fact is that the surface gravity of an object depends not only on its mass, but also on its size. For example, the mass of Jupiter is more than 300 times the mass of the Earth, but at the same time, due to its gigantic size, its surface gravity is only 2.5 times greater than that of the Earth.

It is the same with stars and black holes. A star and a black hole may have the same mass, but the surface gravity of a black hole will always be incomparably greater. For example, for a black hole with a mass equal to 5 solar masses, the radius of the event horizon will be slightly less than 15 kilometers. The radius of a star with such a mass can be measured in hundreds of thousands or even millions of kilometers. The smaller the distance with the same mass, the greater the force of attraction.

It is worth noting that this is a rather crude simplification, since the laws of classical mechanics work very badly for black holes, but still I think it should give some kind of consistent picture.