# Can a black hole attract the earth?

## Big Bang 5 RG, textbook

Mechanics 1 99 Newton's Law of Gravitation 10 Hemispherical Mountain How big are the gravitational forces between objects in everyday life (F2)? For example, how strongly are you attracted to the person sitting next to you? Let us calculate in orders of magnitude and assume that the distance between the body's centers of gravity is 1 m and that each of you has 100 kg (that's just an estimate). The force of attraction is then: F G m m r N N G = = ⋅ ⋅ ≈ - - 1 2 2 11 4 6 6 67 10 10 10, The force of attraction between you and your neighbor is only a millionth of a newton! At the same time, however, you are attracted to the earth with 1000 N, that is a billion times as strong as to the person sitting next to you (Fig. 10.9). Well, let's take something really heavy, like a big mountain. Our model mountain is a hemisphere with a 10 km (10 4 m) radius (Fig. 10.10) - and thus much higher than Mount Everest (8,848 m). The volume of a hemisphere is V = (4 r 3 π) / 6. Rock has a density of around 2500 kg / m 3. Density is mass per volume (see Chapter 2.6, p. 17), mass therefore density times volume: m V kg kg = = ≈ ⋅ ρ 2500 4 10 6 5 10 4 3 15 () π Our mountain has around 5 quadrillion kg! Not bad. How strongly are you attracted to him? We assume that you are 100 kg and 10 km from the center of gravity (this is not entirely true because the center of gravity is not in the base, but for an estimate the assumption is okay). The following then results for the attraction: FG mmr NNG = = ⋅ ⋅ ⋅ ⋅ ≈ - 1 2 2 11 2 15 4 2 6 67 10 10 5 10 10 0 3, (), Despite the gigantic dimensions you will only get around 1 / 3 N attracted to the mountain! You can of course measure this with precision equipment. Due to mountains, valleys or cavities in the earth, the acceleration due to gravity g changes slightly (see Fig. 5.18, p. 39). On the other hand, you are attracted 3000 times more strongly to the earth. So practically only the earth's gravity plays a role in everyday life! i Fig. 10.9: The forces of attraction between you and the earth or between you and your neighbor. The length of the arrows is not to scale. Fig. 10.10: A really large hemispherical mountain. The focus is on 3/8 of the height. Summary NEWTON'S brilliant idea was that one could use a general law of gravity to calculate both the fall of an apple and the orbits of objects in the sky. Every object attracts every object in the universe. For us in everyday life only the attraction of the earth is important. Z Cosmic vacuum cleaner A black hole is created when a star with more than 8 solar masses burns out and collapses. Its gravity then becomes so incredibly large that not even light can escape. So a black hole is a kind of cosmic vacuum cleaner. But this property has nothing to do with the mass alone! Regardless of whether you are near a star or a black hole with the same mass (Fig. 10.3, F7), the force of attraction is the same in both cases. That says the law of gravitation! But what then makes black holes so voracious? The high density or the resulting very small radius (see Fig. 2.20, p. 18). The force of attraction F G is proportional to 1 / r 2. Therefore, when approaching an object F G grows very rapidly. You can only approach the star up to position b (Fig. 10.11). But you get much closer to the black hole. You can see how great the force at c is already. Just before the black hole, F G becomes so gigantic that it cannot be shown in this diagram. That's the devastating effect of a black hole. i Fig. 10.11: Increased force when approaching a star or a black hole with the same mass. For testing purposes only - property of the publisher öbv