Can an object the size of a basketball be so dense as to not allow light to escape?
If this basketball size object was to fall into the sun, would the sun be absorded? Would it dissapear? Would it be the end?
The short answer is yes, such an object could exist. In order for an object to become a black hole (defined as an object so dense that light cannot escape from it), it must contract to a size smaller than its "Schwarzschild radius," a characteristic that is a function of mass. For a Schwarzschild radius equal to that of a basketball, which is about 12 cm, the equivalent mass is 8.17x10^25 kg. That sounds like a lot, but it is only about 85 times the mass of the Earth, or a mere .00004 solar masses. A black hole of this size cannot form in the Universe today, because it requires about 3 solar masses for a black hole to form from the influence of its own gravity, and the required external pressures for non-self-gravitational black hole formation only existed immediately after the Big Bang. However, if such an object had formed at the birth of the Universe, it could still exist today.
If such an object were to fall into the Sun it could cause the Sun to collapse into it. It really could "fall into the Sun," because even though it would be a black hole, it would be much less massive than the Sun. For that reason, it could just as easily fall into orbit around the Sun instead. (A black hole of sufficient mass would instead suck the Sun into it without moving very much itself.) The Sun's mass would then be added to that of the black hole, but everything else that distinguised the Sun from other pieces of matter would most likely be lost forever. Everything living on Earth would soon die due to lack of sunlight. Oddly enough, though, there would probably be very little effect on the orbits and revolution of the Earth and other Solar System bodies, because the Sun would have been replaced by an object of almost identical mass, and it's the Sun's mass that governs most of the behavior of such bodies, not its other properties.
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