How Close Would We Have to Be to Fall Into a Black Hole?

How close would we have to be to be sucked in by a black hole? - Question posed by Amy.

Any object with mass has a gravitational field. This includes you, me, trees, planets, moons and black holes (to name but a few). Things like planets, though, have a really noticeable gravitational field- you have to do a bit of work if you don't want to fall onto one of them, and the closer you get the harder it gets to avoid falling because the force that you feel is stronger the closer you are to its source.

How do Black Holes suck you in?

Black holes take this gravity thing to the extreme. Up to a point, though, you can get away from one: you just have to gun your engines and pick up enough speed to break free of its gravity, just like you do to get away from any planet or moon.

If you get too close, however, you're stuffed. This is because the speed you need to be going to break free is faster than the speed of light, and that's impossible (even light itself, the fastest thing in the universe, can't get out). So you're trapped forever inside...

You can think of this point of no return as an imaginary sphere around the black hole: if you reach the surface of this sphere, there's no going back. Ever. This boundary is known as the 'event horizon'.

How close can you get?

That depends on how big the black hole is. Or, more specifically, how much mass* it contains. A black hole's gravitational field is so strong because there is a lot of mass in a black hole. Heavier black holes have stronger gravity, which means you can feel its effects from further away. More importantly, this also means that the event horizon is further away.

Let's put some numbers on it (we can calculate it using a relatively simple formula**):

If we were to turn the Sun into a black hole right now (not sure why we'd want to, but go with it...), its event horizon would be about 3km away from its centre. That's about the size of Kettering. It's about 0.0004% of the Sun's current size- we wouldn't be able to see something that small from where we were (even if it wasn't black).

In contrast, the black hole which astronomers think is at the centre of our galaxy, with a mass approximately 4 million times that of our Sun, can be calculated to have an event horizon about 10 million kilometres away. That's getting on for the size of our entire solar system.

* Remember that 'mass' is just 'stuff': rocks and cats and planets and biscuits and socks and black holes all have 'mass' and it's measured in kilograms.
** And that formula is:
2GM / c2

Where "G" stands for the gravitational constant (this has a known value); "M" stands for the mass of the black hole (I'm using the mass of our Sun for the first example); and "c" stands for the speed of light (this also has a known value). All we do is whack in the mass we're looking at and, hey presto, we get a number for the radius of the event horizon.


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