sexta-feira, 17 de abril de 2015

Escaping a Supermassive Black Hole

Recently I got interrested in the stars. And with the help of sky charts and iPhone apps, I can already recognize Venus, Saturn, Syrius, Procyon and a few other ones every night that has no clouds (which seams to be less than half here in Wroclaw). I also managed to predict (using tables in the internet) and view my first meteor :) A Virginid in 21st April.

Anyway, when studying the cosmos, very often the topic ends up landing in black holes ... because they are scary, massive and apocaliptic. So I decided to write a bit on the topic.

So, what are the real dangers? How close can we get to such a thing and still survive to escape from it? How likely are we to just crash into one of the millions of black holes suspected to be in our galaxy? Aprox. 1 in every 1000 stars is a black hole and our galaxy has billions of stars, so that makes millions of black holes.

In particular this internet discussion made me want to write this text:

1> Danger of an eventual colision with the earth

Nothing travels faster than light, which travels at 300 000 km per second (3 * 10^8 meters per second). So we don't have to worry, since the closest black hole is probably 7 000 light-years away ( ). Even if someone installed Star-trekish warp engines on it, aimed at the earth, and went with full speed forward, it would still take at least 7 000 years for it to get here. Anyway, knowing that it is impossible for a black hole to accelerate to the speed of light, and that most stars in our galaxy orbit our galatical central black hole with equal speeds, a colision is extremely unlikely.

The center of our galaxy has a supermassive black hole, with 7 million sun masses and 26 000 light years away, but just like everything else in our galaxy, we are orbiting this black hole and we won't crash into it anymore than the moon would crash the earth or the earth would crash into the sun. We are in normal orbit around it with a speed of 220 km/s (792 000 km/h) or 0.073% of the speed of light. It takes the Solar System about 240 million years to complete one orbit of the Milky Way. At this speed, it takes around 1,400 years for the Solar System to travel a distance of 1 light-year.

2> How close can we get and still orbit the largest blackholes ever found? What g (gravitational acceleration) would we feel? How fast do we need to go to orbit it? How close could we get to it and still be able to escape?

I looked up in wikipedia the following equations, simplified considering that the black hole mass is ridiculously higher then ours:

A - Gravitational acceleration
G - Gravitational constant G=6,674 * 10^-11 * m^3 * kg-1 * s-2
M - Mass of the black hole
r - Distance

And similarly the speeds to orbit and escape (get out of orbit) of a black hole are:

Vorbit = square root ( G * M / r)
Vescape = square root ( 2 * G * M / r)

Taking a look at the known black holes, we can see that they range from small ones of 10 times our sun's mass, to small supermassive ones like the on our galatical center (7 million sons), to true monsters of aprox. 20 billion sun masses. Source:

So lets start with the worse one. What if we had an encounter with a beast of 20 billion sun masses. Could we get into orbit and avoid falling into it? The first step was to check if my equations are right, so I applied it to see how fast an satelitte would need to go to orbit the earth. The earth has a radius of 6370 km, so to round the numbers I setup an orbit 7000 km from the center, so 630km from the surface:

Distance in m mass in suns kg per sun G Acceleration (m/s^2) Vorbit (m/s) Vorbit (km/h) Vorbit (in c)
7000000 3,00E-006 1,99E+030 6,67E-11 8,13E+00 7545,78 27164,8 2,52E-05

The result is that at an altitude of 630 km there is g = 8 m/s/s, and we need 27 thousand km/h to orbit it. Which is correct!

Now, let's apply this to the beast:

Distance Distance in m mass in suns kg per sun G Acceleration (m/s^2) Vorbit (km/s) Vorbit (km/h) Vorbit (in c) Vescape (km/h)
1 AU 1,5E+11 2,00E+010 1,99E+030 6,67E-11 1,19E+08 4212691,37 1,5E+10 1,40E+01 21447E+6
100 AU 1,5E+13 2,00E+010 1,99E+030 6,67E-11 1,19E+04 421269,24 1,5E+9 1,40E+00 2144E+6
1000 AU 1,5E+14 2,00E+010 1,99E+030 6,67E-11 1,19E+02 133217,66 4,79E+8 4,44E-01 678E+6
1 light year 9,46E+015 2,00E+010 1,99E+030 6,67E-11 2,97E-02 16752,56 60307E+3 5,58E-02 85E+6
10 light year 9,46E+016 2,00E+010 1,99E+030 6,67E-11 2,97E-04 5297,31 19070E+3 1,77E-02 26E+6
100 light year 9,46E+017 2,00E+010 1,99E+030 6,67E-11 2,97E-06 1675,36 6030E+3 5,58E-03 8528E+3
1000 light year 9,46E+018 2,00E+010 1,99E+030 6,67E-11 2,97E-08 529,13 1907E+3 1,77E-03 2697E+3

So we need to be at least 1000 astronomic units (distance from earth to sun, 150 million km) to be significantly outside the event horizon, but still at this distance the orbit velocity is 44% of the light speed, impossibly high. The gravity is also huge, at 119 m/s/s, although we would not feel it since it would be a free fall. We only feel gravity on earth because of our contact with other objects. Without a surface to contact at this distance, we would be in free fall. Now comes the tricky part. While we would not feel the acceleration that the black hole causes in us, to escape it, by firing the ship engines, we would feel the acceleration that the ship causes on us because of our contact with the ship. At aprox. 15 G humans would die (humans can survive at most 3-6 G), and the ship itself would need to be really, really thoughly built for it to survive itself. So humans basically have no chance of surviving at this distance. Death is a question of time.

At 1 light year away the gravity is smaller, 0,03 m/s/s so it should be easy to avoid a crash by simply aiming our ship engines towards the hole and firing them. Any rocket can easily provide such an acceleration. But this means that we need to burn fuel to keep our position, and fuel will eventually run out. To get into a stable orbit so that we can keep our distance without falling we would need 5,5% of the light speed ... which is insanely high. So at this position we cannot keep an orbit, but it is possible to escape already. And it is 63 times further away from our studied position of 1000 AU.

To keep an orbit, we would need to be at least 1000 ly away. Here we would need 1,6 million km/h to obtain orbit, a huge speed, but still it should be possible to obtain it if we have enough fuel.

Conclusion: We are lucky to be so far away from this develish objects!!!

If you have fuel, its not that hard to escape, and you can go as close as 1 ly and come back alive. The black hole is a patient beast, so it will make a small force at you, so that while a rocket can easily escape, if you have no fuel, bye-bye! Its lunch time, and you are the dish.

3> The same calculation for Sagittarius A, the black hole in our galatic center:

Distance Distance in m mass in suns Acceleration (m/s^2) Vorbit (km/s) Vorbit (km/h) Vorbit (in c) Vescape (km/h)
10 AU 1496E+9 4,10E+006 2,43E+02 19073,77 6,87E+004 6,36E-05 9,71E+004
100 AU 14960E+9 4,10E+006 2,43E+00 6031,66 2,17E+004 2,01E-05 3,07E+004
1000 AU 149600E+9 4,10E+006 2,43E-02 1907,38 6,87E+003 6,36E-06 9,71E+003
1 light year 9,46E+015 4,10E+006 6,08E-06 239,85 8,63E+002 8,00E-07 1,22E+003
10 light year 9,46E+016 4,10E+006 6,08E-08 75,85 2,73E+002 2,53E-07 3,86E+002
100 light year 9,46E+017 4,10E+006 6,08E-10 23,99 8,63E+001 8,00E-08 1,22E+002
1000 light year 9,46E+018 4,10E+006 6,08E-12 7,58 2,73E+001 2,53E-08 3,86E+001
25000 light year 2,37E+020 4,10E+006 9,73E-15 1,52 5,46E+000 5,06E-09 7,72E+000

The picture is similar, but with a mass 1000 times smaller, we could even get as close as 100 AU and a rocket could still guarantee our escape. Don't be too confident, however, since at 10 AU death is certain due to the acceleration which cannot be overcome. The solar system is travelling very fast, at over 200 km/h similar to the orbiting speed at 1 ly, which would be the closest we could get and still be able to obtain a stable orbit.

Note however, that all of these close distances are very optimistic since the disk of stuff close to the black hole, called Accretion Disc, is full of stars and gamma radiation, so a lot of dangerous stuff could be found much further away from the no-return point that ever.

4> Final conclusions:

There is nothing to worry. No black holes are coming in our direction, and even if you take a space ship and go out to find one, well, you will have died a long time before the ship finds one, since the distances in the galaxy are so huge. And even when facing the most insanely huge black holes (which are also insanely far away) one has multiple survival options, like building a rocket to fights its gravity and go to a place where you can obtain a good orbiting position.

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