PhD comics and mini black holes

Bad Astronomy
The entire universe in blog form
Nov. 20 2007 10:14 AM

PhD comics and mini black holes

The second part of the PhD comic strip I mentioned yesterday is out, and lots of astrobloggers are linking to it. But no one seems to have noticed the glaring error in it:

Phil Plait Phil Plait

Phil Plait writes Slate’s Bad Astronomy blog and is an astronomer, public speaker, science evangelizer, and author of Death From the Skies!  

Advertisement

Black holes are at the center of a lot of misconceptions. Basically, they are objects where the escape velocity is greater than the speed of light. If you throw a rock straight up off the surface of the Earth, you must give it a velocity of 11 km/sec for it to be able to get away from the Earth and not fall back down*. That's because the Earth's escape velocity is 11kps. It depends on the size of the object and its mass, or, if you prefer just its density.

Black holes are so small and so massive (or just plain dense) that their escape velocity is faster than light. You literally cannot escape them once inside their ravenous maw. The size of a black hole is actually rather simple to calculate if you know its mass:

radius = 2 x G x mass / c2

G is Newton's Gravitational constant of the Universe, and is just a number. c is the speed of light. It turns out that for a star like the Sun, it would have to be crushed to a diameter of about 6 kilometers to becomes a black hole. But look at the equation! If I double the mass, the size of the black hole doubles. So it's really easy to scale this equation to different mass black holes.

The one in the center of the Milky Way Galaxy has a mass of roughly 4 million times the Sun's mass, so it must be 4 million times bigger, or 24 million kilometers across, far less than the distance between the Sun and Mercury (for comparison, the Sun is about 1.4 million kilometers across right now).

Black holes are small.

However, they can get even smaller. There is a hypothesis that just after the Big Bang, fluctuations in the density of matter may have compressed small amounts of material so much they collapsed into black holes. These are called mini black holes. If you plug in the mass of, say, a typical mountain or asteroid into the equation above, you'll see that a mini black hole is actually far smaller than an atom!

I won't even go into Hawking radiation, which says that a black hole that small would have a surface temperature of 10 billion Kelvins. That would make them a bit obvious if they were pelting us; they'd be pretty bright.

I will add that from a centimeter away, the gravity of a mini black hole can be hundreds of times that of the Earth, but from a few meters away you'd hardly notice it.

So the author of PhD comics got tripped up a bit by the scale of things (a black hole the size of a pea would have a mass comparable to that of the Earth). But that's not too surprising; obviously, black holes are weird, and difficult to comprehend. Now, if only someone were writing a book that had a whole chapter (plus part of another chapter) dealing with the potential dangers of black holes including an easy-to-understand description of how they form, what escape velocity is, and what happens when you fall into one, and what would happen if a mini black hole hit the Earth ...

Mwuhahahahaha. But you'll have to wait until next year for that book.

* Actually, it's a bit more complicated than this. Escape velocity is for an impulse, a forcer applied all at once. If you apply a smaller force, but do it over a long period of time, you can escape the Earth never having gone 11 kps.

TODAY IN SLATE

Culturebox

The End of Pregnancy

And the inevitable rise of the artificial womb.

Doctor Tests Positive for Ebola in New York City

How a Company You’ve Never Heard of Took Control of the Entire Porn Industry

The Hot New Strategy for Desperate Democrats

Blame China for everything.

The Questions That Michael Brown’s Autopsies Can’t Answer

Foreigners

Kiev Used to Be an Easygoing Place

Now it’s descending into madness.

Technology

Don’t Just Sit There

How to be more productive during your commute.

There Has Never Been a Comic Book Character Like John Constantine

Which Came First, the Word Chicken or the Word Egg?

  News & Politics
The Slate Quiz
Oct. 24 2014 12:10 AM Play the Slate News Quiz With Jeopardy! superchampion Ken Jennings.
  Business
Moneybox
Oct. 23 2014 5:53 PM Amazon Investors Suddenly Bearish on Losing Money
  Life
Outward
Oct. 23 2014 5:08 PM Why Is an Obscure 1968 Documentary in the Opening Credits of Transparent?
  Double X
The XX Factor
Oct. 23 2014 11:33 AM Watch Little Princesses Curse for the Feminist Cause
  Slate Plus
Working
Oct. 23 2014 11:28 AM Slate’s Working Podcast: Episode 2 Transcript Read what David Plotz asked Dr. Meri Kolbrener about her workday.
  Arts
Brow Beat
Oct. 23 2014 6:55 PM A Goodfellas Actor Sued The Simpsons for Stealing His Likeness. Does He Have a Case?
  Technology
Technology
Oct. 23 2014 11:47 PM Don’t Just Sit There How to be more productive during your commute.
  Health & Science
Science
Oct. 23 2014 5:42 PM Seriously, Evolution: WTF? Why I love the most awkward, absurd, hacked-together species.
  Sports
Sports Nut
Oct. 20 2014 5:09 PM Keepaway, on Three. Ready—Break! On his record-breaking touchdown pass, Peyton Manning couldn’t even leave the celebration to chance.