What if the Sun turned into a Black Hole?

This week, I’ve been writing about the sun. I blame the summer solstice for this, because the news that Monday was the longest day of the year fired my son’s imagination and got him asking question after question about the sun, and about the stars, and about related astronomical phenomena. So far, I’ve answered his questions about whether or not the sun can melt (it can’t) and what the hottest star is (H1504+65). Now it’s time to move on to his next question, one which demonstrates that he’s learned some interesting things.

“What if the sun turned into a black hole?” he asked, as we walked up the stairs to the front door of our condominium building. “Would it swallow the earth and all the planets?”

That one took me off guard, because I’m pretty sure that when I was five I didn’t even know what a black hole was. But then, I also realized that the first black hole was discovered the year I was born, so it’s not surprising the term wasn’t in common usage when I was five.

It’s a chilling thought, isn’t it? “Nothing escapes a black hole,” science fiction tells us. “Not even light.” Black holes are the great white sharks of space – remorseless predators consuming everything in their path. And we’d never see them coming. But they have one other thing in common with sharks.

black-holes-opener-615

They have an exaggerated reputation.

Newton’s Laws of Motion and Universal Gravitation

Although aspects of his laws have been superceeded by Einstein and his General and Special Theories, Newton’s laws remain an excellent (if ever so slightly inaccurate) model of motion. In brief, his three laws of motion state:

  1. If no forces act upon it, a body in motion will remain in motion and a body at rest will remain at rest, and velocity will remain constant in either case.
  2. If force is applied to an object, there will be a change in velocity proportional to the magnitude to which the force is applied.
  3. If body A exerts force on body B, then body B will exert a force of equal strength but in opposite direction on body A. This is also stated as “for every action there is an equal and opposite reaction”.

In addition, Newton put forth a law of universal gravitation. This law states that “two particles having masses m1 and m2 and separated by a distance r are attracted to each other with equal and opposite forces directed along the line joining the particles. The common magnitude F of the two forces is

eq4-02

where G is an universal constant, called the constant of gravitation, and has the value 6.67259×10^-11 N-m^2/kg^2.”

Yeah? What does this have to do with black holes?

I’ll get to that. But first, let’s cover what a black hole actually is.

Fine. What’s a black hole?

Does it surprise you to know that NASA has some good resources about black holes? It really shouldn’t.

A black hole is a region in space where the pulling force of gravity is so strong that light is not able to escape. The strong gravity occurs because matter has been pressed into a tiny space. This compression can take place at the end of a star’s life. Some black holes are a result of dying stars.

Because no light can escape, black holes are invisible. However, space telescopes with special instruments can help find black holes. They can observe the behavior of material and stars that are very close to black holes.

Black holes come in four size categories, representing both their mass and their physixal size. There are:

  1. Micro black holes. These can run all the way up to about 7.342 x 10-8 M (the mass of our Moon), and can get as big as 0.1 millimeters. Yes, it would suck if one hit you.
  2. Stellar black holes. These range up to 10 M in mass, and can be up to about 30 kilometers in diameter (0.5 x 10-4 R).
  3. Intermediate-mass black holes, which can get up to 1,000 M and up to about the mass of the Earth itself.
  4. Supermassive black holes. These are the monsters that lurk at the center of most galaxies, massing up to 1010 M and up to 400 astronomical units in size.

Wow. So, why do you say they have an exaggerated rep?

It’s true that the escape velocity of a black hole exceeds the speed of light, which is what it means to say that “no light can escape”. However, no black hole will be larger or more massive than the sum of all of the mass that went into making the black hole in the first place. So, outside the event horizon (the point at which gravity becomes too powerful to escape), the black hole has the same effect as any other object of the same mass. With that in mind, Newton’s law of universal gravitation tells us that – if the sun were to be instantly replaced with a 1 M black hole – there would no impact on our solar system. the r2 figure in the equation is measured from center of m1 to center of m2, so nothing changes.

Nothing?

Well, all right. That’s not true. Black holes have no luminosity – no energy would be generated and nothing would reach the Earth. So, to quote Randall Munroe’s Sunless Earth article, “We would all freeze and die.”

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