Week of October 15, 2018

Astronomy

What Is a Black Hole?

An artist's drawing a black hole named Cygnus X-1. It formed when a large star caved in. This black hole pulls matter from blue star beside it.

Credits: NASA/CXC/M.Weiss

An artist's drawing shows the current view of the Milky Way galaxy. Scientific evidence shows that in the middle of the Milky Way is a supermassive black hole.

Credits: NASA/JPL-Caltech

This image of the center of the Milky Way galaxy was taken by the Chandra X-ray Observatory.

Credits: NASA/CXC/MIT/F.K. Baganoff et al.

Sagittarius A* is the black hole at the center of the Milky Way galaxy.

Credits: X-ray: NASA/UMass/D.Wang et al., IR: NASA/STScI

This article is part of the NASA Knows! (Grades K-4) series.
 

A black hole is a place in space where gravity pulls so much that even light can not get out. The gravity is so strong because matter has been squeezed into a tiny space. This can happen when a star is dying.

Because no light can get out, people can't see black holes. They are invisible. Space telescopes with special tools can help find black holes. The special tools can see how stars that are very close to black holes act differently than other stars.

How Big Are Black Holes?
Black holes can be big or small. Scientists think the smallest black holes are as small as just one atom. These black holes are very tiny but have the mass of a large mountain. Mass is the amount of matter, or "stuff," in an object.

Another kind of black hole is called "stellar." Its mass can be up to 20 times more than the mass of the sun. There may be many, many stellar mass black holes in Earth's galaxy. Earth's galaxy is called the Milky Way.

The largest black holes are called "supermassive." These black holes have masses that are more than 1 million suns together. Scientists have found proof that every large galaxy contains a supermassive black hole at its center. The supermassive black hole at the center of the Milky Way galaxy is called Sagittarius A. It has a mass equal to about 4 million suns and would fit inside a very large ball that could hold a few million Earths.

How Do Black Holes Form?
Scientists think the smallest black holes formed when the universe began.

Stellar black holes are made when the center of a very big star falls in upon itself, or collapses. When this happens, it causes a supernova. A supernova is an exploding star that blasts part of the star into space.

Scientists think supermassive black holes were made at the same time as the galaxy they are in.

If Black Holes Are "Black," How Do Scientists Know They Are There?
A black hole can not be seen because strong gravity pulls all of the light into the middle of the black hole. But scientists can see how the strong gravity affects the stars and gas around the black hole. Scientists can study stars to find out if they are flying around, or orbiting, a black hole.

When a black hole and a star are close together, high-energy light is made. This kind of light can not be seen with human eyes. Scientists use satellites and telescopes in space to see the high-energy light.

Could a Black Hole Destroy Earth?
Black holes do not go around in space eating stars, moons and planets. Earth will not fall into a black hole because no black hole is close enough to the solar system for Earth to do that.

Even if a black hole the same mass as the sun were to take the place of the sun, Earth still would not fall in. The black hole would have the same gravity as the sun. Earth and the other planets would orbit the black hole as they orbit the sun now.

The sun will never turn into a black hole. The sun is not a big enough star to make a black hole.

How Is NASA Studying Black Holes?
NASA is using satellites and telescopes that are traveling in space to learn more about black holes. These spacecraft help scientists answer questions about the universe.

More About Black Holes
Space Place in a Snap: What Is a Black Hole?
Black Hole Rescue 
Fall Into a Black Hole

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Read What Is a Black Hole? (Grades 5-8)

Return to NASA Knows! (Grades K-4)

Return to Students K-4

Heather R. Smith/NASA Educational Technology Services

Last Updated: Aug. 21, 2018

Editor: Flint Wild

https://www.nasa.gov/audience/forstudents/k-4/stories/nasa-knows/what-is-a-black-hole-k4.html

Foundations of Algebra

Solving Literal EquationsOne of the dictionary definitions of "literal" is "related to or being comprised of letters", and variables are sometimes referred to as literals. So "solving literal equations" seems to be another way of saying "taking an equation with lots of letters, and solving for one letter in particular."

At first glance, these exercises appear to be much worse than our usual solving exercises, but they really aren't that bad. We pretty much do what we've done all along for solving linear equations and other sorts of equation; the only substantial difference is that, due to all the variables, we won't be able to simplify our work as we go along, nor as much as we're used to at the end. Here's how solving literal equations works:

• Solve A = bh for b

This is the formula for the area A of a rectangle with base b and height h. They're asking me to solve this formula for the base b.

If they'd asked me to solve 3 = 2b for b, I'd have divided both sides by 2 in order to isolate (that is, in order to get by itself, or solve for) the variable b. I'd end up with the variable b being equal to a fractional number.

In this case, I won't be able to get a simple numerical value for my answer, but I can proceed in the same way, using the same step for the same reason (namely, that it gets b by itself). So, following the same reasoning for solving this literal equation as I would have for the similar one-variable linear equation, I divide through by the "h":

$\small{ A = bh }$

$\small{ \dfrac{A}{h} = \dfrac{bh}{h} }$

$\small{ \bm{\color{purple}{ \dfrac{A}{h} = b }}}$

The only difference between solving the literal equation above and solving the linear equations you first learned about is that I divided through by a variable instead of a number (and then I couldn't simplify, because the fraction was in letters rather than in numbers). Because we can't simplify as we go (nor, probably, at the end), it can be very important not to try to do too much in one's head. Write everything out completely; this will help you end up with the correct answers.

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• Solve d = rt for r

This equation is the "uniform rate" equation, "(distance) equals (rate) times (time)", that is used in "distance" word problems, and solving this for the specified variable works just like solving the previous equation.

The variable they want has a letter multiplied on it; to isolate the variable, I have to divide off that letter. So I'll solve for the specified variable r by dividing through by the t:

$\small{ d = rt }$

$\small{ \dfrac{d}{t} = \dfrac{rt}{t} }$

$\small{ \bm{\color{purple}{ \dfrac{d}{t} = r }}}$

https://www.purplemath.com/modules/solvelit.htm