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Module 2
Translating Between Tables and Expressions

Exploring Black Holes in Space

Objectives: Students will learn about black holes through reading a NASA press release and viewing a NASA eClips video segment. Then students will use tables and mathematical expressions to compare black holes’ sizes and temperatures.

Mathematics Skill or Topic Area:

Translating Between Tables and Expressions

Next Gen Science Standards: PS1: Matter and Its Interactions; PS3: Energy; ESS1: Earth’s Place in the Universe; ETS2: Links Among Engineering, Technology, Science, and Society

Common Core ELA for Science: RST.6-8.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions. RST.6-8.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.6-8.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.

Common Core Math Standard: CC.6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers.

Video Engagement: Chandra-Exploring the Invisible Universe Learn why NASA put the Chandra X-Ray Observatory far away from Earth's atmosphere to capture images of the x-rays given off by objects under certain violent conditions. Scientists use those images to learn about our universe (5 minutes). View Program

Engage your students with a press release:

Youngest Nearby Black Hole

A galaxy is a collection of billions of stars held together by gravity. Our Milky Way is a large galaxy shaped like a pinwheel, with over 500 billion stars, gas and dust forming a spiral with at least four arms. Stars come in many sizes from 1/100 the mass of our sun to over 100 times the mass of our sun. The most massive stars eventually use up their nuclear fuel and explode as supernova.

Supernova SN 1979C (the third one discovered outside the Milky Way in 1979) was actually discovered by an amateur astronomer in 1979 while he was studying the galaxy known as Messier-100 in the constellation Virgo. The galaxy Messier-100 is located about 50 million light years from Earth.

Because it was discovered only 30 years ago, it is the nearest example where the birth of a black hole has actually been observed. There have been other supernova that have been observed closer than 50 million light years, but scientists were not available to study these events until long after the supernova occurred.

How do astronomers know that a black hole formed? Data from NASA's Chandra and Swift observatories in space revealed a bright source of X-rays that has remained steady for the 12 years from 1995 to 2007. By carefully studying the X-ray light that SN1979C is producing, astronomers can tell quite a lot about the object in the SN 1979C remnant, such as its temperature, size and density. All of the available data points to a black hole being fed either by material falling back into the black hole after the supernova, or from a companion star that is orbiting the black hole.

Astronomers think that SN 1979C formed when a star about 20 times more massive than our Sun collapsed. The exploded star had ejected some, but not all of its outer layers of hydrogen-rich gas. Since most black holes should form when the core of a massive star collapses, this may be the first time that the common way of making a black hole has been observed.

Because light took 50 million years to get to Earth from M-100, the supernova SN1979C actually happened 50 million years ago and not at the time that it was observed in 1979. Astronomers today can study this delayed light image of the event and study how the object changed during a 30-year period after it formed, even though that 30-year period happened 50 million years ago.

Press release date line - November 15, 2010

Press release location: [ Click Here ]

Explore math connections with


Problem I - Investigating the Mass and Diameter of a Black Hole - Students will interpret data from a table to determine the formula for the diameter of a black hole. Open PDF]

Problem II - Investigating Hot Gases Near a Black Hole - When gas is cold below 500 Celsius, it can only be detected in the infrared portion of the electromagnetic spectrum. At temperatures from 3000 C to 10,000 C, it can be seen with the human eye as dull-red, yellow or even blue-white. At even higher temperatures, most of the energy appears as x-rays or even gamma rays. In this problem, students work with a simple equation that relates the temperature of a gas entering a black hole to its color and wavelength. [Open PDF]

Explain your thinking:

Write your own problem - Using information found in the Math Connection problems, the press release or the video program, create your own math problem. Explain why you set the problem up this way, and how you might find its answer.

Evaluate your understanding:

Challenge Problem: Exploring Hot Gases Near a Black Hole - As gas flows into a black hole, friction heats up the gas to thousands or even millions of degrees. During the brief time that this super-hot gas is outside the black hole, we can see the light from this gas and study it to learn about the environment of a black hole. The temperature of the gas gets hotter and hotter the closer to the black hole that the gas falls. In this problem, students explore the temperature of the gas at different distances from a black hole. [Open PDF]


3-D Solar System

Extend your new knowledge - Using the EOSS simulator, explore the orbit of the Chandra Observatory. [ Open PDF ]