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).
http://www.nasa.gov/audience/foreducators/nasaeclips/search.html?terms=%22Our%20World%3A%2
0Chandra%20-%20Exploring%20the%20Invisible%20Universe%22&category=0000&disp=grid
Investigating the Mass and Diameter of a Black Hole
Mass of Black Hole
Diameter in
kilometers
1.0
6.0
2.0
12.0
5.0
30.0
M
???
Although they are mysterious, black holes are actually very simple astronomical objects!
For black holes that don’t spin, there is a simple relationship between the dieter of such a
black hole, and its mass.
The masses of black holes, M, are usually given in multiples of the mass of our own sun, so
‘1.0’ means that the black hole has exactly the same mass as our sun ( 2,000 trillion trillion
tons!).
Problem 1 – The table above gives the masses and diameters of a few black holes. What is
the formula for the diameter of a black hole given its mass, M, if M is given in multiples of
the mass of our sun? ___________
Problem 2 – A planet was discovered orbiting just outside a black hole at a distance of
18,000 kilometers. What would you conclude about the mass of this black hole?_________
Problem 3 - Suppose that for a black hole that spins, its diameter is 2 times that of a black
hole of the same mass that doesn’t spin. What is the formula for the diameter of such a
spinning black hole given its mass?__________
Investigating Hot Gases near a Black Hole
Temperature
(Kelvin)
9,000
7,000
6,000
5,000
4,000
T
Color (nm)
400 (violet)
500 (yellow)
600 (orange)
700 (red)
900 (infrared)
???
As gas falls into a black hole, friction makes it get hotter and hotter. Just as turning up the
temperature on your stove makes its color change from dull-red to brilliant yellow, as a gas
heats up, the light it produces also changes its color. Photographers and scientists define colors
by the wavelengths of light that they correspond to in the ‘visible’ part of the electromagnetic
spectrum. Wavelengths are measured in nanometers, where 1 nanometer is 1 billionth of a
meter. Temperatures are measured in Kelvins where 0 Kelvin is Absolute Zero (-273° Celsius).
The table above compares the color and temperature of a gas at five different distances from a
black hole that has 10 times the mass of our sun.
Problem 1 – What is the formula that gives, W, the wavelength of the light in nanometers, given
the temperature, T, of the gas in Kelvins?__________
Problem 2 - Suppose that an astronomer detected light from the gas near a black hole that had
a wavelength of Ultraviolet-B (UV-B) radiation at a wavelength of 200 nm. What is the
temperature of the gas at this location?__________
Problem 3 – Gas that is very close to a black hole can be so hot that it shines brightly in x-ray
light with a wavelength of W = 3.6 nm. What is the temperature of this gas?__________
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.
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Evaluate your understanding:
Challenge Problem: Exploring Hot Gases Near a Black Hole
Distance
(Kilometers)
2.0 million
3.0 million
4.0 million
4.5 million
D
Temperature
(Kelvin)
9,000
6,000
4,500
4,000
Black Hole 1
Color (nm)
400 (violet)
600 (orange)
800 (crimson)
900 (infrared)
???
Black Hole 2
Temperature
Color (nm)
(Kelvin)
13,500
267 (UV-B)
9,000
400 (UV-A)
6,800
530 (yellow)
6,000
600 (orange)
???
The table above compares the color and temperature of a gas at various distances from two
black holes. The first black hole has a mass of 10 times our sun. The second black hole has a
mass of 50 times our sun’s mass.
Problem 1 – If you were in a spaceship located 4 million kilometers from a black hole, how
could you tell if it had a mass of 10 times or 50 times our suns mass?__________
Problem 2 – What is the formula that give the temperature T of the gas near a black hole given
your distance from the black hole for A) the 10 solar mass black hole? and B) the 50 solar mass
black hole?__________