Introductory Astronomy_105_01_2020SP
Lab-6: Blackbody Radiation
In this PhET simulation, you will use the Blackbody Spectrum Simulation to investigate how the
spectrum of electromagnetic radiation emitted by objects is affected by the object's temperature. In
this simulation, you can input the temperature and observe the spectrum of the radiation emitted.
Introduction: All visible objects in our universe emit electromagnetic radiation (light) based on their
internal temperature. Colder objects emit radiation with very large wavelength (low frequency, such as
radio or microwaves), while hot objects emit visible/ultraviolet radiation with small wavelength (higher
frequency).
Blackbody Radiation: It is a term used to describe the relationship between an object’s temperature and
wavelength of electromagnetic radiation it emits. A black body is an idealized object that absorbs all
electromagnetic radiation it comes in contact with. It then emits thermal radiation in a continuous
spectrum according to its temperature.
Please go the following site and play with all of the parameters to see if you can answer the following
questions : https://phet.colorado.edu/en/simulation/blackbody-spectrum
(Note: With window it shouldn’t be a problem in running the simulation, however, if you’re using
MacBook be sure to open the site using Chrome or Explorer or Firefox)
Q1. The temperature of stars in the universe varies with the type of star and the age of the star among
other things. By looking at the shape of the spectrum of light emitted by a star, we can tell something
about its average surface temperature.
a) If we observe a star's spectrum and find that the peak power occurs at the border between red and
infrared light, what is the approximate surface temperature of the star? (in degrees C)
__________________________________________
b) If we observe a star’s spectrum and find that the peak power occurs at the border between blue and
ultraviolet light, what is the surface temperature of the star? (in degrees C)
__________________________________________
Q2. Light bulbs operate at 2500 degrees C.
a) What is the wavelength at which the most power is emitted for a light bulb operating at 2500 C?
_________________________________________
b) Explain why regular incandescent bulbs waste a lot of energy. Be sure to include your reasoning.
_________________________________________
Astronomy Lab (Phy106L_2019SP)
Lab1: Units and Conversions
Measurements are a process that uses numbers to describe a physical quantity based on what we
can observe. We can measure several physical parameters such as length, mass, time,
temperature, energy, etc. A unit of measurements is a definite magnitude of quantity, defined and
adopted by convection or by law that is used as a standard for measurements of the same kind of
quantity.
The fundamental SI (System International) units are:
Meter (m) for Length
Kilogram (Kg) for mass
Second (s) for time
All of the unit relationship in the metric system is based on multiple of 10, so it is very easy to
multiply and divide. This system uses prefixes to make multiples of the units. All of the prefixes
represent powers of 10. The table below provides prefixes used in the metric system, along with
their abbreviations and values.
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Temperature Scales:
Temperature is the measure of the hotness or coldness of a substance. Its scale is referenced to
the boiling and freezing point of water.
Energy and Power: Joules and Watts
The SI metric unit of energy is called the joule (abbreviated J). To give you a better sense of the
joule as a unit of energy (and of the convenience of scientific notation), some comparative
energy outputs are listed on the next page.
The SI metric unit of power is called the watt (abbreviated W). Power is defined to be the rate at
which energy is used or produced, and is measured as energy per unit time. The relationship
between joules and watts is:
1 watt = 1 joule/second
What Is Scientific Notation?
Astronomers deal with quantities ranging from the truly microcosmic to the hugely
macrocosmic. It would be very inconvenient to always have to write out the age of the universe
as 15,000,000,000 years or the distance to the Sun as 149,600,000,000 meters. For simplicity,
powers-of-ten notation is used, in which the exponent tells you how many times to multiply by
10. For example, 10 = 101, and 100 = 102.
As another example, 10-2 = 1/100; in this case the exponent is negative, so it tells you how many
times to divide by 10. The only trick is to remember that 100 = 1. (Se Using powers-of-ten
notation, the age of the universe is 1.5x 1010 years and the distance to the Sun is 1.496 x 1011
meters.
The use of scientific notation has several advantages, even for use outside of the sciences:
Scientific notation makes the expression of very large or very small numbers much
simpler. For example, it is easier to express the U.S. federal debt as $7 x 1012 rather than
as $7,000,000,000,000.
Because it is so easy to multiply powers of ten in your head (by adding the exponents),
scientific notation makes it easy to do "in your head" estimates of answers.
Use of scientific notation makes it easier to keep track of significant figures; that is, does
your answer really need all of those digits that pop up on your calculator?
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USEFUL MATH FOR ASTRONOMY
Dimensions of Circles and Spheres
• The circumference of a circle of radius R is 2πR.
• The area of a circle of radius R is πR2.
• The surface area of a sphere of radius R is given by 4πR2.
• The volume of a sphere of radius R is 4/3 πR3.
Measuring Angles - Degrees and Radians
• There are 360° in a full circle.
• There are 60 minutes of arc in one degree. (The shorthand for arcminute is the single
prime (ʹ), so we can write 3 arcminutes as 3ʹ.) Therefore, there is 360 x 60 = 21,600
arcminutes in a full circle.
• There are 60 seconds of arc in one arcminute. (The shorthand for arcsecond is the double
Astronomy Lab (Phy106L_2019SP)
prime ʺ ), so we can write 3 arcseconds as 3ʺ.) Therefore, there are 21,600 x 60 = 1,296,000
arcseconds in a full circle.
We sometimes express angles in units of radians instead of degrees. If we were to take the radius
(length R) of a circle and bend it so that it conformed to a portion of the circumference of the
same circle, the angle covered by that radius is defined to be an angle of one radian. Because the
circumference of a circle has a total length of 2πR, we can fit exactly 2π radii (6 full lengths plus
a little over 1/4 of an additional length) along the circumference. Thus, a full 360° circle is equal
to an angle of 2π radians. In other words, an angle in radians equals the arclength of a circle
intersected by that angle, divided by the radius of that circle. If we imagine a unit circle (where
the radius = 1 unit in length), then an angle in radians equals the actual curved distance along the
portion of its circumference that is “cut” by the angle. The conversion between radians and
degrees is
Trigonometric Functions
In this course, we will make occasional use of the basic trigonometric (or "trig") functions: sine,
cosine, and tangent. Here is a quick review of the basic concepts.
In any right triangle (where one angle is 90°), the longest side is called the hypotenuse; this is
the side that is opposite the right angle. The trigonometric functions relate the lengths of the
sides of the triangle to the other (i.e., not the 90°) enclosed angles. In the right triangle figure
below, the side adjacent to the angle α is labeled “adj,” the side opposite the angle α is labeled
“opp.” The hypotenuse is labeled “hyp.”
Astronomy Lab (Phy106L_2019SP)
• The Pythagorean Theorem relates the lengths of the sides of a right triangle to each other:
(hyp)2 = (opp)2 + (adj)2
• The trigonometry functions are just ratios of the lengths of the different sides:
Similar Triangles:
The sides of any two similar triangles do not have to be equal. However,
there is an important relationship among the sides of similar triangles:
The corresponding sides of similar triangles are in proportion.
𝑨𝑩 𝑩𝑪 𝑨𝑪
=
=
𝑫𝑬 𝑬𝑭 𝑫𝑭
Small Angle Approximation:
In fact, the hypotenuse and adjacent sides of a triangle are always of similar lengths whenever
we are dealing with angles that are “not very large.” Thus, we can substitute one for the other
whenever the angle between the two sides is small.
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Because the angle is small, the opposite side is approximately equal to the “arclength”
For small angles, the physical size h of an object can be determined directly from its
distance d and angular size in radians by
h ≈ d x (angular size in radians)
Activity1:
Q1) (5 points) Convert “normal” to “scientific” notation
a) 3,000,000 kg
b) 150,000,000 km
c) 148000000000 years
d) 0.0000456 miles
e) 0.000036003 light years
Q2) (4 points) Convert “scientific” to “normal” notation
a) 5.46x105 cm
b) 7.34x10-3 m
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c) 20x109 years
d) 50x10-6 km
Q3) (3 points) Add/Subtract with Scientific Notation
a) 5.46x105 cm + 1.32x106 cm
b) 6.6x109 m - 10.5x108 cm
c) 5.46x10-7 cm - 2.2x10-6 cm
Q4) (4 points) Multiplication/Division with Scientific Notation
a) 5.0x108 cm × 1.0x106 cm
b) 7.0x1010 m ÷ 2.0x109 m
c) 3.0x10-11 cm ÷ 4.0x1018 cm
d) 7.61x1010 m × 2.52x10-15 m
Q5) (3 points) Measure the length of any three objects in your lab and express them in kilometer
(Km)
1)
2)
3)
Activity 2:
Q6) (20 points) Measure the height of any object without touching. Show the drawing to your
instructor and explain your plan before taking measurements. (Hint: Using the concept of
similar triangles)
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