SelfPaced Physics Cover Sheet
Activity 1 - Indirect Measure of Circle Size
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Name:____________________
Date Submitted:__________
PHYS 1000 Activity:
Experimental Measure of Circle Area
Background:
Imagine this strange scenario: I’m going to challenge you to figure out the size of a certain kind
of plate, but I have a bunch of weird conditions. First, many of the plates have been hung on
the side of a barn thirty feet away from you. Second, you have to do it totally in the dark and
third, your only tool is a pile of rocks. Sounds crazy, I know… but you can definitely do it!
The good news is that you know how many plates there are on the side of the barn and you
know how big the wall itself is. So here is what you do: You throw rocks at random parts of the
side of the barn. As you listen, you will hear the rocks either striking a plate, or you will hear the
rock hit the side of the barn. If you do this long enough you will start get a sense of what the
probability is that you will hit a plate vs. hitting the wall. Bingo! Knowing how big the wall, how
many plates there are and the probability of hitting a plate you can get a good estimate of the
size of each plate. It just takes a little bit of thought and maybe a few calculations.
This crazy circumstance isn’t totally made up. Physicists use this kind of technique to determine
the size of subatomic particles, like atomic nuclei. They shoot a bunch of particles towards
target nuclei and then count up how often the particles interact with the nucleus. That is how
we know that nuclei are so incredibly tiny (10-15 m or so)!
Objective:
You are going to use a similar technique to measure the area of a circle and compare that to
the standard “theoretical” area formula.
Equipment and Supplies:
Other than the sheet of circles that is included in this document, you will need a ruler with
centimeters on it and either a dart board and dart or a pencil.
Finding the theoretical area:
First, find the area of one of the circles using the traditional theoretical formula.
1. User your ruler to measure the diameter of one of the circles (in cm). Divide this number by
two to get your measured radius. Show your calculations.
Measured radius
in cm (r):
2. Use this radius to calculate the theoretical area of the circle.
The formula is A
r 2 . Show your calculations.
Theoretical area of
one circle in cm2:
Once we have an experimental value for the area of one of the circles we will compare it to this
theoretical area.
Taking the experimental data:
Next, complete the actual experimental piece of this activity. Drop a pencil or dart (with a dart board
behind it), point first, onto the page of circles from a height of around 5 feet. Do your best not
to aim at all except to make sure you are at least hitting the paper. Ignore any drops that miss
the paper. Drop the pencil until you have hit the paper 100 times (D = 100).
3. Find the area of the paper in cm2. Show your calculations.
Area of Paper (AP):
4. Record the number of “hits” from your 100 drops. This means counting how many times the
center of the pencil mark was on or in one of the circles.
Number of hits (h):
5. Count the number of circles on the page.
Number of circles (N):
Finding the experimental area:
You should now have all the information you need to get an experimental measurement of the size of
one of the circles. The probability that a pencil hits a circle is equal to the total area covered by circles
divided by the area of the paper. This probability is equal to the number of hits divided by the number of
drops. These two statements are the key to this entire activity. You should read them carefully and
compare them to the following formula to make sure you understand where it comes from.
h
D
N AC
AP
6. Using the equation above, solve for an experimental value for the area of one circle. This
means doing two steps of algebra, followed by putting the numbers into a calculator. Show
your calculations.
Experimental area of
one circle:
Discussing your results:
7. How do your theoretical and experimental values compare? Which is larger? What is the
percent error of your experimental value?
[The formula for this is % error
experimental theoretical
theoretical
100 .]
8. Lastly, discuss ways that this experiment could be done more accurately. That is, what could
be changed about the process that would lead to an experimental value that is closer to the
theoretical value?
SelfPaced Physics Cover Sheet
Activity 2 - Atoms
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PHYS 1000
Activity: Atoms
Objective
The student should understand (a) how atmospheric atoms diffuse from a
source, and (b) a basic relationship between pressure and temperature of gases.
Background
(Reference: Chapter 2, Physics, Concepts and Connections, Art Hobson)
Atoms in the atmosphere are moving at great speed, continually bouncing off of
each other and off of surfaces. Imagine the smell of cookies baking in an oven. You can
smell those cookies because atoms from the dough have traveled into the air, through
the room, and into your nose, in a process called diffusion. The path that molecules
take can be modeled as a random walk (Figure 1.)
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The faster that the molecules are moving, the harder they will strike a containing surface
such as a wall. The net amount of force per area on a surface is the atmospheric
pressure.
Equipment and Supplies
Diffusion experiment: 5 coins (four pennies and a nickel for flipping)
Temperature: a round balloon, freezer, boiling pot of water, ruler, two large hardcover
books
Procedure part 1: Diffusion
Take four coins and place them on the center tile. Take a fifth coin and flip it. If the
flipped coin reads heads, move one of your four coins one square to the right (+1.) If it is
tails, move it left. Do the same for the other three coins. Do this again for all four coins.
Some of the coins might move back to the center square. Repeat this procedure until a
coin lands on an outer square: either Joe’s nose or your nose. Keep track of how
many steps it takes a coin to reach one of the endpoints. Repeat this experiment
five times and record your results.
Joe
-4 -3 -2 -1 0 +1 +2 +3 +4
You
Procedure part 2: Relationship Between Temperature and the Speed of
Atmospheric Molecules
Blow up a balloon and tie off its end. Measure its diameter by placing it between
two books, and measuring the distance between the books. Put the balloon in the
freezer for 5 minutes. Quickly remove it and measure its diameter again. Hold it over
boiling water for a minute or so, and quickly measure its diameter again.
Worksheet
Questions
1) Do the coins diffuse outward from the center?
2) For the five trials, how many times was (a) Joe’s nose reached first, (b) your
nose reached first, and (c) Joe’s and your nose reached at the same time?
3) For each trial, how many sets of coin flips did it take for a coin to reach either
nose?
Trial 1)______ Trial 2) ______ Trial 3) ______ Trial 4) ______ Trial 5) ______
Average number of coin flips (out of the five trials) ___________
4) Set up a new game where it is 10 squares to either nose (instead of 5). Record
how many sets of coin flips did it take for a coin to reach either nose.
Trial 1)______ Trial 2) ______ Trial 3) ______ Trial 4) ______ Trial 5) ______
Average number of coin flips (out of the five trials) ___________
Did the average number of coin flips double (since the distance to either nose
doubled)? Discuss your result.
5) Do you think if you had only one coin, this experiment would take more steps on
average, or fewer steps? What if you had 100 coins?
6) What are the similarities between this process and the process of physical
diffusion of an odor as discussed in the chapter?
7) Initial diameter of balloon______________
Diameter of cold balloon ______________
Diameter of hot balloon _______________
8) Explain why the balloon shrinks and contracts with temperature.
9) The basic relation between the velocity v and the temperature T is:
! mv2 = 3/2 kBT
where m is the mass of the atom and kB is the Boltzmann constant
kB =1.38 x 10-23 Joule/Kelvin (J/K).
(1)
Most of the atoms you breathe are made of diatomic nitrogen N2, which has a mass of
2.32 x 10-26 kg. If room temperature is about 295 K, how fast is a typical air molecule
moving in units of m/s? HINT: solving equation (1) for v gives:
v=
3k B T
m
Answer: v = _______________________m/s.
SelfPaced Physics Cover Sheet
Activity 3 - Energy and Power
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PHYS 1000
Self Paced
Activity 3: Energy and Power
Objective: To measure the energy and power of a student, and to witness the
exchange of energy.
Background: Physics, Concepts and Connections, Hobson, Chapter 6
Equipment and Supplies : Staircase, stopwatch, tape measure, scale, various types
of balls (tennis, racquetball, basketball, etc.)
Procedure:
(Part 1)
1) Measure the height !h of a staircase. If you used British units (feet, inches),
convert the height to meters (1 ft = 12 in, 1 in = 0.0254 m).
2) Starting from rest at the bottom of the staircase, run to the top, timing yourself.
Do this five times and find the average time. Use a precision of 1/10th of a
second.
3) Measure your weight in pounds.
4) Convert your weight in pounds to your mass in kg using the conversion
1 kg weighs 2.2 lbs.
5) Find your weight in Newtons using
w = mg
and assuming that g = 9.8 m/s2. One Newton = 1 kg m/s2.
6) Calculate the change in gravitational potential energy you experience as you
ascend the stairs: !U = mg!h. The unit of energy is the Joule (J).
1 J = 1 N m = 1 kg m2/s2.
7) Power is the rate of energy expenditure, or the work per time. For this
experiment, P = !U/ !t. Calculate your average power for your trials. The unit for
power is the Watt (W), where 1 W = 1 J/s.
8) How many 100 W light bulbs could you light?
Procedure:
(Part 2)
Measure a tennis ball’s elasticity by dropping it and measuring the height of rebound as
a fraction of the initial height. Repeat this for ten different heights. What fraction of the
initial height was transformed into thermal energy? What fraction was retrieved as
gravitational energy? Do these fractions change as a function of height? Repeat this
experiment for a different ball. Discuss your findings.
Worksheet for Activity 3: Energy and Power
1)
2)
3)
4)
5)
6)
7)
8)
9)
Height of the staircase (m)
_________.
Times:
Trial 1_____ Trial 2 ______ Trial 3_____ Trial 4 _____ Trial 5 _____
Average time (s)
_________.
Weight (lbs.)
_________.
Mass (kg)
_________.
Weight (N)
_________.
Potential energy (J)
_________.
Average power (W)
_________.
Number of light bulbs
_________.
Questions:
1) Why is it important to start from rest at the bottom of the staircase, instead of
giving yourself a running start?
Part 2)
Type of ball______________
Trial
Initial height
Final height
Fraction
retrieved as
gravitational
energy
Fraction lost
to thermal
energy
1
2
3
4
5
6
7
8
9
10
Average Fraction retrieved as Gravitational Energy __________________________
Average Fraction lost to Thermal Energy __________________________________
Type of ball______________
Trial
Initial height
Final height
Fraction
retrieved as
gravitational
energy
Fraction lost
to thermal
energy
1
2
3
4
5
6
7
8
9
10
Average Fraction retrieved as Gravitational Energy __________________________
Average Fraction lost to Thermal Energy __________________________________
Discussion:
SelfPaced Physics Cover Sheet
Activity 4 - Radioactive Decay
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PHYS 1000
Self Paced
Activity 4: Radioactive Decay
Objective: To understand the concept of half-life using a penny simulation.
Background: Physics, Concepts and Connections, Hobson, Chapter 15
Equipment and Supplies : 256 pennies, large container for shaking
Procedure:
Part 1) Imagine that your pennies represent 256 atoms that have a half-life of one year.
Shake the container and toss the pennies onto the floor. Count the number of pennies
that are heads and the number that are tails. If a coin comes up tails, it represents the
decay of the atom. Remove the decayed atoms and toss them again, continuing the
process until your entire sample has decayed. Each toss will represent one year. Make
a graph of the number of undecayed atoms vs. the number of years.
Part 2) Take 4 pennies and repeat the experiment. Calculate how long you expect the
sample to be active (that is, to still have atoms that can decay.) Repeat this experiment
20 times, recording how many tosses it takes. Make a histogram of the number of
tosses it takes to fully decay.
Worksheet for Activity 4: Radioactive Decay
Graph the number of pennies vs. year , starting with 256 pennies at the year zero.
Questions
1) (Part 1) How many non-decayed atoms do you expect after 3 years? Compare
this to the number you actually saw. Try to explain the discrepancy.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________.
2) How many years would theory predict for the sample to completely expire?
Compare this to the number of years your sample took to fully decay.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________.
Graph your histogram of decay time for four pennies here:
1) (Part 2) What was the most likely number of years to decay? How does the most
likely number compare to the theoretical value?
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________.
2) How do you think random error affects our result?
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________.
SelfPaced Physics Cover Sheet
Activity 5 - Measuring the Weight of Your Car
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PHYS 1000
Activity: Measuring the Weight of Your Car
Objective: To measure indirectly the weight of a car by measuring the pressure in the
tires and the surface area of the tires in contact with the road.
Background: Pressure is defined as force per unit area. If we know the force that is
being exerted on an object and know the area over which that force acts, we can
calculate the pressure by using the definition. For example, if a force of 100 lbs is
exerted over an area of 10 square inches, then the pressure resulting from that force is
Pressure = Force/Area = 100 lbs/10 in2 = 10 lbs/in2.
We can use the same relationship to determine the force if we know the pressure and
the area. Simply rearranging the equation, we get
Force = Pressure x Area, or F = P A.
The rims of the wheels of a car are held off the ground primarily by the force of the air in
the inflated tires. The tires theselves are elastic and often have steel belting which tend
to support the car also, but most of the support results from the air pressure.
In this activity you will approximate the weight of your car by assuming the entire weight
is supported by air pressure in the tires. The force of each tire on the ground is related
to the pressure in the tires and the area of the tires in contact with the ground. The force
of gravity pulls the car down and the road pushes up with the same strength. The force
that the road pushes up on each tire is simply the pressure of that tire times the area of
contact the tire makes with the ground.
The sum of the forces on the four tires of the car must be equal to the weight of the car
(otherwise there would be a net force on the car).
Equipment and Supplies :
One car
Tire gauge
Four pieces of paper larger than the area of contact between your tires and the ground
Pencil & ruler.
Procedure:
Park your car on a clean dry level surface. Place four sheets of paper directly in front of
all four tires (or directly behind). Gently roll the car onto the sheets of paper so that the
tires are totally on the pieces of paper. Set the brakes and turn off the engine.
Using a pencil, outline on the sheets of paper the area of the tires in contact with the
paper. You can trace around the side edges of the tires. To determine the line of contact
in front and back of each tire, slip a piece of paper under the tire as far as it will go; then
mark the line of contact with a pencil. You can complete the line after the paper is
removed from under the tires. Be sure to label each piece of paper with the tire (e.g.,
front left, back right,!)
On each piece of paper under the tires, record the air pressure in the tire, which you
should measure with a tire gauge. Most tire gauges read the pressure in pounds per
inch squared (lbs/in2).
Move the car and retrieve the sheets of paper. Using a rulter, draw straight lines to
approximate the area of the tires in contact with the ground. The shape should be
roughly rectangular and the area can be determined by finding the product of the length
and width of the rectangle.
Multiply the area of each tire by the corresponding pressure in that tire to get the force
on that tire.
Add up the four forces. This is your estimate of the car’s weight. Compare the measured
value with the value for the curb weight given in the owner’s manual (or look it up on the
internet).
Worksheet
Tire
Tire Pressure
(lbs/in2)
Tire Contact
Area (in2)
Force on Tire (lbs)
Front left
Front right
Rear left
Rear right
Total Force: Wmeasured = ________________ lbs
1) List the actual curb weight of the car: Actual Weight = W= ___________ lbs
2) Calculate the percent difference between your value of the car’s weight and the
listed weight by using the formula
| Wmeasured ! W |
Percent Difference =
x 100
W
3) Comment on your values and any discrepancies. What do you think are the
sources of error? (Note: if you are deviating significantly from this value, you
should re-check your calculations.)
4) Do your measurements show that the weight is equally distributed between the
front and rear tires? How about between the left and right sides? Why might the
weight not be distributed evenly?
SelfPaced Physics Cover Sheet
Activity 6 - The Period of a Pendulum
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PHYS 1000
Activity: The Period of a Pendulum
Objective: To confirm experimentally that the period of a pendulum is proportional to
L , and to use this to determine the acceleration of gravity at the surface of the Earth,
g.
Background: Physics, Concepts and Connections, Hobson, Chapter 5.
A pendulum is simply a mass hanging from a string which is allowed to oscillate in a
plane. The time for one complete oscillation (back and forth) is called the period of the
pendulum. If the amplitude (angle) of the swing is not too great (less than 15°) the
period does not depend strongly on the amplitude, nor does it depend upon the mass of
the object used as the pendulum bob. However, the period of the pendulum does
depend upon the length of the pendulum and upon the force of attraction between the
bob and the earth, which enters the equations describing the pendulum through the
parameter g, the acceleration due to gravity.
From Newton’s second law of motion, the relationship between period (T), the length
(L), and g can be found to be:
T = 2!
L
.
g
This relationship tells us that the period is period is proportional to the square root of the
length of the pendulum, so that if the length of the pendulum increased by a factor of 4,
the period would only increase by a factor of two. This experiment will test this
prediction.
The period-length relationship can also be expressed so that g is expressed in terms of
T and L:
4! 2 L
g=
T2
Equipment and Supplies : String, a heavy mass, tape measure or meter stick,
stopwatch.
Procedure: NB: The length of the string should be measured from the pivot point to
the center of mass of the pendulum bob.
Pick a pendulum bob that has an evenly distributed mass. Some examples could be a
film box filled with water, a soap bottle or full hand sanitizer dispenser, or a plastic cup
filled with sand. Use a heavy mass so that air resistance is minimized. Tie the
pendulum to a secure overhead point such as a ceiling hook.
Measure the length of the pendulum as per above. Start the pendulum swinging with a
small amplitude: no more than a few inches from the side of the resting position. With a
stopwatch, measure how long it takes for a fixed number of periods (e.g., 50.) (If you
don’t have a stopwatch, count how many periods occur over one minute using a regular
watch.) Remember, one period is the time needed for one complete cycle; and one
complete cycle can be described as the pendulum swinging away from it’s high point
and then back again to the same high point (There and back again!) The more cycles
you count, the more accurate your results will be. Find the measured period Tm by
dividing the total time by the number of cycles (by cycle, we still mean complete cycle or
period.)
Use the measured period and the equation above to determine the value of the
acceleration of gravity, g.
Repeat the experiment for five different lengths. Make sure you use a large range of
values of length. At least one choice for length should be four times another value. Fill
out the table on the worksheet.
Worksheet for Activity 6: The Period of a Pendulum
Length
(cm)
Number
Total
of
time for
Complete N Cycles
Cycles
(s)
N
Measured
Period Tm
(s)
g
(cm/s2)
4! 2 L
g=
T2
Percent
Difference
1) Do your data support the conclusion that the period of a pendulum is proportional
to the square root of the length? Does increasing the length by a factor of 4
increase the period by a factor of 2? ___________________________________
2) Calculate the percent difference between your value of g (the acceleration due
to gravity) and the accepted value of g = 980 cm/s2 by using the formula
| g ! 980 |
Percent Difference =
x 100
980
3) Comment on your values and any discrepancies. What do you think are the
sources of error? (Note: if you are deviating significantly from this value, you
should re-check your calculations.)
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
4) Write a paragraph summarizing this experiment. The purpose of this paragraph is
to have you present evidence that you actually did the experiment and
understand what you did.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
SelfPaced Physics
Activity 7 - Tour of the Solar System
Overview: Layout a scale-model solar system and then go on a tour of it.
Details: Begin with a ball 23 centimeters in diameter (the size of a bowling ball), to represent
the sun. Then lay out nine objects to represent the eight planets and Pluto using the sizes and
locations shown in the table below. If you decide to do this activity you will "turn it in" by
making a movie as you travel from the Sun to Pluto. If you do more than just walk please find a
friend who can help (no riding/driving while recording). Upload your final video to youtube.com
(or the equivalent) and submit the URL through the Q&A on the selfpaced website. As you move
through your solar system, describe how you set it up and any observations you made while
doing so.
Object
Sun
Mercury
Venus
Earth
Mars
Juipter
Saturn
Uranus
Neptune
Pluto
Diameter of object
(on our scale)
23 cm (bowling ball)
1 mm (pinhead)
2 mm (peppercorn)
2 mm (peppercorn)
1 mm (pinhead)
2.4 cm (chestnut)
2.0 cm (acorn)
9 mm (peanut)
8 mm (peanut)
0.5 mm (pinhead)
Distance from the previous object
(in meters)
10
8
7
13
92
108
240
271
234
This activity is inspired by Chapter 1, Hands-on Science #5 from the Activities Manual.
Cover Sheet: Activity: Extra
Transit of Venus
Name:________________________________________________________________'
!
Date'Submitted:____________________________________________________'
Returned'for'Revision:____________________________________________'
Resubmitted:________________________________________________________'
Date'Recorded'as'Satisfactory:___________________________________'
By':_____________________________________________________________'
!
!
PHYS 1000 /AST 1040
Self Paced
Activity: June 5, 2012 Transit of Venus
Objective: To make measurements of the Solar System from observations of the June
5, 2012 transit of Venus.
Background: When an inferior planet (Venus or Mercury) is at a place in the solar
system called inferior conjunction, it is passing the Earth on the way around the Sun.
Another point in the orbit (relative to the Earth) is superior conjunction, where the planet
is aligned with the Sun but farther than it. These points are in contrast to opposition,
which occurs when a superior planet is opposite the Sun in the sky.
For the inferior planets, the vast majority of the passes in front of the sun do not
transit the sun, but traverse north or south of it. Occasionally one does: the tables
below show the transits for Mercury and Venus.
Source: http://eclipse.gsfc.nasa.gov/transit/transit.html
Transits of Mercury:
1901-2050
Date
Universal Time
1907 Nov 14
12:06
1914 Nov 07
12:02
1924 May 08
01:41
1927 Nov 10
05:44
1937 May 11
09:00
1940 Nov 11
23:20
1953 Nov 14
16:54
1957 May 06
01:14
1960 Nov 07
16:53
1970 May 09
08:16
1973 Nov 10
10:32
1986 Nov 13
04:07
1993 Nov 06
03:57
1999 Nov 15
21:41
2003 May 07
07:52
2006 Nov 08
21:41
2016 May 09
14:57
2019 Nov 11
15:20
2032 Nov 13
08:54
2039 Nov 07
08:46
2049 May 07
14:24
Transits of Venus:
1601-2400
Date
Universal Time
1631 Dec 07
05:19
1639 Dec 04
18:25
1761 Jun 06
05:19
1769 Jun 03
22:25
1874 Dec 09
04:05
1882 Dec 06
17:06
2004 Jun 08
08:19
2012 Jun 06
01:28
2117 Dec 11
02:48
2125 Dec 08
16:01
2247 Jun 11
11:30
2255 Jun 09
04:36
2360 Dec 13
01:40
2368 Dec 10
14:43
Equipment and Supplies: Ruler, calculator.
Data:
Sun’s diameter: DSun= 1.39 x 106 km
Distance from the Sun to Earth: dSun-Earth= 1.496 x 108 km
Distance from the Sun to Venus: dSun-Venus= 1.082 x 108 km
Section I: Find the diameter of Venus.
1) Measure the diameter of the solar disk with a millimeter ruler. Take several
measurements and find the average. LSun = _____________ mm.
2) Measure the diameter of Venus with the ruler. (It is the large black dot on the
face of the Sun.) Take several measurements and find the average. LVenus =
______________mm
3) If Venus were crossing the Sun at the distance to the Sun, then the diameter of
Venus would be equal to the product: DVenus =(LVenus/LSun) x DSun. BUT, Venus is
closer to the Earth than the Sun is, so the occultation disk appears larger than
that. How many times farther away is the Sun from the Earth compared to Venus
(from the Earth)? Let’s call this number M = _______________.
4) This factor needs to be introduced into the previous calculation since Venus is
actually smaller by this amount.
DVenus = (LVenus/LSun) x (DSun/M) = _______________ km.
5) Compare your measurements to the standard value of the diameter of Venus:
12100 km. Find your percent error via the equation
| Standard - Observed|
%error =
×100.
Standard
%error = ________________________.
6) Compare the diameter you calculate to the diameter of the Earth: 12800 km. Do
your measurements support the claim that Venus is Earth’s sister planet (due to
them having similar sizes?)
7) What are sources of error? How could this experiment be improved?
Section II: Estimate the orbital speed of Venus.
Here we will attempt to estimate how fast Venus is moving in its orbit by the formula
distance
.
time
speed =
Even though we know that the planets move in curved trajectories called ellipses, for
short periods of time we can approximate the path of a planet as a straight line.
From http://eclipse.gsfc.nasa.gov/OH/transit12.html :!
The principal events occurring during a transit are conveniently characterized by
contacts, analogous to the contacts of an annular solar eclipse. The transit begins
with contact I, the instant the planet's disk is externally tangent to the Sun.
Shortly after contact I, the planet can be seen as a small notch along the solar limb.
The entire disk of the planet is first seen at contact II when the planet is
internally tangent to the Sun. Over the course of several hours, the silhouetted
planet slowly traverses the solar disk. At contact III, the planet reaches the
opposite limb and once again is internally tangent to the Sun. Finally, the transit
ends at contact IV when the planet's limb is externally tangent to the Sun. Contacts I
and II define the phase called ingress while contacts III and IV are known as egress.
Position angles for Venus at each contact are measured counterclockwise from the north
point on the Sun's disk.
!!
1) How long does it take Venus to go from Contact I to Contact III? Convert the
answer to seconds:
ΔtI − III
= _____________ s.
2) Over this short amount of time, it is fair to approximate the path of Venus as a
straight line. Using similar triangles, estimate how far Venus has traveled in
this time (see the figure below.) The similar triangles share the Earth at one
vertex.
ΔxVenus-estimate = _____________________________ km.
3) This estimation is wrong. The Earth has also moved during the transit. We can
approximate the extra distance the Earth has covered by knowing that the
Earth moves at
time using
vEarth = 30 km/s. Calculate how far the Earth moved during that
ΔxEarth = vEarth tI − III .
ΔxEarth = ____________________________ km.
4) Since both Earth and Venus moved over the transit, some extra distance has to
be added to the estimate of Venus’s motion. The amount to add is
approximately Δxextra
=
dSun-Venus
ΔxEarth = ___________________km.
dSun-Earth
5) Sum these two values to get the total distance Venus has moved in this time.
Δxtotal = ΔxVenus-estimate + Δxextra = ________________ km.
6) This estimate is still wrong- why? Because it was assumed that Venus transited
across the diameter of the sun. However, it didn’t go that far, it went across
from one point to another. Use a ruler to measure the diagram ‘2004 and 2012
Transits of Venus’ (above). Measure the distance (in mm) of the track of
Venus, and also across the diameter of the Sun. Call the ratio of the length of
Venus’s track to the length of the diameter p, where p should be a number less
than 1. p = _________________________.
7) The final estimate of the distance that Venus has traveled is obtained by
multiplying the result in part (5) by the multiplicative factor in part (6).
Δxfinal = pΔxtotal = ________________ km.
8) The speed of Venus is therefore
vVenus
Δxfinal
=
=
Δt I − III
______________________ km/s.
9) Compare your answer to the standard value of the orbital speed of Venus:
vstandard = 35.0 km/s . Find the percent error as you did in Section I
%error = ___________________________________.
Section III: Discussion
1) Look at the tables that give the calendar for the transits of Mercury and Venus.
Do you notice any trends amongst the dates? What kind of transits occur more
often, those of Venus or those of Mercury? What is a plausible explanation for
this?
2) The Kepler space mission (kepler.nasa.gov) is designed to discover planets
around other stars by studying the brightness of those stars during planetary
transits. Kepler is sensitive to brightness changes of 1/10000 which occur when a
planet blocks out a tiny fraction of the light being emitted by the star it orbits.
Given the area of Venus and the Sun, do you think that Kepler would be able to
detect a transit of Venus? Why or why not?