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 2A rS . 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.

C

P

N AhD A

u

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 � u .]

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 (1)

where m is the mass of the atom and kB is the Boltzmann constant

kB =1.38 x 10-23 Joule/Kelvin (J/K).

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:

mTkv B3=

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) Height of the staircase (m) _________. 2) Times: Trial 1_____ Trial 2 ______ Trial 3_____ Trial 4 _____ Trial 5 _____ 3) Average time (s) _________. 4) Weight (lbs.) _________. 5) Mass (kg) _________. 6) Weight (N) _________. 7) Potential energy (J) _________. 8) Average power (W) _________. 9) 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

Percent Difference = |Wmeasured !W |W

x 100

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:

gLT !2= .

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:

g = 4!2L

T 2

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 of

Complete Cycles

N

Total time for

N Cycles (s)

Measured Period Tm

(s)

g (cm/s2)

g = 4!2L

T 2

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

Percent Difference = | g ! 980 |980

x 100

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 Diameter of object (on our scale)

Distance from the previous object (in meters)

Sun 23 cm (bowling ball) Mercury 1 mm (pinhead) 10 Venus 2 mm (peppercorn) 8 Earth 2 mm (peppercorn) 7 Mars 1 mm (pinhead) 13 Juipter 2.4 cm (chestnut) 92 Saturn 2.0 cm (acorn) 108 Uranus 9 mm (peanut) 240 Neptune 8 mm (peanut) 271 Pluto 0.5 mm (pinhead) 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

distancespeed = time .

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: I IIIt −Δ = _____________ 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.

Venus-estimatexΔ = _____________________________ 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 Earth 30 km/s.v = Calculate how far the Earth moved during that

time using Earth Earth I IIIx v t −Δ = .

EarthxΔ =____________________________ 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 Sun-Venusextra Earth

Sun-Earth

dx x

dΔ = Δ = ___________________km.

5) Sum these two values to get the total distance Venus has moved in this time.

total Venus-estimate extrax x xΔ = Δ +Δ = ________________ 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).

final totalx p xΔ = Δ = ________________ km. 8) The speed of Venus is therefore

finalVenus

I III

xv

t −

Δ= =Δ ______________________ km/s.

9) Compare your answer to the standard value of the orbital speed of Venus:

standard 35.0 km/sv = . 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?