Celestial Motion Lab PDF

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Old Dominion University Physics 103N, At Home Lab

Celestial Motion

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Experiment A03

Name

Lab Section

Objective 

To review various astronomical topics: Celestial Motion, Constellations, Causes for the Seasons, and the Lunar Cycle

Materials Computer with Internet Access

Procedure Part A: Celestial Motion During this portion of the lab we will be using simulations that have been created at the University of NebraskaLincoln. These simulations will let us test a few astronomical concepts that are either difficult to replicate in the lab or are time consuming. The simulations let us test and adjust things much more easily. These simulations use a combination of Java and Flash. These programs are both free, and you can follow the links below for installing them on your computer. We recommend testing the link below before downloading these programs. You may already have what you need to run the simulation without installing anything.

Download Flash Player: https://get.adobe.com/flashplayer/ - Be sure to uncheck the boxes for the Optional Offers in the middle of the page. You may need to enable ash on your web browser in order to start the animations used in this experiment. The links below provide instructions for the three most popular web browsers.  Google Chrome: https://rb.gy/jrhagd  Safari: https://rb.gy/ubpbdj  Mozilla Firefox: https://rb.gy/rjriwo

Download Java: https://java.com/en/download/

You can visit the first simulations by visiting http://astro.unl.edu/animationsLinks.html You will be using the simulation Rotating Sky Explorer. This simulation has two views: the left view shows the celestial sphere and how the Earth spins within it, the right view is your view from the ground and how you see the celestial sphere move (similar to what you saw on the dome earlier in the lab). Take a few minutes to familiarize yourself with how the simulation works and then answer the questions below. (Hint: Things to try with the simulation are to change your location on the Earth, drag around the globe, add stars to the celestial sphere, and add star trails. Make sure you click the Start Animation button to see the simulation

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Experiment A03: Celestial Motion

run.) 1.

Why do all objects on the celestial sphere rise in the east and set in the west? (This answer requires much more detail than just, “Because the Earth rotates.”)

The earth rotates clockwise, meaning that the west will lose sunlight before the east in a rotation.

2.

Set the location to Norfolk, (latitude = 36.9° N, longitude = 76.2° W). From this location: a. Are there stars that never rise?

Yes b.

Are there stars that never set?

Yes c.

Are there stars that are always up? (What is the name for this type of star?)

Circumpolar stars 3.

From Norfolk, what direction do you have to look to see circumpolar stars?

North

4.

As you increase your latitude do you see more or less circumpolar stars? As you decrease your latitude do you see more or less circumpolar stars?

Increasing show more circumpolar while, decreasing shows less circumpolar.

5.

What do you think the motion of the stars would look like if you were at the North Pole? Where would Polaris (the North Star) be located?

The stars move to different positions that are in the sky, and the North star would be directly above me.

6.

What do you think the motion of the stars would look like if you were at the Equator? Where would Polaris be located?

Old Dominion University Physics 103N, At Home Lab

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All of the stars in the sky would be moving horizontally through the sky.

Part B: Reasons for the Seasons

1.

Draw arrows in the diagram to indicate the direction the Earth travels around the Sun.

2.

Label Northern spring, summer, fall, and winter.

3.

Label Southern spring, summer, fall, and winter.

4.

The distance between the Earth and Sun during 4 months of the year are listed in the chart to the right. Based on this data, what can you conclude about the effect that the Earth-Sun distance has on the seasons? Support your conclusion by citing specific data in the table.

Summer:1 Fall:2 Winter:3 Spring:4 Summer:3 Fall:4 Winter:1 Spring:2

Month March June September December

Earth-Sun Distance 149 million km 152 million km 150 million km 147 million km

The distance that the earth is form the sun does NOT affect the seasons. The colder months such as March and December are closer to the sun even when the temperature is naturally colder. The warmer months like June and September are farther away, but the heat comes from the earth being tilted on its axis towards the sun.

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Experiment A03: Celestial Motion

Describe, in your own words, what causes the seasons. Specifically, why does the tilt of the Earth’s axis result in some warmer months and some cooler months?

The tilt effects the seasons because it controls the amount of light that is heating a certain spot on the earth.

6.

If, somehow, the Earth’s tilt changed from 23.5° to just 5°, what would change about the seasons?

The season between the northern and southern hemispheres would line up together more often and the extremes of summer and winter wouldn’t happen anywhere near as often.

Part C: The Lunar Cycle In this portion you will be using the simulation Lunar Phase Simulator which is located at http://astro.unl.edu/animationsLinks.html This simulation is a top-down view of the Earth looking at the North Pole. It can also show the position of the Moon in its orbit and the associated phase. Take a few minutes to familiarize yourself with how the simulation works, combine what you see in the simulation with the diagram below, and then answer the questions. 1.

What Moon phase will an observer see if the Moon is directly overhead at sunset?

First Quarter Moon

2.

What Moon phase will an observer see if the Moon is directly overhead at sunrise?

Third Quarter Moon

3.

What Moon phase can be seen for half of the night and then half of the day?

Third Quarter Moon

Old Dominion University Physics 103N, At Home Lab

4.

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What Moon phase can be seen for half of the day and then half of the night?

First Quarter Moon

5.

The following sketches of the moon's appearance were made over about four weeks. Identify the phases and put them in the correct numerical order (full Moon is considered as 0, the starting point). One is labeled for you.

Picture

A

B

C

6.

Order

Phase

3

Waning Crescent

1

Wanning Gibbous

Full Moon

0

Picture

Order

Phase

4

First Quarter

E

5

Waxing Gibbous

F

2

Waning Crescent

D

In the diagram below the sun's light is coming in from the right. The moon's location is marked at several points on its orbit. These are the points the moon was at when the sketches above were drawn. Identify each position with the letter of the corresponding sketch.

D

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Experiment A03: Celestial Motion

E

C

A B

1. 2. 3. 7.

F

Kepler’s Laws The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse. An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time. The square of a planet’s orbital period is proportional to the cube of its semi-major axis.

How long does it take the Moon to complete one cycle of phases, in days?

30 Days 8.

If the Moon is full today, what phase do you expect it to be in one week later?

Third Quarter 9.

If the Moon is full today, what phase do you expect it to be in one month later?

Full Moon 10. Is there a dark side of the Moon? (Note: this question can be effectively answered either yes or no, so it is important to thoroughly explain your reasoning.)

Yes, there is a dark side of the moon, because the moon does not rotate it only revolves.

Part D: Kepler’s Laws In the early 1600s, Johannes Kepler, using observations and data from astronomer Tycho Brahe, first published his

Old Dominion University Physics 103N, At Home Lab

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three laws of planetary motion. These laws were empirically determined with any references to any underlying physical theory. They were determined by examining the shape and speed of planetary orbits. Nearly 70 years later it was shown by Isaac Newton, while formulating his theory of gravitation, that Kepler’s Laws are a direct consequence of Newton’s Laws.

Kepler’s First Law - The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse. Kepler’s main achievement with his empirical laws was in showing that the orbits of the planets were best described by ellipses. Since the ancient Greek astronomers, orbits based upon circles and epicycles were the accepted theory for planetary orbits. An ellipse appears as a somewhat flattened circle. Open an internet browser and visit http://astro.unl.edu/animationsLinks.html Open the simulation Planetary Orbit Simulator. On the left side of the applet, choose the tab for Kepler’s 1st Law. Select ‘Mercury’ from the drop down menu in the top right and click OK. Check all 5 options in the bottom middle of the screen: ‘show empty focus’, ‘show semimajor axis’, etc... Click and drag the planet (the gray dot) around on its orbit. Place the planet at its perihelion position, all the way on the left side of the orbit. At this position, the value for r1 is the distance from the planet to the Sun in AU (this is found at the bottom of the screen). In the table below record the perihelion distance and the semimajor axis for the planet. Move the planet to its aphelion position on the far right of the orbit. Here, r1 is the aphelion distance. Record this value in the table below. Repeat the steps above for both Earth and Pluto. Planet

Eccentricity

Semimajor Axis (AU)

Perihelion Distance (AU)

Aphelion Distance (AU)

Mercury

.206

.387

.307

.467

Earth

.017

1

.983

1.02

Pluto

.249

39.4

29.6

49.3

In the table below, again write in your perihelion and aphelion distance for the Earth. If you subtract the perihelion distance from the aphelion distance you can find how much closer the Earth is to the Sun when at perihelion as compared to aphelion. Convert this distance to miles (hint: 1 AU = 9.296 x107 miles).

1.

Planet

Perihelion Distance (AU)

Aphelion Distance (AU)

Difference (Aphelion – Perihelion) (AU)

Difference (Aphelion – Perihelion) (miles)

Earth

.983

1.02

.037

3,439,520

How many miles closer to the Sun is the Earth when at perihelion vs. aphelion?

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Experiment A03: Celestial Motion

3,439,520 miles closer

2.

Look up online what months of the year we are closest to and farthest from the Sun. Closest – January

Farthest – July

3.

Increase the eccentricity of the orbit. What happens to shape of the orbit? What do you notice about the about speeds at perihelion and aphelion for large eccentricity? The orbit becomes more of an oval shape. The perihelion decreases in au and the aphelion increases au.

4.

What shape is an orbit with an eccentricity of zero?

A perfect circle

Kepler’s Second Law - An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal amounts of time. While Kepler’s 2nd Law is probably the most difficult of his laws to understand or visualize, this portion of the lab will investigate several aspects of this law. The main significance of this law is that planets will orbit faster when they are closer to the Sun and orbit slower when farther away. Planetary orbit speeds are not constant, but instead change with time. Clear the optional features from step 1 in the previous portion of the lab, and select the Kepler’s 2nd Law tab. Set the semimajor axis to 1.00 AU and the eccentricity to 0.5 by using the sliders or by typing the values into the appropriate boxes. Click the ‘Start Animation’ button and then click on the ‘Start Sweeping’ button. When the planet is near the opposite side of its orbit click the ‘Start Sweeping’ button again. Try to obtain two sections that are on fairly opposite sides of the orbit. If needed, use the ‘Animation Rate’ slider to slow down how fast the planet orbits. Click the ‘Pause Animation’ button. 5.

If you click on each of the two areas, what do you notice about the ‘Sweep Area’ that is given at the bottom of the screen? The numbers remain the same.

Old Dominion University Physics 103N, At Home Lab

6.

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If you click and drag around the sweep areas, where is the sweep segment the thinnest? Where is it the widest? What are the names for these two positions in a planets orbit?

The thinnest segment is when the planet is as far away from the sun in orbit and the widest is the closest the planet is from the sun.

Kepler’s Third Law - The square of a planet’s orbital period is proportional to the cube of its semi-major axis. Kepler’s 3rd Law tells us that more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical concept.

P2=k a 3 where P is the planet’s orbital period in years, a is its semimajor axis (or average distance from the Sun) in astronomical units (AU), and k is a constant. k is not a universal constant like the speed of light or Newton’s Gravitational Constant G. Rather, k depends on the particular body that is being orbited (e.g., the Sun). For this portion of the lab, it is up to you to determine the value of k for our solar system. We can take the above equation and solve it for k: 2

k=

P a3

7.

Use your book or various internet sources to look up and record the orbital period and the semimajor axis for each of 4 random planets in our solar system. Be sure to use units of years and AUs.

8.

Calculate k for each of the planets.

Planet

Period – P (years)

Semimajor Axis – a (AU)

k

Saturn

29 years

9.54 au

.97

Jupiter

12 years

5.20 au

1.02

Mars

687 days

1.52 au

1

Venus

225 days

.723 au

1

9. What do you notice about k for each of the planets? Are they similar? Are they vastly different? All of the numbers are either 1 or within hundredths of 1.

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Experiment A03: Celestial Motion

Old Dominion University Physics 103N, At Home Lab

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