earth science...earth science – ms. holton day 2: coordinate systems – degrees, arcminutes, and...

Earth Science REMOTE LEARNING PACKET WEEK OF MARCH 23-27

DAILY SCHEDULE DAILY MINUTES ESTIMATED

Monday: Read the Introduction for this packet Read “Day 1: Coordinate Systems – Latitude/Longitude Review.” Complete any vocabulary relevant to the Day 1 reading. Complete “Day 1: Complete the Exercises”

20 Minutes

Tuesday: Read “Day 2: Coordinate Systems – Degrees, Arcminutes, and Arcseconds” Complete any vocabulary relevant to the Day 2 reading. Complete “Day 2: Complete the Exercises”

30 minutes

Wednesday: Read “Day 3: Coordinate Systems – Equatorial Coordinate System” Complete any vocabulary relevant to the Day 3 reading. Complete “Day 3: Complete the Exercises” Not Required: For more info, see https://www.youtube.com/watch?v=WvXTUcYVXzI

25 minutes

Thursday: Read “Day 4: Mapping the Sky – Reading a Star Chart” Complete any vocabulary relevant to the Day 4 reading. Complete “Day 4: Complete the Exercises”

25 minutes

Friday: Read “Day 5: Observing” Complete “Day 5: Complete the Exercises” Finish the vocabulary list

20 minutes

Total 2 hours.

Upon return to school, please be prepared to turn in the following:

● Vocabulary Sheet

● The “Complete the Exercise” sections for each day (provided at the end of the packet).

NOTE: All exercises may be completed on a separate sheet of paper, if needed. If you choose this option,

please be sure to neatly sketch any diagrams or tables needed an answer the question.

Declaration of Academic Honesty

I, the parent/guardian of _______________________, affirm that the work contained here was

completed independently.

Parent Name (print):

Parent Signature:

https://www.youtube.com/watch?v=WvXTUcYVXzI

Name: _____________________________ Earth Science, Period: _____

Scottsdale Preparatory Academy 2 Earth Science – Ms. Holton

Introduction

This packet introduces a coordinate system used by astronomers to locate objects in the sky. First, we

will review the latitude/longitude coordinate system used here on the Earth. Second, we introduce you

to the units of arcminutes and arcseconds. We will then investigate the Equatorial Coordinate System, a

coordinate system fixed to the stars instead of the earth. Next, we will discuss how to read star charts

using Equatorial Coordinate System. Finally, we will ask you to go outside and observe the night sky.

Vocabulary

As you read through this packet, fill in the following vocabulary definitions.

Latitude

Equator

Longitude

Prime Meridian

Arcminutes

Arcseconds

Equatorial Coordinate System

Celestial Equator

Declination

Right Ascension

Ecliptic



Day 1: Coordinate Systems – Latitude/Longitude Review

Maps of the Earth:

Coordinates are essential for accurately locating objects both on Earth (e.g., cities, states, islands, etc.)

and in the sky (e.g., stars, galaxies, etc.). Before we discuss how to find your way in the night sky, we

must first review maps of the Earth. On the Earth, we use the latitude/longitude coordinate system.

Latitude is the distance north or south of the Earth’s equator, measured in degrees. The Earth’s equator

is an imaginary line that circles Earth halfway between the North and South poles. The equator is at a

latitude of 0. Latitude is defined by the angle from the equator to the point on Earth, measured from

the Earth’s center. Thus, the North Pole is at a latitude of 90N because the angle from the equator to

Earth’s center to the pole is 90. The South Pole is at a latitude of 90 S. Scottsdale’s latitude is 33.5N.

Longitude is the distance (measured in degrees) east or west of the prime meridian. Unlike latitude

there is no natural or physical characteristic of the Earth from which to set the zero point in longitude.

As a result of global navigation, and what is now history, the British established a zero point in longitude

in Greenwich, England at the Greenwich Royal Observatory. Thus, the prime meridian is the imaginary

line that goes from the North Pole to the South Pole through Greenwich, England. The prime meridian

has a longitude of 0. Longitude is defined by the angle from the prime meridian to the point on Earth,

measured from Earth’s center. A location with a longitude of 60E is east of the prime meridian with an

angle of 60 between the prime meridian and that point, as measured from Earth’s center. The

longitude of Scottsdale, AZ is 111.9 W.

For Day 1, do the “Complete the Exercises” section at the end of the packet.



Day 2: Coordinate Systems – Degrees, Arcminutes, and Arcseconds

Coordinates are essential for accurately locating places such as cities, towns, mountain tops, islands, etc.

Latitude and longitude refer to the angle from the equator or prime meridian to the point on Earth,

measured from the Earth’s center. Because they are both angles, latitude and longitude both use units

of degrees. You are most likely familiar with degrees from math. A circle is 360; a semi-circle is 180;

and a quarter-circle is 90.

Just as hours can be split into minutes and seconds, degrees can also be split into smaller units – that of

arcminutes and arcseconds. Just as there are 60 minutes in 1 hour and 60 seconds in 1 minute, there are

also 60 arcminutes in 1 degree and 60 arcseconds in 1 arcminute, as demonstrated in the right-hand

figure above. Note that degrees use the degree symbol ( ). Arcminutes use a single apostrophe ( ‘ )

while arcseconds use a double apostrophe ( ‘’ ). Written out, the conversions shown above are:

1 degree = 60 arcminutes and 1 arcminute = 60 arcseconds

Note: The apostrophe notation is often used in the United States as shorthand for inches and feet. We

will always write inches as in. and feet as ft.

Mixed units:

When we talk about time, we will often use mixed units – that is, we will speak about the number of

hours, minutes, and seconds rather than as a decimal number of hours. Let’s take, for example, the

runtime of your favorite movie. If you look at the back of the DvD case, you may see a time that says 135

minutes. Although this is a perfectly accurate way to state the movie’s runtime, few people have a good

understanding of that number. We could convert that time to hours:

135 minutes ×1 hour

60 minutes= 2.25 hours

Again, this is a perfectly accurate way to state the time. However, what you will likely hear someone say

is “two hours and fifteen minutes.” How did they come to that conclusion? They kept the whole number

(2 hours) and converted the remainder (0.25 hours) to a smaller unit.

0.25 hours × 60 minutes

1 hour= 15 minutes

When written in mixed units, the length of a 135 min. long movie can also be written as 2 hrs 15 min.

The same thing can be done with angles, like the ones that define latitude and longitude. Yesterday, I

told you that the latitude of Scottsdale is 33.5 N. This means that the angle from the equator to

Full Circle Semi Quarter



Scottsdale, as measured from the Earth’s center, is 33.5. To write this as mixed units, we would keep

the whole number (33) and convert the remainder (0.5) to a smaller unit. In this case, arcminutes.

0.5 × 60′

1= 30′

Thus, the latitude of Scottsdale can be written as 33.5 N or it can be written as 33 30’ N in mixed units.

Let’s do the same thing with Scottsdale’s longitude of 111.9 W. Keep the whole number (111) and

convert the remainder (0.9) to arcminutes.

0.9 × 60′

1= 54′

The longitude of Scottsdale can be written as 111.9 W or it can be written as 111 54’ W as mixed units.

To go from mixed units back to a decimal answer in degrees, you only need to convert everything to

degrees and add them together.


Day 3: Coordinate Systems – Equatorial Coordinate System

The latitude/longitude coordinate system is fixed with regard to the Earth. The latitude and longitude of

Scottsdale is always the same. As the Earth rotates on its axis, the coordinate system moves with it.

The Equatorial Coordinate System is an astronomical coordinate system that is fixed to the stars. As the

Earth rotates on its axis, the stars seem to move with respect to the Earth, but the Equatorial System

moves with it. As an extension of our Earth-based coordinate system, the Equatorial Coordinate System

is a similar set of coordinates on the sky. The Celestial Equator is a projection of the Earth’s equator onto

the sky, but where the Earth’s equator is fixed to the Earth, the Celestial equator is fixed to the stars.

Similarly, directly above the Earth’s north pole is the North Celestial Pole, while directly “below” the

Earth’s south pole is the South Celestial Pole. The celestial coordinates that are analogous to latitude

and longitude (on Earth) are called declination and right ascension (on the sky).

Declination (abbreviated: dec) is similar to the Earth-based system of latitude; it is the angular distance

north or south of the Celestial Equator. The Celestial Equator is the extension of Earth’s equator onto

the celestial sphere. The celestial equator has a declination of 0; the North Celestial Pole has a



declination of 90N; and the South Celestial Pole has a declination of 90S. Like latitude, declination is

measured in degrees, arcminutes and arcseconds.

Right Ascension (abbreviated: RA) is similar to the Earth-based system of longitude; like longitude, there

is not natural or physical characteristic from which to set the zero point. Instead, by international

agreement, the zero point is the imaginary line that goes from the North Celestial Pole to the South

Celestial Pole through the location of the sun at the time of the Spring Equinox (March 21st).

Unlike longitude, right ascension is NOT measured in degree, arcminutes, or arcseconds; instead, it is

measured in hours, minutes, and seconds. One rotation of Earth on its axis takes roughly1 24 hours, and

so, we see the same stars again every 24 hours. Instead of using units of angle (e.g., degrees),

astronomers chose to use units of time, splitting the sky into 24 hours of RA. The zero point of RA is 0h,

and the part of the sky we see 12 hours later has an RA of 12h. This system allows astronomers to use

the stars as a sort of clock. Stars with RA = 3h will appear in the sky 3 hours later than stars with RA = 0h.

Earth rotates 360 on its axis in that 24 hours, so we can also talk about how much Earth has rotated in a

given amount of time. We find that every hour, Earth rotates 15 on its axis.

360

24 hours=

15

1 hour

Thus, in 3 hours of time, Earth rotates 45 on its axis, and we see stars that have a right ascension 3h

greater than the stars we started with. In 1 hr of time, the sky moves through 1 hr of right ascension.

Similarly, in 4 min of time the sky moves through 4 min of RA. Additionally, 1 hr of RA corresponds to a

15 movement of the sky, and 24 hrs of RA corresponds to a full 360 rotation of the Earth.


Day 4: Mapping the Sky – Reading a Star Chart

When looking at maps of Earth, we considered different map projections. The most common map

projection is the Mercator (aka cylindrical) projection, where all the lines of longitude and latitude are

straight and parallel. In this projection, the globe touches the cylinder at the equator, so the equatorial

region is distorted the least. The poles, which are the furthest from the equator, are distorted the most.

Star charts are maps of the sky using celestial coordinates. If

you look at the star charts at the end of this packet, you will

notice that there is a lot in common with maps you have seen

of Earth, but with units of right ascension (RA) and declination

(Dec) instead of longitude and latitude. The two charts

provided (SFA Star Chart 2 & 3) are meant to be used together

as one long map. Together, they make a Mercator projection

of the celestial equator and the middle declinations.

1 Turns out the Earth rotates on its axis once every 23 hrs 56 min 4.1 sec. While not important for discussing coordinate systems, this information does become important when we talk about long-term motion of the stars.

Mercator Projection



Remember that declination is similar to latitude. The 0 mark is the celestial equator, and the lines of

declination are marked with tick marks along the vertical axis. Declination is labeled in 10 increments,

and each smaller tick mark corresponds to 1. You may also notice that this map does not label

declinations as north or south of the celestial equator. Instead, these maps use a plus (+) sign to

indicate northern declinations and a minus (-) sign to indicate southern declinations. Maps of Earth will

sometimes use this notation as well. Both methods are correct, and I will accept answers using either

notation (e.g., +45 is the same as 45N and -60 is the same as 60S).

Recall that right ascension is similar to longitude. On these charts, RA is labeled with units of hours on

the horizontal axis. The smaller tick marks are in 5 minute intervals. The sinusoidal (curvy) line on the

star charts shows the position of the sun throughout the year. It is labeled with the date when the sun is

at that position. The path of sun through the sky is known as the ecliptic. Notice that, as it should, the 0h

mark of RA goes through the location of the sun at the time of the Spring Equinox (March 21st).

Because these charts are meant to be used when looking at the sky, RA increases from right to left. You

will also notice that the compass rose looks different than what you see on maps of Earth. Instead of

NESW (“never eat soggy waffles”), the compass rose is ordered NWSE. This will make more sense when

we start using these charts for observation!

Because RA and Dec are coordinates fixed to the stars, stars and other distant objects will keep their

location in RA and Dec throughout the year (just like we stay at the same latitude and longitude in

Scottsdale). For example, the star Betelgeuse in the Orion constellation (chart 2) has Equatorial

coordinates of approximately RA = 6h, Dec = +7.5°. Because Equatorial coordinates are fixed to the stars,

Betelgeuse will always have these coordinates. The RA and Dec of the stars do NOT change throughout

the year. In the Equatorial Coordinate System, the coordinates are fixed relative to the stars. Our view

of the stars changed over the course of the night because Earth rotates on its axis. Our view changes

over the course of the year because we orbit around the sun. However, the location of the stars in the

sky remain fixed with respect to the other stars just like the location of Scottsdale remains fixed with

respect to the other cities on Earth. The city of Scottsdale keeps the same latitude and longitude. Stars

keep the same right ascension and declination.


Day 5: Observing

Now that you understand star charts, their units, and how to locate stars on them, the only thing left to

do is to go out and observe! Orion, the hunter, is the most easily located constellation in the night sky.

You can recognize it by the line of 3 stars in the middle of the constellation, known as Orion’s Belt. On

star chart 2, Orion is right in the middle. Keep the following in mind when observing:

• NEVER look directly at the sun. You will burn your retinas and risk going blind.

• Avoid areas with too much light, as it will ruin your night vision.

• It takes 10-15 minutes for your eyes to fully dark-adapt. This will allow you to see dimmer stars.

• Do not use bright white lights, as it will ruin your night vision. Dim or even red light is better.




Day 1: Complete the Exercises

1. Use the map below to fill in the table. The first 3 rows are filled in for you.

Place ID City, State Latitude Longitude

1 Los Angeles, CA 34 N 118 W

2 Casper, WY 43 N 106 W

3 Dallas, TX 33 N 97 W

A Boise, ID

B Denver, CO

C Phoenix, AZ

D Detroit, MI

E Atlanta, GA

F Tampa, FL



2. On the map below, label the following:

o Prime Meridian

o Equator

o North Latitudes

o South Latitudes

o West Longitudes

o East Longitude


Answer the following questions in complete sentences.

1. How many minutes are in 1 hour?

2. How many arcminutes are in 1 degree?

Complete the following problems. You do not need to use K/F/S, but you must show your work with

proper unit cancellation. Write the final answer in a complete sentence. The first 2 are done for you.

3. Convert 24 hours into seconds.

24 hours ×60 minutes

1 hour×

60 seconds

1 minute= 86,400 seconds

Note: The units of hours and minutes cancel, leaving units of seconds.

Answer: There are 86,400 seconds in 24 hours.



4. Write 1.83 as mixed units of degrees, arcminutes, and arcseconds. You may write arcseconds to

a single decimal place, if needed.

Keep the whole number: 1

Convert the remainder to arcminutes: 0.83 ×60′

1= 49.8′

Keep the whole number: 49’

Convert the remainder to arcseconds: 0.8′ × 60′′

1′ = 48′′

Answer: You can write 1.83 in mixed units as 1 49’ 48’’

5. Convert 2.1 to arcseconds.

6. Convert 0.5 to arcminutes.

7. Write 6.53 hrs as mixed units of hours, minutes, and seconds.

8. Write 12.885 as mixed units of degrees, arcminutes, and arcseconds.

9. BONUS: Write 44 23’ 12’’ as a single, decimal number in degrees.




Complete the following sentences by filling in the blank(s):

1. Latitude/longitude is a coordinate system fixed with regard to the ______________________.

2. Declination and right ascension are part of the ________________________ Coordinate System,

which is fixed to the __________________.

3. In 1 hour, the sky moves through ________________ of right ascension, and Earth rotates

________ degrees on its axis.

Answer the following question in complete sentences:

4. Explain how latitude and longitude are measures of angle. Hint: See Day 1 material.

5. In what way(s) is declination similar to latitude? In what way(s) is right ascension similar to

longitude?

6. What imaginary line defines the zero point of latitude? Of longitude?

7. How are the zero points of declination and right ascension defined?




Review the information from Day 3 again, if needed.

Answer the following in complete sentences:

1. Why do we only use a Mercator projection to show the area near the celestial equator?

2. The right ascension and declination of the stars do not change over the course of the year. Why?

Complete the following by filling in the blank(s):

3. On star charts 2 and 3, declination is labeled in _________________ increments, but the smaller

tick marks are in ______________ intervals.

4. On star charts 2 and 3, right ascension is labeled with units of _______________, but the smaller

tick marks are in __________________________ intervals.

5. The star _____________________ in the Orion constellation has Equatorial coordinates of

approximately RA = 6h, Dec = +7.5°.

Use the star charts to complete the table. Write declination to the nearest degree (e.g., +53). Write

right ascension to the nearest 5 minutes (e.g., 2h 10m) . The first one is filled in for you as an example.

Star Name Constellation RA Dec

Rigel ORION 5h 15m – 8

CANIS MAJOR 6h 45m – 16

AURIGA 5h 15m +46

Vega LYRA

Spica 13h 25m

Arcturus BOOTES

CARINA 6h 25 m – 53




NOTE: Ask your parent or guardian before completing this activity; they should know where you are. If

you are going further than your own backyard, they may wish to come with you.

It’s time to do some observing! We will be looking for the constellation Orion in the night sky. Before

you go outside, be sure you have the following: (1) Star chart 2: Know what Orion looks like, (2) this

page, (3) a pencil, and (4) something to write on (clipboard, study book, etc.)

Once you are ready, go outside around 8pm, and find a dark location, as far from lights as possible. The

more of the sky you can see, the better. Determine the cardinal directions (N, S, E, and W). You do not

need to know them perfectly. A rough estimate of which way is N, S, E, and W is fine. If you need help, a

parent may be able to help. Many cell phones also include a compass. Turn to face south and look up.

Try to find Orion, using your star chart as a reference, if needed. Orion is best identified by the 3 stars in

the middle of the constellation called Orion’s Belt. If you can’t find it, give yourself 10-15 min to dark

adapt, and try again. If you still cannot find it, go inside and try again another night.

You may notice that Orion’s Belt “points” to a bright star East of the constellation. This star is Sirius – the

dog star. You may also notice a bright object in the West, toward the horizon. This is Venus.

In the space below (or on a separate sheet of paper), sketch the night sky around Orion.

• Only sketch what you see; it is ok if you do not see the entire constellation. Size the dots

according to each star’s brightness – a large dot for a bright star and a small dot for a dim star.

• Include any nearby stars or bright objects in other parts of the sky around Orion.

• Label whichever named stars or bright objects that you can identify (e.g., Rigel, Sirius, etc.).

• Don’t forget to include the date, time, and location of your observation!

Date: _________________ Time: _________________ Location: _________________

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