lab report

Telescopes and Daytime Observations 1. Introduction

In this laboratory activity, we will focus on the application of lenses and mirrors in telescopes. We will direct our attention towards the telescopes we will be using for this project's daytime observations and later this semester.

2. The Basic Telescope

Laboratory Activity Images, Lenses and Mirrors addressed the

phenomenon of image formation and ways and means to accomplish this. The final question we should ask ourselves is: "So how do we make a telescope with all this knowledge on lenses and mirrors?" The answer is surprisingly simple.

With a lens or mirror we can gather light to create an image in a location

behind the lens or in front of the mirror (the focal plane). Although we can visualize this image using a film or screen, we do not necessarily have to. Even when not projected onto a screen or film, the image will still be there, in space, at the location of the focal plane.

With respect to observation of the object with the naked eye, this image is bright since we used a lens or mirror, which has light gathering properties. Bright images allow for examination of details, and we can do this in the same way we would examine the fine print on a car lease or rental agreement, by using a magnifying glass. 2.1 Elements of a Telescope

Examine figure 2.1, which outlines the idea of using a magnifying glass to study details of the image. A lens (now called the objective) gathers light of an object, and creates an image in its focal plane. There, a magnifying glass, referred to as the eyepiece, is set-up to examine a detail of the image and re- route that part to an observer's eye. Let's scrutinize these two essential elements a bit closer.

1. The objective gathers light of an object. Since the object is usually far away, the light enters the objective in virtually parallel rays and creates an image in the focal plane.

2. The eyepiece, which is merely a lens with properties similar to the objective, is used in a fashion opposite to the objective. It examines a detail of the image formed in the focal plane of the objective. Light 'emerges' from a

detail of the image in divergent rays, and the eyepiece is positioned such that after passing through it, light rays are again virtually parallel. It is at this

point that the light rays are suitable to be presented to the eye of an observer1.

In order for the focal plane of the eyepiece to be positioned such that light passing through it is suitable for presentation to the eye, we may need to move the eyepiece back and forth. We commonly refer to this process as

focusing.

Question 1: Light from far away (notably astronomical) objects reaches us in

virtually parallel rays. So why go through the trouble of first changing the direction of the rays with respect to each other with the objective lens or main mirror, and then turn them back into parallel rays with the eyepiece (ocular)

just so that the are acceptable to the eye to form an image on our retina? Why not look at the object straight away?

1 The ciliary muscles (Lenses 1, section 3.2) can deform the crystalline lens of our eye to a limited extent only. In order for this lens to form an image on the retina, light needs to enter our eyes in virtually parallel rays. If not, the image forms somewhere behind our retina, and we will perceive it as out-of-focus.

Object Objective Focal Eyepiece To observer plane

The principle of the telescope

An objective gathers light from an object, and creates an image in its

focal plane.

An eyepiece (equivalent to a magnifying glass) examines a detail of the

image and re-routes this detail to an observer. Elements in this image are

NOT to scale.

Figure 2.1

2.2. Light gathering power of a telescope

The larger the lens or mirror in a telescope, the larger the light gathering power. In fact, the light gathering power is proportional to the area of the lens

or mirror. For circular objects, the area is related to the square of the diameter according to:

Area = /4 x d2, where  = 3.14159… , d = diameter of lens or mirror

E.g., when doubling the diameter of a lens/mirror, we quadruple light gathering power.

Question 2: The pupils in our eyes have a diameter of approx. 0.2 inch (5 mm). When considering a telescope with a mirror that is 8 inch in diameter (200

mm), how many times more light than the naked eye does the telescope gather?

2.3. Magnification of a telescope

The magnification of a magnifying glass indicates how many times larger an object appears through the magnifying glass than with the naked eye. Magnifying glasses are available with different powers of magnification.

Similarly, eyepieces, the 'magnifying glasses' of a telescope, are available

with different powers of magnification. For a given telescope, the magnifying

power is determined by the focal length of the eyepiece. Without going into detail, we present the magnifying power of a 'telescope – eyepiece combination'

as:

Magnification = Focal length of Objective / Focal length of Eyepiece

The focal lengths of objectives and eyepieces are numbers that are provided by the equipment manufacturer.

Question 3: Given the following typical values provided by a manufacturer for a telescope and eyepiece, calculate the magnifying power of the system. Focal length of objective: 2000mm; focal length of eyepiece: 25mm.

2.4 Telescope Types

Small lenses can be manufactured with near perfection. Therefore, we

can find a wide array of excellent quality small refractor telescopes. However, small lenses have low light gathering abilities. Refractor telescopes with high light gathering ability require high quality, large diameter lenses. But, the

larger a lens, the more difficult to make it flawless, i.e., without cracks, air bubbles, inclusions, etc.

Figure 2.4.2

Newtonian telescope design

Figure 2.4.2

Figure 2.4.3

Cassegrainian telescope design

Figure 2.4.3

This is where the reflecting telescope makes its entrance. In contrast to

a refractor-style telescope, where the surface as well as the interior of lenses are of major importance, the reflector-type telescope 'only' requires the high-quality

surface on a accurately ground mirror. Large mirrors are much easier to produce than large lenses.

2.4.1 Reflector-type Telescopes

In Project Images, Lenses and Mirrors, we briefly touched upon the image-forming abilities of a parabolic mirror. You will have noticed that the

location of the focal plane, in front of the mirror, was awkward to say the least. There are two ways in which we can 'relocate' the location of this focal plane.

2.4.2 The Newtonian Telescope

In this type of telescope, we use a small mirror to intercept light reflected by the parabolic mirror, and on its way to the focal plane. It is redirected sideways out of the telescope towards a new location for the focal plane, where we find the eyepiece. When observing, we look sideways into the telescope. See figure 2.4.2.

2.4.3 The Cassegrain Telescope

This telescope also has a small mirror intercepting light on its way from the parabolic mirror to the focal plane. Here, it reflects light back towards the parabolic mirror, which has a centrally located hole. The new location of the focal plane is just behind the parabolic mirror, where we find the eyepiece. See figure 2.4.3. Question 4: The Cassegrain design provides more compact (shorter) telescopes. Why? (Examine figures 2.4.2 and 2.4.3). The shorter design is usually preferred in situations where the telescope is transported frequently.

2.5 Remarks

The manufacturing of spherical mirrors is simpler and less costly than parabolic mirrors. To correct for deviations (so-called aberrations) in the focal plane due to the 'wrong' shape of the mirror, a glass corrector plate is put in front of the telescope. The combination corrector plate – spherical mirror is designed such that the system acts as a single parabolic mirror. Telescopes that use this system are referred to as Schmidt-Cassegrain telescopes. The telescopes we will use for our nighttime observations are of this design.

The Celestar 8 telescope

Fig 4.1

The telescope's left

fork tine with DEC Tangent Arm Fig. 4.2

3. Retrospective

We have seen

• why and how images can be formed

• how eyepieces allow images to be examined at different magnifications

• how the diameter of a lens or mirror relates to a telescope's light gathering power

• how to determine the magnification of a telescope-eyepiece combination

• what type of telescopes exist

At this point you have acquired sufficient theoretical knowledge and we will now focus on acquiring some daytime experience with handling a telescope

to facilitate nighttime observations that will be held later during the semester. 4. The celestial coordinate system - Right Ascension and Declination

How would you point out the location of a star to someone? "Just over

the tree in my backyard"? That won't work unless you give access to your yard. Moreover, stars move and what is over your tree now will likely not be over your tree in 2 hours…

Astronomers use a celestial coordinate system that unambiguously

defines the position of a (fixed) star for observers living on Earth. This

coordinate system introduces two angles, Right Ascension (RA) and Declination (DEC), to describe the position of a star at the moment of vernal equinox (Ref. your textbook). The RA-DEC system is virtually the only coordinate system used in ground-based observational astronomy.

Right Ascension (RA) of a celestial object is the angular distance from the

vernal equinox eastward along the celestial equator to the point from where the

object's declination is measured. Declination (DEC) is defined as the angular distance (North or South) of a celestial object from the celestial equator.

4.1 RA and DEC on the Telescope

The lecture addressed the movement of the Sun and stars across the sky. It was seen that trajectories of celestial objects are circles around a common

point, the North Celestial Pole, which is the intersection of the (infinitely) extended rotation axis of the Earth with the celestial sphere.

To simplify the operation of telescopes, most are constructed using this characteristic of celestial motion: The main axis of most telescopes is aligned parallel to the rotational axis of the Earth. Consequently, the movement of

stars is observed as circles around this axis. From a mechanical point of view, this type of alignment greatly simplifies tracking a star. This can be achieved

by merely rotating the main axis of the telescope at the same rate as the rate of movement of a star (one full rotation per 23 hours, 54 minutes and 4.09

seconds).

In practice, alignment of the Celestar C8 is achieved by setting its Tilt

Plate (see figure 4.1) at the local geographical latitude (for USC: 34° N), and pointing the rotation axis of the telescope at the North Celestial Pole (very close to where we find Polaris).

4.2 Setting the Right Ascension (RA)

Examine figure 4.1. Locate the Right Ascension Setting Circle (‘RA Setting Circle'). This circle

is divided into 24 equal parts, each division indicating the equivalent of one hour of star movement. You will also notice 5 and 15-minute subdivisions. There are two rings of RA numbers: the numbers on the inner circle are for the

Northern Hemisphere, those on the outer circle are for the Southern Hemisphere. We will use the inner circle only.

After proper initial alignment, this ‘RA Setting Circle' allows us to position the telescope at the RA coordinate of a star. This is accomplished by

releasing the ‘RA Clamp' and slowly turning the ‘RA Slow Motion Control Knob' until the desired RA value is reached. The ‘RA Clamp' is then tightened again.

The RA value is read from the inner circle near the scale markers under the ‘RA Slow Motion Control Knob'.

RA fine control is achieved by half way releasing the ‘RA Clamp', such that the ‘RA Slow Motion Control Knob' can be turned with some noticeable, but not excessive, resistance.

4.3 Setting the Declination (DEC)

Examine figure 4.1.

Declination of the telescope is set in a fashion similar to RA. First, while

holding the telescope tube with one hand to prevent it from toppling over, the declination clamp (‘DEC Clamp') is released, and the telescope tube is set at

the desired declination value by reading the ‘Declination Setting Circle' on the side of the telescope tube's fork mount. The ‘DEC Clamp' is then set again in its locked position.

DEC fine control is achieved by turning the ‘DEC Slow Motion Control

Knob'. To use this fine control, the DEC Clamp does NOT have to be released

first. However, the range of this control is very limited. NEVER FORCE IT BEYOND ITS LIMITS!

When the DEC fine control reaches its limit, the following, rather

cumbersome procedure needs to be followed. Turn the ‘DEC Slow Motion Control Knob' in the opposite direction until the ‘DEC Tangent Arm' (on the

inside of the fork mount near the ‘Slow Motion Control Knob') is in the center of the fork tine. Then, while holding the telescope tube with one hand, release the ‘DEC Clamp', manually center the object you are looking at by using the

‘Finder Scope', and again tighten the ‘DEC Clamp'.

Handling and Positioning WARNINGS

When positioning a telescope, NEVER push or pull on the EYEPIECE, FOCUS KNOB OR FINDER SCOPE to set

the telescope into the desired position. This will damage the telescope optical system!

To adjust RA: 1. Release the ‘RA Clamp' 2. Gently rotate the ‘RA Slow Motion Control Knob' to set RA 3. Tighten the ‘RA clamp' To adjust DEC: Minor DEC Adjustment - Fine Control:

Gently turn ‘Dec Slow Motion Control Knob' Do not force it beyond its limits! In case ‘DEC Slow Motion' runs out: Use, ‘Major DEC Adjustment' procedure

Major DEC Adjustment: 1. Set ‘DEC Tangent Arm' in center position 2. Support the telescope tube with one hand 3. Release the ‘DEC Clamp' 4. Gently push and pull the telescope tube to set DEC at the desired position, using the ‘Finder Scope' 5. Tighten the ‘DEC Clamp' 5. Day Time Observation Outline

We will now start using a good quality 8'' telescope. All issues of image formation, magnification and positioning that were addressed will 'come to life'

in this project.

First, we will acquaint ourselves with telescopes and see how to safely handle these. Then we will address positioning, magnification and field of view of a telescope. The last two factors give insight into size and extent of areas and objects observed.

5.1 The Celestron 8'' Schmidt-Cassegrain Telescope

The telescopes available are Celestar 8 telescopes. As we have noted in our laboratory experiments, lens and mirror systems invert an image: left

becomes right, up becomes down, and visa versa. The eyepieces of the Celestar 8 are connected to the telescope through a prism, to allow for more convenient viewing. This prism restores the up/down inversion that was

originally introduced. So, the image seen through the Celestar 8 telescope will still have left and right reversed, but up and down as normal.

5.2 Telescope Handling

Handling a telescope is basically a simple matter. All that is required is some feel of direction and reading the instructions. Using figure 4.1, identify the following items on the sketch, as well as on the telescope:

• Declination Clamp (DEC Clamp), controls up-down (north-south) motion of tube

• Right Ascension Clamp (RA Clamp), controls left-right (east-west) motion of tube

• DEC Slow Motion Knob

• RA Slow Motion Knob

• Eyepiece

• Focus Knob

• The DEC Setting Circle (showing the declination value)

• The RA Setting Circle (showing the right ascension value. Use the inner circle)

5.2.1 Pointing the telescope

A telescope is pointed at an object by moving it in right ascension (RA) and declination (DEC). Loosely stated, right ascension corresponds to East-

West movement while declination corresponds to North/South movement. To make considerable changes in the direction in which the telescope is pointing:

1. Loosen the RA and DEC clamps on the telescope 2. Move the telescope until pointing in the desired direction 3. Lock the RA and DEC clamps to hold the telescope in place

For fine adjustments in right ascension, release the RA clamp. The RA Slow Motion Knob now rotates freely. Turn it to center the object, then tighten

the RA clamp. For fine adjustments in declination, turn the Declination Slow Motion

Knob. The DEC clamp does not have to be loosened. Once you have the desired target, stop rotating the DEC Slow Motion Knob.

WARNINGS to prevent costly damage

Do not force the DEC Slow Motion Knob if it will not turn

If the DEC knob will not turn, the DEC travel arm may have reached the end of its threaded

rod (see figure 4.2, and the telescope).

To correct this, rotate the DEC Slow Motion Knob in opposite direction until

the travel arm is in the center of the fork tine.

Then, release the DEC clamp, and center your object. Tighten the DEC clamp.

The DEC Slow Motion Knob will again allow fine adjustments

Do not hold the eyepiece assembly to move the telescope. This will damage the optical system

Do not force the fork mount to swivel when the RA clamp is

fully engaged

5.3 Project 1 - Field of view of the eyepieces

You have to your disposition 3 eyepieces, with focal lengths of, respectively, 35mm, 25mm and 10mm. Given that the focal length of the

telescope mirror is 2035mm, what are the magnifications you can obtain? Use the space provided in the Answer Book for calculations and to tabulate your

answers. Magnification does not tell the whole story on the image that is observed.

An equally important question is: 'What is the field of view we have with a

telescope-eyepiece combination?' This number, expressed in degrees, tells us the size (expressed in degrees) of the patch of sky we are observing. Looking out of the lab towards the east, you'll see the Hedco

Neurosciences Building, built with red bricks. Point your telescope at this building and focus on the red bricks. Look through the eyepiece of the telescope and slowly adjust the focus (with the Focus Knob) until the image is

clear and sharp.

Data: For the Hedco building:

The bricks are 29.5 cm (0.295 m) wide and 5.5 cm (0.055 m) high

The grout on the sides is 1.2 cm (0.012 m) wide The grout over and under the bricks is 1.2 cm (0.012 m) high

The building is 100m from the observation site For the Parking Structure A:

The bricks are 39 cm (0.39 m) wide and 9 cm (0.09 m) high

The grout on the sides is 1.5cm (0.015 m) wide The grout over and under the bricks is 1.5 cm (0.015 m) high The building is 69 m from the observation site

All measures are approximate.

With the size of the bricks known, as well as the width of the grout lines, the true length of the wall segment observed can be calculated. Figure out how to do this, then calculate the length (or height) of the stretch of wall that is

visible in the eyepiece. To increase accuracy, count the bricks in vertical direction only.

Repeat this for all eyepieces. Note your observations and calculations in

the table in the Answer Book. With the distance of the building and the length

of the wall segment known, the field of view (FoV), in degrees, for each eyepiece can be calculated by using the 'small angle formula':

FoV  57.3 * Length of structure observed in eyepiece / Distance of structure

Note the results of your calculations in the table.

5.4 Project 2 – Determination of distance using known FoV values

The telescopes will have been set up in the lab pointing at PSA. Each of

the telescopes has 3 different eyepieces, 35mm, 25mm or 10 mm. Using your Field of View calculations from the previous exercise, calculate the distance between where the telescopes are set up and Parking Structure A.

Distance to Structure  (57.3 * Length of the structure in eyepiece)/FoV

6. Choosing an Eyepiece

When observing astronomical objects, the method for choosing eyepieces and determining field of view is a bit different from what we did in the first part of the lab. In the field, you decide what you want to look at first. Then, you find

out its angular size in the sky. From there, you decide the eyepiece that will give you the best magnification and field of view. How do we go about doing

this?

First, let's look at typical angular sizes of some astronomical objects:

Object Angular Size

Planets 5" - 40"

Planetary Nebulae 10" - 20'

Globular Star Clusters 20' - 1°

The Moon about 30'

Galaxies 10' - 2° or more

Diffuse Nebulae 20' - 3° or more

Open Star Clusters 20' - 3° or more

Comets 30' - 5° or more (if you include the tail)

For our example, let's say we want to look at the moon. From the table, we see it has an angular size of 30'. What eyepiece should we pick if we want to fit the whole thing in the field of view?

You don't typically take your telescope and point it at something you know the

size of and the distance to so that you can determine the field of view. Instead, the manufacturer of the eyepiece tells you the field of view of the eyepiece by itself. So, if you just looked through the eyepiece at an object, that would be its field of view.

However, we are using the eyepiece in combination with the telescope. To get

its field of view in conjunction with the telescope, you have to divide it by the magnification.

FoV = Field of View of eyepiece alone / magnification

For instance, if you have a 28mm eyepiece with a 48° field of view, and you use it with your telescope with a 448mm focal length, what magnification do

you get, and what field of view for the eyepiece?

First, let's get the magnification:

M = 448mm/28mm = ____16_____

So the object will look 16 times as big as with the naked eye. What about the field of view?

FoV = 48°/16 = ___3___

This is too big if we just want to look at the moon. You probably won't be able to see much detail on the moon's surface. This eyepiece would be really good

for looking at a large open star cluster, like the Pleiades. Let's see what other eyepieces we have for the moon.

It looks like we have an 8mm eyepiece with a 36° field of view. What if we try this one, while using the same focal length as above (448mm)?

First, we need the magnification:

a) Magnification = _record on answer sheet_

Then we can find the field of view of the eyepiece in the telescope:

b) FoV = record on answer sheet

So we can compare this with the size of the moon in arcminutes, we'll multiply the field of view by (60’/1°):

c) FoV = record on answer sheet

This is much closer to the size of the moon! So, for the view of the moon that

we're looking for, this would be a good eyepiece to use.

Telescopes and Daytime Observations

Name:________________

Lab Partner:________________

Answer to question 1:

Calculation for question 2:

Calculation for question 3:

Answer to Question 4, the Cassegrainian telescope:

Project 1 - Field of View a. Calculation of Magnification

35 mm eyepiece:

Magnification = _________________________________________________________

25 mm eyepiece:

Magnification = _________________________________________________________

10 mm eyepiece: Magnification = _________________________________________________________

b. Calculation of Field of View

Number

of bricks

Number

of grout lines

Calculated length of wall segment

(in meters!)

For 35mm

eyepiece

For

25mm eyepiece

For

10mm eyepiece

Using the ‘small angle formula’, the Field of View is calculated as (show calculation):

35mm eyepiece: FoV =

25mm eyepiece: FoV =

10mm eyepiece: FoV =

Project 2 Distance to Object

Number

of bricks

Number

of grout lines

Calculated length of wall segment

(in meters!)

For 35mm eyepiece

For

25mm eyepiece

For 10mm

eyepiece

Calculated distance using 10 mm eyepiece:

Calculated distance using 25 mm eyepiece

Calculated distance using 35 mm eyepiece

Part 6: Eyepieces

a) Magnification = ______________

b) Field of View (in degrees) = _____________

c) Field of View (in arcminutes) = _____________