Download THE SUN AND THE MOON

Lab 6
THE SUN AND THE MOON
LAB 6
The Sun and the Moon
Learning Objectives
• Identify basic properties of the Sun and the Moon
• Define synchronous rotation
• Utilize basic geometric concepts such as the small angle approximation
INTRODUCTION
The Sun and the Moon are the two largest objects in the sky
that are visible to the naked eye. The Sun is the largest and
most massive object in our Solar System. It is 1 AU away from
the Earth and weighs an impressive 1.98 × 1030 kg. The Moon
is our closest neighbor in the Solar System. It weighs ~1.0 x
1024 kg and has a surface gravity of 1.6 m/s2 (that’s about 6
times less than Earth’s gravity). The Moon and the Sun have
been used as references for humans for millions of years. The
Farmer’s Almanac is a good example of how people use solar
and lunar indicators to try to understand how conditions might
systematically affect crop growth on Earth.
PROPERTIES OF THE SUN
If you survived a trip to the Sun, you would find that you
weighed 27 times more. Its massive size gives it a larger gravity that influences objects up to hundreds of AU away. Light
from the Sun is very important for sustaining life on Earth. It
is therefore not surprising that many ancient civilizations gave
homage to the Sun by naming many deities after it.
Astronomers classify the Sun as a type of star called a “G2 V”
star. This classification describes our Sun’s size (main sequence star) and mass (0.8–1.04 Mʘ) as well as its temperature (5,200–6,000 K) and lifetime status. Our current stellar
Figure 1. Composite photograph of the Sun using two different wavelengths captured by the Atmospheric Imaging Assembly on NASA’s Solar Dynamics Observatory. On the left, the Sun is imaged at extreme ultraviolet light at 304 angstroms
(colorized red); on the right, it is imaged using extreme ultraviolet light at 171
angstroms (colorized bronze). More detail is seen in the 171-angstrom image,
including the Sun’s corona. Image courtesy of NASA.
classification scheme is called the Morgan-Keenan (MK) system. This classification scheme is based on a star’s spectral characteristics, or the properties of the electromagnetic radiation it emits. The MK system assigns a star the letter O, B, A, F, G, K, or
M, with O being the hottest and M being the coolest. In addition, each letter is subdivided using numeric digits 0 through 9, with 0
being the hottest and 9 being the coolest. Lastly, a luminosity class is assigned to a star using 0, Ia, Iab, Ib, or Roman numerals II,
III, IV, or V.
The Sun is presently about middle-aged at ~4.6 billion years old. It is composed mostly of hydrogen (91%) and helium (8.9%), with
traces of other heavier elements. The Sun is an active place that rotates and has magnetic fields that twist with the star’s rotation,
creating active regions on the Sun such as streamers, coronal mass ejections, sunspots, prominences, and solar flares (Figure
1). Every 11 years, the Sun undergoes a cycle of activity, alternating between Solar Maximum and Solar Minimum. At Solar Maximum, there are more flares, sunspots, and other active regions on the Sun than at Solar Minimum.
The Sun does not have a solid surface or core, but it does contain layers (Figure 2, next page) that have different properties and
exhibit different behaviors. The interior of the Sun is broken into three layers: 1) the core, 2) the radiative zone, and 3) the convective zone. The core is the innermost layer and makes up ~20% of the interior of the Sun. It is where frequent, violent nuclear reactions take place, causing the core to reach a temperature of about 15 million K. The radiative zone transports energy from the core
to the outer layer of the Sun’s interior, the convective zone. As its name suggests, the convective zone transports energy to the
Sun’s outer layers through convection cells.
The Sun and the Moon
There are also three outer layers of the Sun: 1) the photosphere, 2) the chromosphere, and 3) the corona. Although it may seem
counterintuitive, the temperature of the outer layers of the Sun increase as you move farther from the surface. The photosphere
is the deepest layer of the Sun that we can observe directly and extends from the visible surface (6,500 K) to ~400 km (4,000 K)
above the surface. The chromosphere extends from ~400 km (4,000 K) to ~2,100 km (8,000 K) above the solar surface to its
contact with the outermost layer of the Sun, the corona. The temperature of the corona fluctuates from 500,000 K to a few million
K. The corona does not have a distinct outer boundary—it stretches for millions of kilometers—and can be seen with the naked
eye only during a total solar eclipse. The corona is also responsible for producing solar wind: charged particles consisting mostly
of protons and electrons moving almost 1 million miles per hour. Earth’s atmosphere and magnetic field protect us from most of
the solar wind, but at the poles, the solar wind often comes into contact with the air and glows, producing a beautiful effect called
an aurora.
The Sun balances its huge gravitational energy by radiating heat from the photosphere. The Sun is expected to continue generating energy the way it is at present for another 5 to 6 billion years. After that time, its hydrogen will be depleted, and it will expand
into a red giant and start to burn helium. This change will alter its classification to become another type of star (Red Giant) in a
different stage of its life.
Figure 2. Illustration of the structure of the Sun.
Did You
?
Know
The study of the movement of acoustic pressure waves in the Sun is known as
helioseismology. These solar sound waves are produced in the convective zone
from pressure fluctuations. When the waves hit the photosphere, they reflect back
inward, resulting in millions of different vibration patterns from the trapped sound
waves. Helioseismologists use the properties of the waves to determine the composition, density, temperature, and motion of the interior of the Sun (much like
seismologists use seismic waves to locate the epicenter of earthquakes). The Sun
is actually a very loud and noisy place, but we will never hear these sound waves
because they cannot propagate through the vacuum of space. However, scientists
developed a way to translate the changes in light on the surface of the Sun caused
by these pressure waves into sound waves. The result is a sound something like a
low hum that is interspersed with deep thumps. Listen to the Sun at this National
Science Foundation website. Image credit: SOHO (ESA & NASA).
The Sun and the Moon
PROPERTIES OF THE MOON
The Moon is about the same age as the Earth and is the
fifth-largest moon in the Solar System. Theories of how it
formed include: 1) It was torn out of the Earth by a collision
with an asteroid; 2) It was formed elsewhere and was gravitationally captured by the Earth on its way to the Sun; or 3) It
formed independently from material left over from the formation of the Earth. Regardless of how it formed, the Moon has
a significant influence on life on Earth. The gravitational pull
of the Moon is responsible for tides, and tides are believed to
have potentially sped up the evolutionary processes of life on
Earth.
The Moon has no atmosphere and no magnetic field. Its surface is subjected to the harsh solar winds of the Sun and
more direct impacts from meteors than Earth. As a result, the
surface of the Moon is heavily cratered (Figure 3). The Moon
takes 27 days to rotate about its axis. This is the same amount
of time that it takes the Moon to orbit around the Earth. This
type of orbit is referred to as synchronous rotation and
causes the same side of the Moon (called the near side of
the Moon) to face Earth at all times. The side that never faces
the Earth is referred to as the far side (or the dark side) of the
Moon. The similarity in its rotation and orbital rates causes the
Moon to be tidally locked to its parent body, the Earth.
The Moon has a differentiated structure similar to that of the
Earth (Figure 4). According to seismic data from the Apollo
missions, the Moon has a solid core composed primarily of
iron, with a radius of approximately 240 km. It also has a liquid
outer core, with a radius of approximately 330 km. In total,
only about 40% of the entire core is solid. Unlike the Earth, the
Moon has, partially molten boundary (PMB) layer outside of
the core that has a radius of approximately 480 km. Outside
of the PMB is the mantle, which is about 1,200 km thick. The
upper boundary of the mantle is the crust of the moon, which
is 40–45 km thick on average. However, in the “Apollo Zone”
(the region where the Apollo missions landed), the crust is only
30–38 km thick.
To date, the Moon is the only other place in the Solar System
on which humans have set foot. The first humans made it to
the Moon on July 20, 1969, on the Apollo 11 Lunar Module
(LM). The trip to the Moon took about one week. In total, six
Apollo missions landed on the Moon: Apollo 11, 12, 14, 15, 16,
and 17. Only Apollo 13 did not succeed in its mission to land
on the Moon; an explosion 200,000 miles from Earth caused
the astronauts to abort their mission, and they managed to return home safely. The Apollo missions collected an abundance
of scientific data that scientists continue to analyze to this day.
Astronauts conducted a variety of experiments on subjects
including (but not limited to) meteoroids, lunar heat flow, the
lunar magnetic field, soil mechanics, and solar wind.
Figure 3. Color-enhanced picture of the near side of the moon taken by NASA’s
Galileo spacecraft in 1992. Many large impact craters are visible (light-colored
areas with radiating lines). Image courtesy of NASA.
Figure 4. Illustration of our current understanding of the interior structure of
the Moon.
Because we have completed many scientific missions to the Moon and collected samples from the lunar surface, we know a lot
more about the properties and processes of the Moon than the other bodies in our Solar System. In total, the Apollo missions
brought back over 400 kg worth of lunar rock and sediment samples. Analyses showed that the composition of lunar rocks is very
similar to some rocks on Earth. The lunar crust contains minerals and rocks abundant in oxygen (O), silicon (Si), magnesium (Mg),
iron (Fe), calcium (Ca), and aluminum (Al), with small amounts of titanium (Ti), uranium (U), thorium (Th), potassium (K), and hydrogen (H).
The Sun and the Moon
We also learned a lot about gravitational effects on the Moon from
the Apollo missions. The Earth’s gravity on the Moon does not cause
tides because there is no liquid on the surface of the Moon. However, thanks to the data from the Apollo mission seismometers placed
on the Moon, we know that Earth’s gravity causes disruptions near
the core of the Moon that generates deep “moonquakes.”
THE SMALL ANGLE APPROXIMATION
Galileo Galilei (1564–1642) was a famous Italian astronomer who
lived during the Renaissance period. One of his great achievements
was to improve the telescope so that scientists could observe stars,
planets, and their moons. In order to see an object using a telescope,
the size of the object (namely, its diameter) should be large enough to
produce a measurable angle (α) at the point of observation (Figure 5).
If the angle α is measurable, then the small angle approximation can
be used to derive the size (diameter) of the observed object. The small
angle approximation states that the tangent of an angle that is less
than ~17° is approximately equal to the angle in radians (Figure 6):
Equation (1)
Recall from the previous lab that converting the unit of an angle between degrees and radians can be done by using the equivalency of
2π radians and 360°. Therefore, one radian is ~57°. Alternatively, one
degree is 0.017 radians.
In Figure 5, the distance to the object of diameter AB is d. The angle
of the object on the observing point O is α. The trigonometric properties of the half-angle can be used to determine the size of the distant
object when its half-angle is known by using Equation 2:
Equation (2)
where R is the radius of the object, and d is the distance to the object.
Figure 5. An observer at point “O” on Earth looks at an object of diameter “D” (radius R) using a telescope. The angle subtended by the
object is α. The half-angle of the observed object is α/2. The distance
to the object is d.
Rearranging and solving for R gives you:
Equation (3)
Alternatively, the diameter D of the object can be determined by multiplying both sides of Equation 3 by 2:
Equation (4)
If the diameter of an object and the angle it subtends to the observing
point are known, then its distance can be calculated. This is a helpful tool if one already knows the size of the object being observed by
assuming it is similar in size to another object of a known size. Alternatively, if the distance to an object and the angle it subtends at the
observing point are known, then its size can be calculated.
Figure 6. Plot of x, sin(x) and tan(x) where x is an angle in
radians. The small angle approximation equates the angle x (in
radians) to its tangent. This approximation is a good one when
x is less than ~0.3 radians, where the three lines overlap.
Exercise 1
Solar Diameter
Exercise Inventory
Materials
Sheet of cardboard (8.5 in x 11 in)
(1) Sheet US letter paper (8.5 in x 11 in)
Piece of aluminum foil
Safety pin
Ruler
Scissors
Clear tape
Candle
Matches
*Pencil
*Calculator
Note: You must provide the materials listed in *red.
EXERCISE 1: SOLAR DIAMETER
In this exercise, you will make a pinhole viewer and use it to measure the diameter of the Sun. This procedure may take more
than one day depending on the visibility of sunlight. Please read the procedure through completely before starting the exercise so
you can plan your time accordingly. For Part 1 of the exercise, you will need to perform the procedure in an area where the lights
can be turned off, leaving a dark room. In Part 2 of the exercise, you will need to perform the procedure in a sunny area over the
span of several hours or possibly several days.
PROCEDURE
Part 1: Using the Pinhole Viewer
1. Using the ruler and a pencil, trace a 2 cm x 2 cm square in the center of the cardboard sheet.
2. Using the scissors, cut the square out of the center of the cardboard.
3. Measure and cut a 5 cm x 5 cm square of the aluminum foil, and place the piece of foil over the opening in the cardboard.
Tape the foil in place at the edges.
4. Using the safety pin, puncture the center of the foil to produce a small hole. You have just built a pinhole viewer.
5. Place your ruler on a table top or other flat surface, and secure it there with tape.
6. Place the candle about 8 cm in front of the viewer. Use the ruler as a guideline to space your candle. You may need to prop
up your candle on some books or boxes in order to get the candle at the same level as the hole in your pinhole viewer.
7. Using the matches provided in your kit, carefully light the candle.
Note: Exercise caution around the flame. Do not wear loose clothing or flammable materials around the flame. Tie
back any objects that may come into contact with the flame, including hair and clothing. Do not let the paper or cardboard come into contact with the flame. Do not leave the candle unattended for the remainder of the exercise.
CAUTION: Candle wax will be hot. Allow the wax to cool completely before moving the candle to avoid spilling the
hot wax on yourself or other items.
8. Place the sheet of paper about 8 cm behind the viewer. Use the ruler as a guideline to space your paper and viewer. Your
setup should look similar to that shown in Figure 7.
Figure 7. Example of the setup for Exercise 1. The pinhole viewer should be placed between the candle
and the sheet of paper, and the items should be spaced 8 cm apart.
9. Turn off all the lights in the room. The darker you can make the room, the better. You should be able to see an image of
the flame projected on the paper.
10.Slowly move the paper back and forth, and observe what happens to the image. Record your observations in Table 1 on
the Exercise 1 Data Sheet.
11.Replace the sheet of paper at 8 cm behind the viewer.
12.Carefully move the candle back and forth, and observe what happens to the image on the paper. Record your observations in Table 1.
13.Blow out the candle, and remove the ruler from the table or flat surface.
Part 2: Measuring the Diameter of the Sun
1. Move to a sunny area inside or outside. Record your date and location, as well as the time of day, in Table 2 on the Exercise 1 Data Sheet.
2. Hold the pinhole viewer in a place where sunlight can pass through the pinhole and cast an image on the paper held behind the hole. Try to make the distance between the pinhole and the paper as large as possible.
Note: Depending upon the time of day (the height of the sun in the sky), it might be helpful for you to elevate the
pinhole viewer. You can do this by placing the pinhole viewer on the top of the lab kit box and propping it up. You
will then be able to obtain a greater distance between the pinhole viewer and the white paper.
3. Once a good (sharp) image is obtained, mark the location of the pinhole and the paper on the floor or ground. You can do
this by using scrap pieces of paper and clear tape or other objects of your choosing.
4. Trace the image of the Sun on the white paper with a pencil.
Note: You may need someone to hold the pinhole viewer and paper for you while you complete this step. If someone is not available, use household items to hold your pinhole viewer in place.
5. Use the ruler or the measuring tape to measure the distance from the pinhole to the image (in centimeters) by using the
marked locations on the ground that you made in Step 3. Record this measurement as S1 in Table 2 on the Data Sheet.
6. Using the ruler, measure the diameter of the image of the Sun (in centimeters) you traced on the paper. Record this measurement as D1 in Table 2.
7. Calculate the diameter of the Sun using the small angle approximation, as described below:
The angle subtended by the Sun has a tangent D1/S1 , where D1 is the diameter of the image of the Sun on the white
paper and S1 is the distance between the pinhole and the white paper. The same angle subtends the Sun, so this tangent is also equal to D2/S2, where D2 is the diameter of the Sun and S2 is the distance between the pinhole and the
Sun. From previous labs, you know that S2 is 1 AU = 1.49 × 1011 m. Therefore:
Equation (5)
8. Use Equation 5 to solve for the diameter of the Sun, D2, and record your answer in Table 2. Make sure you convert your
S1 and D1 measurements to meters before using Equation 5. Remember, 1 m = 100 cm.
9. Repeat steps 1–8 four more times, in different locations at different times. You should wait at least one hour between measurements. It is alright to take measurements on different days if necessary.
10.Record each measurement in Table 2. You should have a total of five calculations for D2 when you are done.
11.Calculate the average diameter and the standard deviation of your D2 measurements. Record your answers in the spaces
provided below Table 2.
12.Answer the Post-Lab Questions.
Data Sheet
Exercise 1 Data Sheet
Table 1. Pinhole Viewer Observations
Task
Observation
Bringing the paper closer to the
pinhole viewer
Moving the paper farther away
from the pinhol viewer
Bringing the candle closer to the
pinhole viewer
Moving the candle farther away
from the pinhole viewer
Table 2. Sun Measurements and Calculations
Measurement
#
Date/Location
1
2
3
4
5
Average diameter of the Sun (D2):
Standard Deviation of D2 measurements:
Time of Day
S1 (cm)
D1 (cm)
D2 (m)