DAY-TO-DAY CHANGES

Definitions
Universe: It is the totality of all space, time, matter and energy
Solar day: The period of time from one sunrise (or noon, or sunset) to the next (24 hrs).
Diurnal motion: The daily progress of the Sun and the other stars across the sky.
Sidereal day: A day measured by the stars
Earth's revolution: The motion of the Earth relative to the Sun
Earth's rotation: The spinning of the Earth around its axis
Synodic month: The time required for the Moon to complete a full cycle of phases

Reasons for difference between Solar day and Sidereal day

Figure showing the reason for the difference between a solar and a sidereal day

Each time Earth rotates once on its axis, it also moves a small distance along its orbit
about the Sun. Earth therefore has to rotate through slightly more than 360° for the Sun to return
to the same apparent location in the sky. Thus, the interval of time between noon one day and
noon the next (a solar day) is slightly greater than one true rotation period (one sidereal day). Our
planet takes 365 days to orbit the Sun, so the additional angle is 360°/365 = 0.986°. Between
noon at point A on one day and noon at the same point the next day, Earth actually rotates
through about 361o. Because Earth takes about 3.9 minutes to rotate through this angle, the solar
day is 3.9 minutes longer than the sidereal day. The apparent motion of the Sun in the sky,
expressed relative to the stars follows a path known as ecliptic.

THE MOTION OF THE MOON

The Moon is our nearest neighbour in space. Apart from the Sun, it is by far the brightest
object in the sky. Unlike the Sun and the other stars, however, it emits no light of its own and as
such it shines by reflecting sunlight. Another difference is that the Moon's
appearance changes from night to night. On some nights it cannot be seen at all.

The Moon's appearance undergoes a regular cycle of changes, or phases, taking a little
more than 29 days to complete. The Figure below illustrates the appearance of the Moon at
different times in this monthly cycle. Starting from the so-called new Moon, which is all but
invisible in the sky. The waxing and waning phases are not merely time reversals of each other,
however. The waxing Moon grows from the western edge of the disk, while the waning Moon
shrinks toward the eastern edge. The Moon doesn't actually change its size and shape on a
monthly basis, of course; the full circular disk of the Moon is present at all times.

Diagram showing the Phases of the moon

The difference between a synodic (29.5 days) and a sidereal month (27.3 days)

Diagram showing the difference between a synodic (29.5 days) and a sidereal month (27.3
days)
 As the Moon revolves around Earth, its position in the sky changes with respect to the
stars. Because of the motion of the Earth around the Sun, the Moon must complete slightly more
than one full revolution to return to the same phase in its orbit Because the Earth orbits the Sun
in 365 days, in the 29.5 days from one new Moon to the next (one synodic month), Earth moves
through an angle of approximately 29°. Thus the Moon must revolve more than 360° between
new Moons. The sidereal month, which is the time taken for the moon to revolve through exactly
360°, relative to the stars, is about 2 days shorter. That is, the synodic month is a little longer
than the sidereal month for the same reason that a solar day is slightly longer than a sidereal day.

ECLIPSES

Eclipses are astronomical events where a celestial body partially or totally covers another
celestial object.
Lunar Eclipse occurs when the Moon enters Earth’s shadow and it occurs during full moon
Total Lunar Eclipse occurs when the entire Moon is (temporary) darkened.
Partial Lunar eclipse occurs if only a portion of the Moon surface is darkened
Solar eclipse occurs when the Moon passes between Earth and Sun and it occur during new
Moon.
Total solar eclipse occurs when the Moon completely covers the Sun, as seen from Earth.
Partial solar eclipse happens when the Moon only partially covers the disk of the Sun.
Annular solar eclipse occurs when the New Moon covers the Sun's center, leaving its outer
edges to form a “ring of fire” or annulus.

Solar and Lunar Eclipse

Diagram of a solar eclipse

Diagram of a lunar eclipse

UMBRA AND PENUMBRA

The umbra is the dark center portion of a shadow/The Umbra is that part of a shadow in which
all light from a given source is excluded. The Moon's umbra causes total solar eclipses, and the
Earth's umbra is involved in total and partial lunar eclipses.

The penumbra is the lighter outer part of a shadow/It is the region in which only a portion of the
light source is obscured by the occluding body.

WHY ECLIPSE ARE REAR EVENTS

Eclipses are relatively rare events. Moreover, they can occur only at certain times of the
year. During a lunar month of about 29.5 days, the moon goes through a set of phases from new
moon to crescent to half moon to gibbous to full moon and back again to new moon. We know
that a new moon occurs when the moon comes between the sun and the earth and the full moon
occurs when the earth comes between the sun and the moon. In that case, it is therefore necessary
to know why we do not get a solar eclipse every new moon and a lunar eclipse every full moon.
As shown in the diagram below, the orbit of the Moon around the Earth is inclined to the
orbit of the Earth around the Sun, and hence these orbits are not in the same plane. This
inclination angle is about 5 degrees. This means that during most new moons or full moons, the
three bodies are not in an exact straight line. During most new moons, the moon passes a few
degrees to either side of the sun on the sky and during most full moons; the shadow of the earth
passes a few degrees to either side of the moon. It is only when all three bodies fall in an exact
straight line does an eclipse takes place. Unfavorable configurations are much more common
than favorable ones

Another way to think about this is to imagine the planes of the orbit of the earth around
the sun and the orbit of the moon around the earth. Since these two planes are inclined at about 5
degrees to each other, they will intersect along a line which cuts the two orbits at two points.
These two points are called the ascending and descending nodes (as shown in the diagram
below). Seen from the earth, these two nodes are opposite each other in the sky and mark the
positions where the two orbits meet. It is only when the moon and the sun reach the same node at
the same time that we have a solar eclipse and it is only when the moon and the sun reach
opposite nodes at the same time that we have a lunar eclipse. During a new moon, the sun and
the moon are very close to one of these nodes, but not coincident.
OBSERVATIONS AND MEASUREMENT

RADIATION

Astronomical objects are more than just things of beauty in the night sky. Each object is a
source of information about the material aspects of our universe--its state of motion, its
temperature, its chemical composition, even its past history. When we look at the stars, the light
we see actually began its journey to Earth decades, centuries--even millennia--ago. It is therefore
important to study how astronomers extract information from the light emitted by astronomical
objects. For example, an Andromeda Galaxy is about 2.2 million light years away and contains
a few hundred billion stars. A single light year equals about 10 trillion kilometers (or 6 trillion
miles); thus an Andromeda is 2 million times that far away. Objects at such a distance is truly
inaccessible, in any realistic human sense. Even if a space probe could miraculously travel at the
speed of light, 2 million years would be needed for the probe to reach its destination and 2
million more for it to return with its findings.

Astronomers therefore employs the laws of Physics, as we know them here on Earth, to
interpret the electromagnetic radiation emitted by these objects.
Electromagnetic radiation

Electromagnetic (E.M) radiation is the process in which energy is transmitted (in the form of
rapidly fluctuating electric and magnetic fields), through space from one point to another without
the need for any physical connection between those two locations.

All the knowledge about the universe beyond the Earth's atmosphere has been discovered by
systematic analysis of electromagnetic radiation received from afar.

Components of Electromagnetic spectrum

 Visible light: This is the particular type of electromagnetic radiation to which our human
eyes happen to be sensitive.
 Invisible electromagnetic radiation: e.g Radio, infrared, ultraviolet waves, X rays
and gamma rays.
All types of electromagnetic radiation travel through space in the form of waves
A wave can be described as a disturbance that travels through a medium, transporting
energy from one location (its source) to another location without transporting matter.

Wave motion

V = velocity; f = frequency and = wavelength

Diffraction and Interference

Light is said to exhibit two key properties that are characteristic of all forms of wave
motion: diffraction and interference.
 Diffraction Diffraction is the slight bending of light as it passes around the edge of an
object. The amount of bending depends on the relative size of the wavelength of light to
the size of the opening. The longer the wavelength, and/or the smaller the gap, the greater
the angle through which the wave is diffracted. Thus, visible light, with its extremely
 short wavelengths, shows perceptible diffraction only when passing through very narrow
openings. Diffraction results from the interference of an infinite number of waves emitted
by a continuous distribution of source points.
 Interference is the combination of two or more electromagnetic waveforms to form a
resultant wave in which the displacement is either reinforced or cancelled. Interference between
waves of visible light as well as diffraction of visible light are not noticeable in everyday
experience.
The wave interference is said to be a constructive wave interference if the crest of a wave
meets the crest of another wave of the same frequency at the same point.
or
Constructive wave interference is a wave interference which occurs when waves that are in phase
meets with each other and forms a new wave with greater amplitude.
The wave interference is said to be a destructive wave interference if the crest of a wave
meets the trough of another wave of the same frequency.
or
Destructive wave interference is a wave interference which occurs when waves that are out of
phase meets with each other and forms a new wave with lower amplitude or zero amplitude.
 ELECTROMAGNETIC WAVES

The laws of physics tell us that a magnetic field must accompany every changing
electric field. Magnetic fields also exert forces on moving electric charges (that is, electric
currents)—electric motors rely on this basic fact. Conversely, moving charges create magnetic
fields (electromagnets are a fairly familiar example). In short, electric and magnetic fields are
inextricably linked to one another: a change in either one necessarily creates the other. The
disturbance produced by a moving charge actually consists of rhythmically oscillating
electric and magnetic fields, always oriented perpendicular to one another (as shown in the
diagram below) and moving together through space. These fields do not exist as independent
entities; rather, they are different aspects of a single physical phenomenon: electromagnetism.
Together, they constitute an electromagnetic wave that carries energy and information from one
part of the universe to another at the speed of light.
ELECTROMAGNETIC SPECTRUM

This is the entire distribution of electromagnetic radiation according to frequency or wavelength

.

To the low-frequency, long-wavelength side of visible light lie radio and infrared radiation. At
higher frequencies (shorter wavelengths) are the domains of ultraviolet, X-ray, and gamma-
ray radiation.
 Radio radiation includes radar, microwave radiation, and the familiar AM, FM, and TV
bands.
 Infrared radiation is perceived as heat
 Ultraviolet radiation, lying just beyond the violet end of the visible spectrum, is
responsible for suntans and sunburns.
 X rays are perhaps best known for their ability to penetrate human tissue and reveal the
state of our insides without resorting to surgery.
 Gamma rays are the shortest-wavelength radiation. They are often associated with
radioactivity and are invariably damaging to living cells they encounter.

ATMOSPHERIC BLOCKAGE
Only a small fraction of the radiation produced by astronomical objects actually reaches our
eyes, because of the opacity of Earth 's atmosphere.
Opacity is the extent to which radiation is blocked by the material through which it is passing-in
this case, air.
What causes opacity to vary along the spectrum?
Certain atmospheric gases are known to absorb radiation very efficiently at some
wavelengths. For example:
 Water vapor (H2O) and oxygen (O2) absorb radio waves having wavelengths less than
about a centimeter
 Water vapor and carbon dioxide (CO2) are strong absorbers of infrared radiation.
 Ultraviolet, X-ray, and gamma-ray radiation are completely blocked by the ozone
layer high in Earth's atmosphere
 Source of atmospheric opacity in the visible part of the spectrum is the blockage of light
by atmospheric clouds.
 The ionosphere reflects long-wavelength radio waves (wavelengths greater than about 10
m)

Effect of Atmospheric Blockage

The effect of all this blockage is that only a few windows exist, at well-defined locations
in the electromagnetic spectrum, where Earth's atmosphere is transparent. In much of the radio
and in the visible portions of the spectrum, the opacity is low, so we can study the universe at
those wavelengths from ground level. In parts of the infrared range, the atmosphere is partially
transparent, so we can make certain infrared observations from the ground. Moving to the tops of
mountains, above as much of the atmosphere as possible, improves observations. In the rest of
the spectrum, however, the atmosphere is opaque. Ultraviolet, X-ray, and gamma-ray
observations can be made only from above the atmosphere, from orbiting satellites.

Blackbody Radiation
All macroscopic objects emit radiation at all times, regardless of their size, shape, or
chemical composition microscopic, because the charged particles they are made up of are in
constantly varying random motion. Whenever charges change their state of motion,
electromagnetic radiation is emitted. The temperature of an object is a direct measure of the
amount of microscopic motion within it. The hotter the object is, the faster its constituent
particles move--and the more energy they radiate.
Intensity is a term often used to specify the amount or strength of radiation at any point in space
and it is a basic property of radiation

No natural object emits all of its radiation at just one frequency. Instead, the energy is
generally spread out over some fairly broad portion of the electromagnetic spectrum.
The intensity of radiation emitted by a heated object is greatest at one particular frequency and
falls off to lesser values above or below that frequency.
Blackbody curve or Planck curve (diagram below) represent the distribution of radiation
emitted by an object.
 A blackbody is an object that absorbs all of the radiation that it receives (that is, it does
not reflect any light, nor does it allow any light to pass through it and out the other side). The
energy that the blackbody absorbs heats it up, and then it will emit its own radiation. The only
parameter that determines how much light the blackbody gives off, and at what wavelengths, is
its temperature. There is no object that is an ideal blackbody, but many objects (stars included)
behave approximately like blackbodies. Other common examples are the filament in an
incandescent light bulb or the burner element on an electric stove.
A blackbody, which is an “ideal” or “perfect” emitter (that means its emission properties do not
vary based on location or the composition of the object), emits a spectrum of light with the
following properties:

1. The hotter the blackbody, the more light it gives off at all wavelengths. That is, if you were
to compare two blackbodies, regardless of what wavelength of light you observe, the hotter
blackbody will give off more light than the cooler one.
2. The spectrum of a blackbody is continuous (it gives off some light at all wavelengths), and it
has a peak at a specific wavelength. The peak of the blackbody curve in a spectrum moves to
shorter wavelengths for hotter objects. If you think in terms of visible light, the hotter the
blackbody, the bluer the wavelength of its peak emission. For example, the sun has a
temperature of approximately 5800 Kelvin. A blackbody with this temperature has its peak at
approximately 500 nanometers, which is the wavelength of the color yellow. A blackbody
that is twice as hot as the sun (about 12000 K) would have the peak of its spectrum occur at
about 250 nanometers, which is in the UV part of the spectrum.
Below is a plot of the spectrum of a blackbody with different temperatures:

Diagram of a two-dimensional plot of the spectrum of a blackbody with different temperatures

Wein’s Law
Wien’s law, also called Wien’s displacement law, gives the relationship between
the temperature of a blackbody (an ideal substance that emits and absorbs all frequencies
of light) and the wavelength at which it emits the most light. It is named after German
physicist Wilhelm Wien. It is useful for determining the temperatures of hot radiant objects such
as stars, and indeed for a determination of the temperature of any radiant object whose
temperature is far above that of its surroundings.

Maximum wavelength,
If maximum wavelength is measured in centimeter and temperature in Kelvin, then,

This relationship is known as the Wein’s law.

For example, at 6000 K,

An object with a temperature of 6000 K emits most of its energy in the visible part of the
spectrum, with a peak wavelength of 480 nm.

Example
The wavelength of maximum solar emission is observed to be approximately 0.475μm. What is
the surface temperature of the sun (assumed as blackbody)?

Solution:

Given max= 4.75×10−7 m.

Apply Wien's law to get surface temperature of the sun

; = = 6105 K

Questions

(1) The temperature of the human body is 37oC. At what wavelength will the intensity of
radiation emitted by the human body be maximum?

(2) The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510
nm and that emitted by the North Star has its maximum value at 350 nm. If these stars behave
like black bodies, what is the ratio of the surface temperature of the sun and the North Star is?

(3) A star has a surface temperature of 10000 K. At what wavelength will this star emit most of
its light, and what wavelength region is this?

(4) Calculate the peak emission wavelength for an object at room temperature.

(5) The sun emits maximum radiation of 0.52 micron meter. Assuming the sun to be a black
body, Calculate the surface temperature of the sun

(6) A furnace emits radiation at 2000 K. Assuming it behaves like a black body radiation,
calculate the wavelength at which emission is maximum