Post Midterm Notes
Meteoroid → A small rocky object (smaller than 10m across) in the solar system.
Meteor → The visible phenomenon of a meteoroid or a small asteroid entering the
Earth's atmosphere, glowing as it heats up.
Meteorite → A rock that has fallen to the ground from outer space.
Newton's Law of Universal Gravitation
Any two objects attract each other with a force proportional to the product of
their masses and inversely proportional to the square of the distance
between their centres.
This means that, for example, the moon exerts a greater force on a piece of
the Earth close to the moon than on the centre, or the opposite side.
Tides are mostly noticeable in the oceans, but the Earth's crust itself also
bulges slightly in response to tidal forces.
Over time, tidal bulges can affect an objects rotation.
The synchronous rotation of the moon is probably a result of "tidal locking"
What is Light?
The warmth of sunlight reminds us that light is a form of energy.
Energy can take many forms and can be converted from one form to another.
Some other forms of energy: kinetic energy, heat, sound, chemical energy.
When light from the Sun warms the ground or your skin, light energy is being
converted into heat.
Solar power plants convert light into electrical energy. Green plants convert light into chemical energy through photosynthesis.
Light is a Form of Energy
Units of energy : joules.
1 joule of energy is enough to :
→ Start a 2-kg object moving at 1m/s
→ Heat up one gram of water by approx 0.25 degrees C.
Watts are a unit of power.
→ Energy per unit time.
→ 1 watt = 1 joule/sec.
A 100w light bulb is using 100 joules per second.
→ Only part of that energy is actually emitted as light, the rest of it becomes
Quantifying Light Intensity
Intensity of light can be measures in W/m . 2
If the intensity of light from a source is measured to be 1W/m , then that
means the amount of energy falling every second on every square meter of
surface is 1 joule.
→ If that surface is perpendicular to the direction the light is coming from.
The intensity of light is related to its brightness.
Light involves a flow of energy.
Intensity tells you how much energy is passing through each unit of
perpendicular area each second.
But if a surface is at an angle, then the same energy is spread over a larger
Inverse Square Law
As you get farther from the source, the same energy gets spread over a
That means the intensity decreases as you get farther away from the source. Stars that are farther away look dimmer than they would close up.
Mathematically speaking, light acts like gravity:
→ If you double the distance, the intensity becomes 1/4 as much.
→ Triple the distance, intensity becomes 1/9 as much.
This is because if you double the distance, the same amount of light energy
gets spread over four times as much area.
That's the same type of mathematical behaviour as in Newton's law of
→ Gravity gets weaker as distance increases but never really goes away.
Is Light a Wave or Particle?
Light travels through space as a wave.
But some of its interactions with matter are best understood in terms of
What is a Wave?
A wave is a periodic motion that can carry energy without carrying matter
along with it.
→ Water waves.
→ Sound waves.
Wavelength → Distance between two wave crests.
Frequency → Number of times per second that a wave vibrates up or down.
Wave speed = wavelength x frequency.
Wave speed depends on the type of wave and what its moving through.
The frequency depends on the source it's coming from.
Light as a Wave
James Clerk Maxwell understood light as an electromagnet wave
→ A vibration of electric and magnetic fields together.
Light interacts with matter through these electric and magnetic fields. Visible light and radio waves are two forms of the same thing.
→ Both are electromagnetic waves.
Electromagnetic waves in a vacuum travel at the speed of light.
Wavelength, Frequency and Colour
Wavelengths and frequencies are related to colours.
Longer wavelengths mean lower frequencies and that is represented with
Short wavelengths mean higher frequencies and are represented with bluer
Newton showed that white light consists of many different colours
(wavelengths) mixed together.
The Electromagnetic Spectrum
Human eye cannot see most forms of electromagnetic radiation.
Electromagnetic spectrum is the full range of possible frequencies.
→ There is really no upper or lower limit.
Visible light is only a small part of the electromagnetic spectrum.
It consists of electromagnetic waves with a certain range of frequencies.
Light: Our Messenger from the Universe
Light is our window on the Universe.
→ Almost everything we know about any object outside Earth comes from
observing either visible light or other forms of light.
Some objects emit light processes that convert other forms of energy into
→ Example: Stars including the Sun.
Others, such as planets, do not emit their own light but are visible through
By understanding how light interacts with matter, we can get a lot of
information from light about the temperature and chemical composition of
distant objects, and about their motion. Not all forms of light can get through Earth's atmosphere.
→ This is one of the reasons for building observatories in space.
→ On Earth, we can only see astronomical objects through visible light and
How Telescopes Help
Light intensity describes the amount of energy falling on a surface per unit
Some objects are hard to see because they are too dim.
Not enough energy from them is reaching our eyes.
But you can increase the amount of energy collected by increasing the
Pupils of eyes have a small area, so telescopes concentrate light from a larger
The ability for a telescope to collect more light is called "light-gathering
Brightness and Magnitude of Stars
Stars are classified by apparent visual magnitude.
→ A number representing their brightness.
Originally, there were just six numbered classes.
→ First magnitude = Brightest stars.
→ Sixth magnitude = Faintest visible with the unaided eye.
Ptolemy used this magnitude system in his writing, others may have used it
More recently it became possible to measure flux of light more precisely,
allowing a more precise numerical measurement of brightness.
→ Energy per square meter per second.
Smaller numbers mean brighter, larger numbers mean fainter.
With the new scale, some of the brightest objects have negative numbers. Visual magnitude only counts visible light.
Photons: Particles of Light
When light energy interacts with matter it is emitted or absorbed in discrete
chunks or packets: photons.
The size of a photon depends on its frequency.
Photons of higher frequency light have more energy than for lower frequency
Medical consequences of this :
→ Higher-energy photons can do more damage to living cells when absorbed.
→ So visible light is pretty harmless but ultraviolet light can cause sunburn
and skin cancer.
X-ray and gamma ray photons have even higher energies, so too much
exposure to them can be more dangerous.
Limitation of human eyes : Diffraction.
Diffraction is the bending of the edges of waves as they pass through an
Diffraction blurs images, so if two stars are too close together in angular
distance, their images blur into one.
This puts a limit on the smallest angular sizes we can observe with a
Other Factors Affecting Angular Resolution
Telescopes are based on either reflection or refraction of light.
Both reflection and refraction are basic wave behaviours that also happen
with sound, water waves, as well as light.
Refraction is the bending of waves when they cross a boundary between two
different media where they travel at different speeds. Ray Tracing is often helpful to describe refraction and other wave phenomena
by drawing rays which represent the direction a wave is moving.
A wave moving from a faster to slower medium bends so that its direction is
closer to perpendicular to the surface.
→ From slower to faster is the opposite.
Refracting telescopes use two lenses:
→ Objective lens creates a very small real image at its focus.
→ Eyepiece lens then magnifies the real image, forming a larger virtual image
that you can see.
Powers of a Telescope
Light-gathering power is the ability to collect and concentrate light. The
wider the objective lens, the greater the light-gathering power.
Resolving power is the ability to see fine detail clearly. This is partly limited
by diffraction and partly by the quality of the lend, and partly by the
Magnifying power is the increase of apparent angular size. This is easily
changed by changing the eyepiece, and in some ways is the least important,
since magnifying a faint or blurry image doesn't help.
Limitations of Lenses
Spherical aberration or other imperfection prevent a sharp focus.
Different colours focus at different points, because different wavelengths of
light refract at different angles this is known as Chromatic aberration.
This is actually what is used to separate colours in a prism, but it's a problem
for telescopes or cameras.
Coatings on lenses or sets of multiple lenses can reduce chromatic
Large, high quality lenses are difficult and expensive to make.
Large lenses are also very heavy, so they tend to sag under their own weight
when supported only at the edges.
Chromatic aberration is never completely eliminated. To get around these problems, Newton built the first reflecting telescope.
Use a curved mirror instead of a lens to focus light.
Light reflects off a reflective coating and does not have to pass through glass.
→ That means no chromatic aberration.
Only the surface needs to be polished, while a lens needs to be free of
defects all the way through to work well.
Mirrors can easily be supported from behind.
Another Challenge for Astronomers
Distortion cause by Earth's atmosphere is called "seeing".
Uneven temperature and moisture cause refraction as light travels through
the air, blurring and distorting images.
As atmospheric conditions change, image is unsteady and stars appear to
Why don't planets twinkle? They have bigger angular sizes, so light from
different parts of the planet's image is affected differently.
What to do About Seeing
Adaptive optics technology uses a computer and small motors to compensate
for atmospheric distortion by continuously changing the shape of the
Requires a bright source in a known location for the computer to focus on and
calculate the correction.
Or create an artificial guide star by bouncing a laser beam off the upper
layers of the atmosphere.
Observing Non-Visible Light Earth's atmosphere is transparent to visible light and radio waves.
With adaptive optics, we may soon be able to get visible-light images from
the ground that are as clear as we get from the Hubble Space telescope.
But to observe other types of light that don't get through the atmosphere, we
still need telescopes in space.
Why Look at Other Types of Light
Infrared and radio waves can pass through clouds of gas and dust that are
opaque to visible light.
This allows us to see more of our own galaxy.
Different types of sources emit different ranges of wavelengths.
Objects that care cooker than stars emit mostly infrared.
Cosmic microwave background shows us the last remaining heat from the Big
Bang and gives us clues to the early history of the Universe.
Some radio sources include active galactic nuclei.
Many stars emit at least some X-rays.
→ Including the Sun.
Matter falling into black holes emits a lot of X-rays.
Short gamma-ray bursts from distant galaxies may come from the explosions
of very large dying stars.
Radio telescopes are reflecting telescopes for radio waves.
Since radio waves have large wavelengths, diffraction is a problem. We need
large mirrors to get a good angular resolution.
The good news: an optical mirror needs to be smooth compared to
wavelengths of visible light, but a radio mirror just needs to be smooth
compared to radio waves.
Interferometry Another way to improve angular resolution is to combine signals from several
Interferometry is easiest with radio waves, but it can now also be done with
As far as angular resolution is concerned, it's like having a much bigger
In most ways, infrared optics are not that different from visible light.
The problem is that Earth's atmosphere blocks a lot of infrared radiation.
IR telescopes also need to be insulated from heat.
Shorter Wavelengths: X-ray and Gamma-ray Astronomy
X-ray and gamma-ray telescopes need to be above the atmosphere.
X-ray and gamma rays are very difficult to focus: an ordinary lens or mirror
To focus X-rays, we use grazing-incidence mirrors.
Spectroscopy: Getting more information from light
We can learn more from light if we understand more about how light interacts
with matter: how it is emitted and absorbed.
Spectroscopy is the breaking of light from an object into its different
wavelengths, and comparing the amounts of light emitted at different
Continuous Spectrum (Thermal Radiation)
A hot, dense object emits light at all wavelengths at once in a continuous
Examples: A standard incandescent light bulb, the sun, a glowing heating coil
on the stove, a human body. This emission is also called blackbody radiation.
The spectrum depends on the temperature.
Stefan-Boltzman Law: Hotter objects emit more radiation than cooler ones.
Wien's Law: Hotter objects emit photons with a higher average energy. The
wavelength of peak intensity shifts toward lower wavelengths as temperature
This means that we can figure out the temperature of a star by looking at its
Betelgeuse is redder in colour than Rigel: it is a cooler star.
Objects at temperatures around room temperature or body temperature emit
most infrared light.
Continuous spectra are produced by dense objects with many atoms packed
together. To understand the other two types of spectra, it helps to understand
a bit about atoms, and how individual atoms absorb or emit light.
A full understanding involves quantum mechanics, a branch of physics
developed in the 11920s and '30s.
Electrons in an atoms can only orbit in specific orbits with particular energies.
They can only absorb or emit energy by moving from one level to another.
Under normal conditions, an atom spends most of its time in the ground
state (lowest energy state).
If a photon with the right energy comes along, the electron can absorb the
energy and bounce up to an excited (high-energy) state.
The energy is emitted again as the atom falls back to the ground state.
Each type of atom has particular energies of photons that it is able to absorb
These photon energies correspond to particular transitions between energy
levels of that atom.
The set of all these energies form a kind of chemical fingerprint for that atom. Molecules often have more complicated spectral fingerprints than single
When we observe spectral lines from an astronomical source, we can
compare them with a reference spectrum from hydrogen gas in the lab.
If the source is moving toward us, the spectral lines will be shifted to higher
frequencies compared to the reference spectrum.
If the source is moving away from us, the lines will be shifted to lower
Solar System Objects: Planets
→ Mercury, Venus, Earth, Mars
→ Are small, rocky and closer to the Sun.
→ Jupiter, Saturn, Uranus, Neptune.
→ Are large, and gassy, they contain a lot of hydrogen, helium and methane.
→ They are farther from the Sun.
Jovian planets also have more moons than the terrestrial planets.
Jovian planets all have rings, but Satur