Astronomy 151

What defines a planetary system?

- A planetary system is the collection of a star and all the objects orbiting it - Our solar system is the planetary system where the Sun is the star.

Blackbody

- An idealized object that completely absorbs all light (no light reflected), and re-emits that light according to the object's temperature - The perfect thermal body (absorbs all light, then perfect thermal radiation out) *Doesn't really exist bc we can't see it

Advantages of Radio Telescopes

- Continuous Operation -can operate under any weather conditions - 24 hours of operation time - Through the Obscuring Dust - Radio waves pass through the dust that visible light is blocked by - The Radio Universe

Diffraction-limited Angular Resolution

- Diffraction limits the angular resolution of images in a telescope. The (diffraction-limited) angular resolution (A.R.) of a telescope is proportional to the wavelength (𝜆) of light being observed and inversely proportional to the diameter (D) of the telescope - Equation: 𝐴.𝑅.[𝑎𝑟𝑐𝑠𝑒𝑐]=0.25(𝜆[μm]/D[m])

Light-collecting Area/Light-gathering Power

- How much light a telescope can focus depends on the diameter of the primary mirror/lens. - The size of the primary determines the total area of the mirror, which determines the brightness of images it can make.

The Speed of Light

- Light is not infinitely fast, so it takes time for light to reach us - 299,792,458 m/s or 3.0 x 108m/s

Major Problem of Radio Astronomy

- Radio telescopes suffer from inherently bad (large value) angular resolution due to radio waves having long wavelengths

Light is...

- an electromagnetic radiation - a transfer of electromagnetic energy through space *Light is a wave and a particle simultaneously (wave-particle duality)

electromagnetic wave (EM wave)

- is composed of an oscillating electric field and magnetic field - a double wave of a couples electric field oscillation to a magnetic field oscillation *electromagnetism is a fundamental force of nature (like gravity)

Radio telescopes

- simplified reflecting telescopes - Use metal dishes to reflectradio waves

Atoms more massive than hydrogen have:

-Different electron energy levels (what does that mean about how those atoms absorb and emit light?) -More complicated spectra -Unique sets of spectral lines associated withionsof the element

Ways molecules can create spectral lines:

-Still have electron transitions -The movement of electrons between electron energy levels -Appear as UV, Visible, and infrared lines -Molecular Vibrations -Bending and stretching of the chemical bonds -Think of the bonds as "tiny springs" -Appear as infrared lines -Molecular Rotations -Molecules can rotate in 3D space -Appear as microwave and radio wave spectral lines

Why is telescope size important?

-Telescope area, or collecting area, determines how bright an object is. Hence how bright something appears scales with the SQUARE of the telescope diameter -Telescope diameter determines the angular resolution limit of a telescope

A Problem of the Atmosphere

-The atmosphere blurs images and makes stars twinkle -Moving pockets of air, with different densities, act like lenses making it so light rays don't focus perfectly. This causes stars to appear to twinkle.

In general, know that we study...

-The cold and molecular universe with longer wavelength (radio, microwave, and infrared) telescopes. -The hot and energetic universe with shorter wavelength (ultraviolet, X-ray, and gamma-ray) telescopes.

Example Question: Star Alpha is 6 times hotter than Star Beta. Star Beta's blackbody spectrum peaks at 2.8 μm. At what wavelength, does Star Alpha's blackbody peak at?

6 times hotter => 6 times smaller peak wavelength2.8 μm/6 = 0.467 μm

Example

A telescope that is 6 times bigger than another telescope, will make images 6^2= 36 times brighter.

Distinct lines of "color" removed (absorbed); Continuous spectrum with absorption lines removed

Absorption Spectra (bright rainbow w dark absorbtion lines) *Observe a hot blackbody through a relatively cooler cloud of gas

This refers to technology on telescopes that uses rapid response small actuators to reshape the optics in real time to cancel out atmospheric blurring

Adaptive optics *Drastically improves angular resolutionto almost the diffraction limit

What wavelength regions are required for space-based astronomy?

All other wavelengths of the EM spectrum require space-based telescopes

How does an interferometer increase angular resolution?

An astronomical Interferometeris a collection of multiple, widely spaced, telescopes linked together to act as one larger "super telescope" to improve angular resolution (make the number smaller)

The term astronomers use to describe how much atmospheric turbulence is blurring an image. It is measured in size, and it limits the angular resolution

Astronomical Seeing *a numerical quantification of how much the atmosphere is blurring images

A measure of how opaque the atmosphere is at a certain wavelength of light

Atmospheric opacity *1.0= 100%; 0.5= 50%; 0.0= 0%

Any transition into or out of the 1stexcited state (n=2) from a higher excited state

Balmer Series (VISIBLE PHOTONS)

The light that is re-emitted has the same amount of total absorbed energy, but is emitted over large range of wavelengths. The re-emitted light is called

Blackbody radiation, or thermal radiation

Not our current model of the atom, but it is commonly used because it quantizes the electron energy levels

Bohr Model

astronomical interferometer

By linking telescopes together, and exploiting the wave property of interference, we can build this

Why are almost all professional telescopes reflectors?

Can make very large mirrors for reflecting telescopes. You can't make lenses much larger than 1 meter in size.

Created by good approximations to a blackbody: A sufficiently dense object. This is thermal radiation (e.g., Star, planet, light bulb filament, hunk of iron, very dense gas)

Continuous Spectra (looks like a rainbow) *Observe a full rainbow

Distinct lines of "color" in emission; Dark background with bright emission lines

Emission Spectra (dark rainbow with bright lines) *A hot thin gas will emit only specific wavelengths

The point where all light rays converge

Focus

Example

How much better (smaller) is the angular resolution of a 10 m telescope compared with a 2 m telescope that is operating at the same wavelength of light?Answer: The 10 m telescope has 5 times the diameter of the 2 m telescope, so the angular resolution will be 5 time smaller (Remember smaller is better)

Example Question: Star Caloris 9 times hotter than Star Gelidus. The two stars are the same size (only have toconsider temperature difference). How much more energy is Caloremitting than Gelidus?

If same area, then energy is proportional to the temperature to the 4thpower.Caloris emitting 94= 6,561 times more energy than Gelidus

Seeing limits the practical angular resolution we can get with telescopes.

If the seeing is 0.8 arcsec, two stars with an angular separation of 0.5 arcsec would be blurred into a single blob of light... regardless of the power of a telescope

What wave property limits the angular resolution of a telescope?

If two objects are separated by -Less than the optic's (eye or telescope) angular resolution the objects are blurred into a single blob -More than the angular resolution, then the two objects can be resolvedinto two distinct objects/point

Every element has its own, unique set of spectral lines. This means we can determine the composition(what something is made up of) of an object by observing its emission or absorption spectrum

Kirchoff's Laws

Any transition into or out of the ground state (n = 1)

Lyman Series (ULTRAVIOLET PHOTONS)

Is it the same at all wavelengths of the electromagnetic spectrum?

No

Motion of towards and away

Radial motion

Wavelengths on the EM Spectrum (longest to shortest)

Radio (redder), Micro, Infrared, Visible, Ultraviolet, X-rays, Gamma Rays (bluer)

Light wavelengths

Red= 650 nm (long WLs, small frequencies) Green= 525 nm Blue= 450 nm (short WLs, large frequencies)

The bouncing of light off a surface, i.e., a mirror. Light will reflect with the same angle as it hit the surface.

Reflection *The distance to focus the light is the focal length

What are the two main types of telescopes and how do they gather and focus light?

Reflectors (using mirrors) ; Refractors (using lenses)

The bending of light as it passes from one medium to another

Refraction (of light)

This is the science of how light (electromagnetic radiation) interacts with matter (atoms, molecules, etc.)

Spectroscopy

Gives a method to determine the brightness of celestial objects that emit light like a blackbody (or if we can determine the brightness, a method to determine the size of the object)

Stefan-Boltzmann's Law

Stefan-Boltzmann Law

The energy (E) emitted by an object is proportional (∝) to its temperature (T) to the fourth power Relationship: 𝐸∝𝑇^4 Full Equation: 𝐿=𝜎𝐴𝑇^4, 𝜎 is the Stefan-Boltzmann Constant

Wein's Law

The peak wavelength (λpeak) of an object's blackbody spectrum is inversely proportional the the temperature (T) Equation: 𝜆peak= [μm]= 2900/T[K]

Side-to-side motion that is neither toward nor away from the observer

Transverse motion

Lights humans can see

Visible Spectrum of Light

What is meant by the phrase spectral window?

Wavelength ranges that have a significant amount of light reach the ground *The two primary spectral windows are Visible Light and Radio

Gives us a method to determine the temperature of objects that emit light like a blackbody (it's a thermometer for celestial objects)

Wein's Law

All of the colors combined

White light

What is angular resolution?

ability to distinguish two adjacent points as individual points instead of a blurred together object *Smaller number is better angular resolution

We can actively correct the blurring of the atmosphere with a technology called

adaptive optics

How height of the oscillation (how high up and down), and it is a measure of the wave strength

amplitude

At some point, you can no longer see the individual dots. This is where the _____________ (in degrees, arcmin, arcsec, etc.) between the adjacent dots has gotten smaller than the angular resolution of your eye

angular separation

Radiation

any way that energy is transported through space

how large (how much energy emitted) AND at what wavelength is the peak of the curve (what wavelength is brightest) is located

blackbody curve

Tells how bright each wavelength of light is

blackbody spectrum *Every temperature has its own unique blackbody spectrum

Wave Speed

c=λf

The specific wavelengths give us _____________ and things like width of spectral lines indicates ______________________________.

composition; temperature, density, rotations, and magnetic field strength

A blackbody emits a _____ spectrum

continuous

The angular resolutionof a telescope is _____________ to the wavelength of light and _________________ to the diameter (size) of the telescope

directly proportional; inversely proportional

The distance between the farthest telescopes defines the...

effective diameter

For an electron to transition from one orbital, or electron energy level, to another, it must....

either absorb (gain) or emit (lose) the exact amount of energy difference between the two orbitals *E.g., For an electron to jump from the 1stExcited State (n=2) to the 2ndExcited State (n=3) in hydrogen, the electron must absorb (gain) an energy of 1.89 eV to do so

Each allowable electron energy is called an

electron energy level *An electron cannot have energy other than these specific allowable energies

neutral atom will have an ___________ of electrons as protons

equal number

The ________ the radial motion (either toward or away) the _________ the Doppler Shift

faster; larger

The number of wave crests (or troughs) that pass a given point per second

frequency (Hertz)

The seeing value tells you....

how large a point of light will be blurred to. Cannot see finer detail than that value.

A technological advancement called ____________ gives a way to increase the diffraction-limited angular resolution

interferometry

Frequency f and wavelength λ are ________________ to each other

inversely proportional

The angle of refraction (how much it bends) is ______________ to the wavelength of light.

inversely proportional

The energy of a photon is _____________ to the wavelength

inversely proportional

our primary source of information about most every object in the universe

light

Use the terms __________,______________,& ___________ interchangeably

light, electromagnetic radiation, and electromagnetic wave

The surface area of the primary mirror or lens determines the ____________________, which is the same as light-gathering power

light-collecting area

the total amount of energy per second

luminosity (L) *𝐿=𝜎𝐴𝑇^4

Tightly bound group of atoms held together by interactions between their orbiting electrons (chemical bonds)

molecule

What determines an element?

number of protons

Electrons orbit around the nucleus at very specific distances in this, each of which has a very specific electron energy associated with it

orbitals

Light comes in distinct packets, quanta, with distinct energies. We call these packets of light

photons

the total amount of energy per second a blackbody object emits is _________________ to the surface area and the fourth power of the temperature

proportional

How does telescope size relate to angular resolution?

proportional to

Nucleus contains...

protons and neutrons

Electron energy levels are

quantized (meaning no in-between states)

the amount of emitted energy per second per square meter

radiant flux

How much light bends due to ______________ depends on the wavelength of light.

refraction *The distance from lens to focus is the focal length

The expected wavelength, what we would measure with an object at rest

rest wavelength

If an object is moving toward radially (toward or away from us) its spectral lines are shifted with respect to the ______________ due to the __________________.

rest wavelength; Doppler Effect *towards us = Blueshift to shorter wavelengths *away from = Redshift to longer wavelengths

Typically microwave and radio wavelength energies

rotations

Light spread out into its different wavelengths

spectrum

EM wave speed is the

speed of light, c

Where does nearly the entirety of our knowledge of the universe come from?

the study of light

Every photon has a certain amount of energy that is determined by

the wavelength of the light

Blackbodies emit ________________ in all directions _________

thermal radiation; equally

Typically infrared wavelength energies

vibrations

Disturbance that propagates energy from one location to another through oscillations or vibrations of a medium or a field

wave *Light (electromagnetic waves) exhibit all of these wave properties

The distance between two wave crests (or troughs) measured in distance units [e.g., meters, micrometers, nanometers]

wavelength of a wave (λ)