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Solar Eclipses● Despite the short duration and remote location, people go to

extremes to view eclipses.● Phenomena that are usually washed out by the blue sky become visible –

the solar corona and solar prominences.

http://www.mreclipse.com/

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also

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also

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Shadow Bands● Turbulence/refractive index variations in the Earth’s atmosphere

interact with the Sun acting as a point source/slit at the moment before totality.

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Note the nearly identical eclipses 18+ years apart. The Moon's exact position repeats relative to the Earth and Sun every 18 years creating a family of eclipses – the Saros cycle.

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Saros Cycles● The coincidence of three periodic lunar phenomena after 18 years

(and 11 days) leads to repeats of identical eclipse circumstances at 18 year intervals.

● Except the Earth is turned by 8 hours for each successive one.

https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html

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Saros Cycles● The coincidence of these three periodic phenomena after 18

years (and just 11 days) leads to repeats of identical eclipse circumstances at 18 year intervals.

● Except the Earth is turned by 8 hours for each successive one.

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Solar Eclipses from Charlottesville?● You have to wait several hundred years on average for a total

solar eclipse to happen at your location.● Partial eclipses, which cover more area, are common however.

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Eclipses in the 21st Century

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Solar Eclipses on Other Worlds● The outer planets have lots of moons...

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Io’s Shadow Seen from Junocam

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Lunar Eclipses● The Earth casts a shadow on the Moon

● To be specific the Moon moves through the Earth's shadow.

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Lunar Eclipses● The Moon takes a couple of hours to cross the Earth's shadow.

● The Earth's umbral shadow is large enough to consume the whole Moon.

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The Shape of Earth’s Shadow● Round… Substantially bigger than the Moon.

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Lunar Eclipses● Everybody on the night side of the Earth (and then some) can see

the eclipse.

Lunar Eclipses at Jupiter

To Earth

To Earth

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Lunar Eclipse at Jupiter

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Terrestrial Lunar Eclipses● The Moon takes on a reddish hue during the total eclipse because

of light refracted through the Earth's atmosphere.● This is the combined light of all of the world's sunrises and sunsets!

The View from the Moon

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Works for Pluto, too!

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Light and Wavelength• Wavelength alone distinguishes types of light

At visible wavelengths – short wavelengths are blue; long are red

Wavelength, color, and energy of a photon are all the same thing

λ∗ν=c

E=hν=hcλ

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Wavelength vs. Frequency● The product of the wavelength and frequency of a photon (the

separation between wavecrests times the number of wavecrests passing per second) naturally equals the speed at which the wave moves.

λ∗ν=c

ν =cλ

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Wavelength vs. Energy

E=hν=hcλ

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Photon Production● Accelerated charges (typically electrons) produce photons.● Synchrotron radiation (from electrons spiraling in a magnetic field)

may be conceptually the most easily motivated.● Consider whirling an electron around at the end of a string.

● An observer at a distance sees a varying electromagnetic field.

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Photon Production● Accelerated charges (typically electrons) produce photons.● Synchrotron radiation (from electrons spiraling in a magnetic field)

may be conceptually the most easily motivated.● Consider whirling an electron around at the end of a string.

● An observer at a distance sees a varying electromagnetic field.

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Sorting Light – Filters and Spectra• Light can be sorted and/or restricted by wavelength.

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Spectra• Light can be sorted and binned by wavelength. The resulting

spectrum can be projected on a screen or plotted on a graph.

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Two Fundamental Types of Spectra• Spectra can be from one of two classes

Continuous – a smoothly varying distribution of all colors

Discrete – emission (or absorption) at precise wavelengths

Often a spectrum is a combination of both

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The Solar Spectrum

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Pluto’s Infrared Spectrum

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Continuous Spectra: Thermal Radiation• Any hot object glows

The hotter the object the brighter and bluer the glow

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The Nature of Temperature• Temperature is a measure of the energy of motion of particles in a

gas or in a solid. In a gas the particles (atoms or molecules) are independently flying about

colliding with one another or with the walls of the chamber.

At high temperature the particles move quickly. At low temperatures they are sluggish.

In a solid the particles are vibrating in place.

The lowest possible temperature is the point at which all thermal energy has been removed – absolute zero.

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The Nature of Temperature• Temperature is a measure of the energy of motion of particles in a

gas or in a solid. In a gas the particles (atoms or molecules) are independently flying about

colliding with one another or with the walls of the chamber.

At high temperature the particles move quickly. At low temperatures they are sluggish.

In a solid the particles are vibrating in place.

The lowest possible temperature is the point at which all thermal energy has been removed – absolute zero.

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Continuous Spectra: Thermal Radiation• Any hot object glows

The hotter the object the brighter and bluer the glow

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Continuous Spectra: Thermal Radiation• Dense spheres of gas (stars) are good approximations to

blackbodies as well. The hot stars below are blue. Cooler ones are yellow and red.

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The Planck Equation● The Blackbody/Planck equation defines, for a given temperature,

the spectrum of emergent energy per unit time into a unit solid angle (i.e. the specific intensity) from a unit area of a blackbody per unit frequency.

Bν(T ) =2h ν

3

c2 (1

ehνkT−1 )

In general, we care about the amount of energy launched into a given solid angle from a unit area of a blackbody

Watts = Bν(T ) × Δ ν ×ΔΩ × Δ Area

Watts / m2 Hz sr

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The Planck Equation● The Blackbody/Planck equation defines, for a given temperature,

the spectrum of emergent energy per unit time into a unit solid angle (i.e. the specific intensity) from a unit area of a blackbody per unit frequency.

Bν(T ) =2h ν

3

c2 (1

ehνkT−1 )

In general, we care about the amount of energy launched into a given solid angle from a unit area of a blackbody

Watts = Bν(T ) × Δ ν ×ΔΩ × Δ Area

Watts / m2 Hz sr

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Solid Angle● A solid angle is the three-dimensional equivalent of a two

dimensional angle – basically a cone defined by its apex angle.● Solid angle is measured in units of steradians, where there are

exactly 4p steradians on a full sphere (41,253 square degrees)

● For small cone apex angles the solid angle, W, is given by:

Ω = π θ2

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dΩ = sinθd θd ϕ

In spherical coordinates a differential unit of solid angle is

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Visualizing Solid Angle

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Filter Profiles – Delta(l) vs. Delta(n)

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Statistical Mechanics 101 - kT

● Energy injected into a coupled/interacting system (imagine a network of springs or a gas of colliding atoms) tends to distribute itself evenly amongst the degrees of freedom of the system.

● A typical degree of freedom has energy, ½ kT.

● A free particle has a typical energy of 3/2kT (three degrees of translational freedom)

● Bulk system properties – e.g. the equilibrium temperature, the distribution of velocity of particles in a gas - are dictated by statistics/probabilities.

● States which require higher energy are less probably populated by the factor

● However, each energy may have many identical configurations corresponding to that energy

ni α e−E ikT

ni = (density of states) x e−E ikT

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Maybe the Most Important Thing You'll Ever Learn in Astronomy

ν =cλso d ν = ( cλ2 )d λ

Bν(T ) =2hν3

c2 (1

eh ν

kT−1 )wattsm−2Hz−1 sr−1

Bλ(T ) =2hc2

λ5 (

1

ehc

λ kT−1 )wattsm−2m−1 sr−1

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The Planck Function

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The Planck Function

http://resources.jorum.ac.uk/xmlui/bitstream/handle/123456789/957/Items/S381_1_009i.jpg

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Continuous Spectra: Thermal Radiation• The equations below quantitatively summarize the light-emitting

properties of solid objects.

The hotter the object the “bluer” the glow.

The Sun (6000K) peaks in the middle of the visible spectrum (0.5 micrometers / 500 nanometers)

Room temperature objects (300K) peak deep in the infrared (10 um).

The hotter the object the “brighter” the glow.

The power emitted from each square centimeter of the surface of a hot object increases as the fourth power of the temperature.

Double the temperature and the emission goes up 16 times!

Stefan-Boltzman LawWien's Law

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Motivations for Derivation● Stefan-Boltzman Law

● Integrate the Planck Law over all wavelengths and 2p solid angle to get emergent total flux. - Solution

● Wien's Law● Take the derivative vs. l and set equal to zero.

● Must be solved iteratively, not analytically.

● Solution

Bλ(T ) =2hc2

λ5 (

1

ehc

λ kT−1 )

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The Planck Function – Two Extremes

http://resources.jorum.ac.uk/xmlui/bitstream/handle/123456789/957/Items/S381_1_009i.jpg

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Two Extremes● Rayleigh Jeans

● Long wavelengths for a given temperature

● Longward of the Wien's Law peak

● Wien tail● The exponential dominates

h ν = hcλ

≪k T

h ν = hcλ

≫k T

Bλ (T ) =2hc2

λ5 (

1

ehc

λ kT−1 )

Bλ(T ) =2ckT

λ4

because e x = 1+x for x≪1

Bλ(T ) =2hc2

λ5 e

−hc

λ kT

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Sunspots and Thermal Radiation• Sunspots are relatively cooler regions of the Sun's 6000K surface.

Being only about 1000K cooler than their surroundings, they do glow brightly, but due to the strong, T4, dependence of a hot solid object's brightness on its temperature they appear dark.

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Thermal Radiation and Circumstellar Disks

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Thermal Radiation and Circumstellar Disks