This Set of Slides

• This set of slides covers finding distance in space, parallax review and limitations, some more physics (of light), the Inverse Square Law, magnitude system for measuring stellar brightness, and spectral classification system.

• Units covered: 52, 23, 54, 55.

Triangulation

We can use triangulation to calculate how far away objects are.

• The Moon is a relatively close object, and measuring the necessary angles is not too difficult.

• Other astronomical objects of interest are much farther away, and measuring the necessary angles in degrees is impractical.

• Degrees have been sub-divided into arc-minutes and arc-seconds.– 1 degree = 60 arc-minutes– 1 arc-minute = 60 arc seconds

Finding the distance to the Moon by Triangulation

• Apollo astronauts left faceted mirrors behind when they returned to Earth.

• Scientists can bounce laser beams off these mirrors, and measure the time it takes the laser pulse to travel to the Moon and back.

• We know the speed of light, c, so calculating the distance is easy!

Another way of finding the distance to the Moon

Parallax

• As a person’s viewing location changes, foreground objects seem to shift relative to background objects.

• This effect is called parallax, and can be used to measure the distance to closer astronomical objects.

Measuring the Distance Using Parallax

Moving Stars

• The positions of stars are not fixed relative to Earth.– They move around the center of the

galaxy, just as Earth does.

– This motion of stars through the sky (independent of the Earth’s rotation or orbit) is called proper motion.

– Over time, the constellations will change shape. (Here delta = 50,000 yr)

• The speed of a star’s motion toward or away from the Sun is called its radial velocity. (Doppler shift…)

A problem…

• Parallax method has its limitations.

• Earth’s atmosphere interferes with angle measurements for stars beyond 100 parsecs away.

• Space-based scopes (Hipparcos) gets us out to 500 parsecs.

• But, just in our galaxy, stars are 1000’s, tens of thousands, 100’s of thousands of parsecs away. Now what?

Blackbodies

• A body that absorbs all energy incident on it and emits energy of all wavelengths is called a blackbody.

• The Sun, a stovetop element, or a piece of charcoal approximate a blackbody.

• As a blackbody is heated, the atoms in it start to move faster and faster. – When they collide, they emit a

photon with an energy proportional to how hard they hit

• Some collide lightly, and produce long-wavelength radiation.

• Some collide very hard, and produce short-wavelength radiation.

• Most are somewhere in between.

– As the body gets hotter, the number of collisions increase, and the number of hard collisions increase.

Gentle collisions

Hard collisions

The Blackbody Spectrum

• It is useful to think of temperature in a slightly different way than we are accustomed to.– Temperature is a measure of the

motion of atoms in an object.

– Objects with low temperatures have atoms that are not moving much.

– Objects with high temperatures have atoms that are moving around very rapidly.

• The Kelvin temperature scale was designed to reflect this– 0 K is absolute zero –the atoms in

an object are not moving at all.

Measuring Temperature

• Additional collisions mean that more photons are emitted, so the object gets brighter.

• Additional hard collisions means that more photons of higher energy are emitted, so the object appears to shift in color from red, to orange, to yellow, and so on.

• Of course we have a Law to describe this…

Results of More Collisions

• Wien’s Law: – Hotter bodies emit more

strongly at shorter wavelengths. The hotter it is, the shorter the wavelengths.

• SB Law: – The luminosity of a hot body

rises rapidly with temperature.

Wien’s Law and the Stefan-Boltzmann Law

• Wien’s Law lets us estimate the temperatures of stars easily and fairly accurately.

• We just need to measure the wavelength (max) at which the star emits the most photons.

• Then,

max

6 nmK 109.2

T

Taking the Temperature of Astronomical Objects

• If we know an object’s temperature (T), we can calculate how much energy the object is emitting using the SB law:

is the Stefan-Boltzmann constant, and is equal to 5.6710-8 Watts/m2/K4

• The Sun puts out 64 million watts per square meter – lots of energy!

4TL

The Stefan-Boltzmann Law

• Brighter objects are not necessarily the closer objects.

– Comet Halley, to the upper left, is within our Solar System.

– The background stars are just as bright, but tens, hundreds or thousands of light years more distant.

• The total amount of power a star emits to space is its luminosity, measured in watts.

• The amount of light reaching us from a star is its brightness.

Light and Distance

• A star emits light in all directions, like a light bulb. We see the photons that are heading in our direction.

• As you move away from the star, fewer and fewer photons are heading directly for us, so the star seems to dim – its brightness decreases.

• The brightness decreases with the square of the distance from the star.– If you move twice as far from the

star, the brightness goes down by a factor of 22, or 4.

• Luminosity stays the same – the total number of photons leaving a sphere surrounding the star is constant.

The Inverse-Square Law

• More distant streetlights appear dimmer than ones closer to us.

• It works the same with stars.• If we know the total power output of a

star (luminosity), and we can count the number of photons we receive from that star (brightness), we can calculate its distance

• Some types of stars have a known luminosity, and we can use this standard candle to calculate the distance to the neighborhoods these stars live in.

B

Ld

4

You see this every day

• We can quantify the brightness of a star by assigning it an apparent magnitude.– Brighter stars have lower

magnitudes, possibly negative numbers.

– Dimmer stars have higher positive numbers.

• Differences in magnitudes correspond to ratios in brightness:– Ex: One star of interest has a

magnitude of 6 (dim), and another star has a magnitude of 1 (easily seen). The magnitude difference of 5 means that the brighter star is 100 times brighter than the dimmer star…

The Magnitude System

• It is easier to compare two stars’ luminosities if they were at the same distance from the Sun.

• We can calculate how bright the stars would appear if they were all the same distance from us, say, 10 parsecs.

• The magnitude of a star “moved” to 10 parsecs from us is its absolute magnitude.

Absolute Magnitude

• Photons have a difficult time moving through a star’s atmosphere.• If the photon has the right energy, it will be absorbed by an atom and

raise an electron to a higher energy level.• Creates absorption spectra, a unique “fingerprint” for the star’s

composition. The strength of this spectra is determined by the star’s temperature.

Photons in Stellar Atmospheres

• Remember from Unit 23 that the peak wavelength emitted by stars shifts with the star’s surface temperatures:– Hotter stars look blue.

– Cooler stars look red.

• We can use the star’s color to estimate its surface temperature.– If a star emits most strongly in a wavelength

(in nm), then its surface temperature (T) is:

• This is Wien’s Law

nmK109.2 6

T

Stellar Surface Temperatures

nmK109.2 6

T

Measuring Temperature with Wein’s Law

• Around 1901, Annie Jump Cannon developed the spectral classification system.– Arranges star

classifications by temperature.

• Hotter stars are O type

• Cooler stars are M type

• New Types: L and T– Cooler than M

• From hottest to coldest, they are O-B-A-F-G-K-M– Mnemonics: “Oh, Be A Fine Girl/Guy,

Kiss Me– Or: Only Bad Astronomers Forget

Generally Known Mnemonics

Spectral Classification

• Each classification category is further subdivided into 10 subcategories.

• Labeled 0 through 9 (for hottest to coolest)• Example: B0, B1, B2…B9• Our Sun is a G2 star.

Spectral Classification continued