Homework #8 1) Suppose a comet of mass 2000 kg smashed into the Sun. It was measured to be traveling at 10 km/s. How much momentum was transferred to the Sun? 2) How much kinetic energy was transferred? 3) compare that to the amount of energy the sun gives off every second…

f a 1 / d2 Luminosity of Stars Luminosity – the total amount of power radiated by a star into space. Apparent brightness refers to the amount of a star’s light which reaches us per unit area. the farther away a star is, the fainter it appears to us how much fainter it gets obeys an inverse square law its apparent brightness decreases as the (distance)2 f a 1 / d2

The apparent brightness (flux of radiant energy (f )) of a star depends on two things: How much light is it emitting: luminosity (L) [Watts = Joules/sec] How far away is it: distance (d) [meters] f a L / d2 = L / area

f = L / 4pr2 4pr2 Luminosity of the Sun, L = 3.9x1026 Watts Flux of radiant energy from the Sun = luminosity / area = f f = L / 4pr2 r 4pr2 (Units are W/m2)

Colors of Stars Stars come in many different colors. The color tells us the star’s temperature according to Wien’s Law. Bluer means hotter!

lmax = 2.9x10-3 T f = 5.67x10-8 T4

Masses of Stars Mass is the single most important property of any star. at each stage of a star’s life, mass determines… what its luminosity will be what its spectral type will be The mass of a star can only be measured directly by … observing the effect which gravity from another object has on the star This is most easily done for two stars which orbit one another…a binary star!

The orbit of a binary star system depends on strength of gravity I’m not sure where this came from, if it’s not on the CD, let me know. The orbit of a binary star system depends on strength of gravity

Binary Stars (two stars which orbit one another) Optical doubles two unrelated stars which are in the same area of the sky Visual binaries a binary which is spatially resolved, i.e. two stars are seen (e.g. Sirius)

Binary Stars Spectroscopic binaries a binary which is spatially unresolved, i.e only one star is seen; the existence of the second star is inferred from the Doppler shift of lines.

Binary Stars Eclipsing binaries a binary whose orbital plane lies along our line of sight, thus causing “dips” in the light curve.

P2 = 42 a3 / G (m1 + m2) Binary Stars The stars orbit each other via gravity. So the laws of Kepler & Newton apply! Remember Newton’s version of Kepler’s Third Law: P2 = 42 a3 / G (m1 + m2) If you can measure the orbital period of the binary (P) and the distance between the stars (a), then you can calculate the sum of the masses of both stars (m1 + m2).

SO...

For a few thousand stars we can now find: the distance the total luminosity the temperature (color or spectral type) the radius CAN WE FIND ANY RHYME, REASON, OR RELATIONSHIPS?

Looking for correlations: Height vs. IQ ? Height vs. Weight ?

L B – V (Temperature or spectral type)

The Hertzsprung-Russell Diagram A very useful diagram for understanding stars We plot two major properties of stars: Temperature (x) vs. Luminosity (y) Spectral Type (x) vs. Absolute Magnitude (y) Stars tend to group into certain areas BRIGHT COOL HOT FAINT

burning stars reside on the main sequence of the H-R diagram High-Mass Stars Normal hydrogen- burning stars reside on the main sequence of the H-R diagram Low-Mass Stars

The Main Sequence (MS) 90% of all stars lie on the main sequence!

Stars with low temperature and high luminosity must have large radius SUPERGIANTS Stars with low temperature and high luminosity must have large radius GIANTS

H-R diagram depicts: Temperature Color Spectral Type Luminosity Radius *Mass *Lifespan *Age Luminosity Temperature

Which star is the hottest? B Which star is the hottest? D Luminosity A Temperature

Which star is the hottest? B Which star is the hottest? D A Luminosity A Temperature

Which star is the most luminous? B Which star is the most luminous? D Luminosity A Temperature

Which star is the most luminous? B Which star is the most luminous? D Luminosity C A Temperature

C B Which star is a main-sequence star? D Luminosity A Temperature

C B Which star is a main-sequence star? D D Luminosity A Temperature

C B Which star has the largest radius? D Luminosity A Temperature

C B Which star has the largest radius? C D Luminosity A Temperature

Which star is most like our Sun? D Luminosity B C Temperature

Which star is most like our Sun? D B Luminosity B C Temperature

A Which of these stars will have changed the least 10 billion years from now? D Luminosity B C Temperature

A Which of these stars will have changed the least 10 billion years from now? D Luminosity B C C Temperature

A Which of these stars can be no more than 10 million years old? D Luminosity B C Temperature

A Which of these stars can be no more than 10 million years old? D A Luminosity B C Temperature

Regions of the H-R Diagram

How can two stars have the same temperature, but vastly different luminosities? The stars have different sizes!! The measured brightness of a star depends on 2 things: surface temperature surface area (radius) The largest stars are in the upper right corner of the H-R Diagram. f =  T4 f = L / 4  R2 so: L =  T4 4  R2

L =  T4 4  R2 T R Luminosity L = constant Temperature