Download Summer 2001 Day 07: Intro to Solar System

Stellar Nomenclature, Distances and the HR Diagram
Pathways Units 52, 54, 55
1) Stellar Parallax: The only geometric method to determine stellar distances.
A) Stellar parallax works only for the nearest stars out to 500 parsecs
B) Based on a slightly different angle of viewing the stars as the Earth moves around
the Sun
i) Thumb demo
C) The formula: d(parsecs)=1/p(arc seconds)
i) 1 parsec is the distance an object must have to exhibit a parallax of 1 arc
second
ii) PARSEC is a contraction of PARallax SECond
iii) The star Proxima Centauri has a parallax of about ¾ of an arc second
corresponding to a distance of 1.3 parsecs
D) What is a parsec?
i) a unit of distance commonly used to express astronomical distances between
stars
ii) In the solar neighborhood 1 parsec is about the average distance between stars
iii) 1 parsec = 3.26 ly = 3.09x1013 km = 206,137 AU
(1) Analogy: if an AU was a foot, a parsec would be 39 miles
(2) Analogy: if an Au was a foot, the Solar System would fit in a 40-foot
circle (i.e. within the confines of this building), the NEAREST next star
would be in CORTLAND!
(3) A parsec is real big!
(4) Miles – km analogy
Practice Problem #1 & #2
2) Proper Motion and Radial Velocity
A) Stars are not truly fixed in the sky, but move in two ways
B) Towards or away from the Sun is Radial motion
i) Measured from the Doppler shift
ii) Spectrum demonstration
(1) Gases
(2) Solar Spectrum
C) Across the sky, tangential to our line of sight is proper motion.
i) Proper motion will cause the constellations to change shape over very long
time periods
ii) Barnard’s Star 30’x30’ image
iii) The Big Dipper.
iv) Relationship to distance vTangent=4.74 km/sec x μarc-sec/yr x dpc
D) Space Velocity: Pythagorean Theorem
3) Apparent Magnitude, m
A) A numerical representation of brightness
B)
C)
D)
E)
i) a “backward” scale similar to placing in a sports event
m =5 implies a brightness change of 100
m=1 implies a brightness change of about 2.5
typical values
i) “bright stars” are first magnitude
ii) brightest star Sirius in Canis Major is m=–1.4
iii) Stars in the Big Dipper are between m=1 and 2
iv) limit of naked eye visibility taken as m=6
m depends on how luminous the star is AND the distance to the star
4) What does the brightness of a star depend on?
A) Define brightness as the watts/m2 received from a star.
B) Brightness follows an inverse square relation B=L/(4πR2). Draw the picture (see
figure 54.2
C) Calculate the brightness of the Sun as seen from Earth B=1,355 W/m2
i) Typical stellar brightness is about 2x10-8W
D) Distances can be calculated by measuring B and modeling L Practice Problem #3
i) Example: Distance to Alkaid (η UMa)
(1) Luminosity = 700 LSun = 2.68x1029 W
(2) Brightness = 2.337x10-8 W/m2
(3) D= 9.55x1017 m = 101 ly
E) Ratio problems: Suppose star A is 81 times dimmer than Star B, but we believe
that they are the same luminosity.
i) Which star is farther away?
ii) How much farther?
5) Absolute Magnitude, M
i) A numerical representation of luminosity
ii) the apparent brightness at a standard distance of 10 parsecs
B) M is an intrinsic property of the star that is it depends only on the star and not on
any external factor like distance.
i) Absolute magnitude kinematics
(1) If a star is closer than 10 parsecs, m<M
(2) If a star is at 10 parsecs, m=M
(3) If a star is farther than 10 parsecs, m>M
C) The difference between the apparent and absolute magnitudes is a measure of the
distance to the star
i) m-M called the distance modulus
ii) The method of estimating stellar distances using m-M is called
SPECTROSCOPIC PARALLAX: the most common method of estimating
stellar distances
(1) Not very precise
(2) Based on our knowledge of how luminous a star should be.
iii) Ironically, we believe we understand stars so well because we can build good
nuclear bombs and reactors (controlled bomb). The nuclear physics are
closely related (in bombs anyway).
6) What does the M of a star depend on? Two properties of the star.
A) Temperature: determines the luminosity per unit area of the star’s surface
B) Size: determines the total luminosity through the surface area
C) The formula: L = f(R, T) = 4R2T4
D) M depends both on R and T
7) Stellar Temperature: Spectral Type
8) Stellar size and stage of evolution: Luminosity Class