Download Distances of the Stars

“The Stars in their Courses”
The Distances of the
Stars
The Observed Properties of Stars
Why are Distances Important?
The Problem of measuring distances
Distances are necessary for estimating:
Q: What do you do when an object is out
• Total energy released by an object
(Luminosity)
• Masses of objects from orbital motions
(Kepler’s third law)
• Physical sizes of objects
of reach of your instruments?
Examples:
• Surveying & Mapping
• Military range-finding for targets
• Distances to any astronomical object
But, distances are hard to measure…
A: You resort to using GEOMETRY.
Parallax
Method of Trigonometric Parallaxes
Apparent displacement of an object
because of a change in the observer’s
location.
June
p
Larger the distance, smaller the parallax
(for the same change in the observer’s
location)
December
p = parallax angle
Foreground
Star
Distant Stars
Parallax decreases with distance
Closer stars have larger parallaxes:
Distant stars have smaller parallaxes:
Parallax Formula
d
1
p
p = parallax angle in arcseconds
d = distance in “Parsecs”
Parallax Second = Parsec (pc)
Examples:
Fundamental distance unit in Astronomy
 Centauri has a parallax of p=0.76 arcsec:
“A star with a parallax of 1 arcsecond has a
distance of 1 Parsec.”
1 parsec (pc) is equivalent to:
206,265 AU
3.26 Light Years
3.085x1013 km
d =
1
1
=
= 1.3 pc
p
0.76
A distant star has a parallax of p=0.02 arcsec:
d =
1
1
=
= 50 pc
p
0.02
Stellar Parallaxes
Limitations
All stellar parallaxes are less than 1 arcsecond
• The nearest star to the Sun,  Centauri,
has p=0.76-arcsec
If stars are too far away, the parallax can be too
small to measure accurately.
Cannot measure parallaxes with naked eye.
First parallax observed in 1837 (Bessel) for the
star 61 Cygni.
Use Photography or Digital Imaging today.
The smallest parallax measurable from the
ground is about 0.01-arcsec
• Measure distances out to ~100 pc
• Get 10% distances only to a few parsecs.
• But, only a few hundred stars this close
Hipparcos Satellite
The Future: FAME
Launched by the European Space
Agency in 1989
NASA Explorer Mission
Designed to measure precision parallaxes
to about ±0.001 arcseconds!
• Parallaxes for ~100,000 stars!
• Got 10% distances out to 100 pc
• Good distances out to 1000 pc
Light Year (ly)
• 200?? Launch
• 2.5 year mission
Goals:
• Parallaxes of 40 Million stars
• Precision of 50 micro-arcseconds!
• 10% or better distances out to 2000 pc
Summary:
Alternative unit of distance
“1 Light Year is the distance traveled by light in one
year.”
Relation to other units:
1 light year (ly) is equivalent to
0.31 pc
63,270 AU
1013 km
Distance is important but hard to measure
Trigonometric Parallaxes
• direct geometric method
• only good for the nearest stars (~500pc)
Units of distance in Astronomy:
• Parsec (Parallax second)
• Light Year
How “Bright” is an Object?
“Starlight, Starbright”
We must define “Brightness” quantitatively.
Two ways to quantify brightness:
Intrinsic Luminosity:
• Total Energy Output.
Apparent Brightness:
• How bright it appears to be as seen from a
distance.
Stellar Brightness
Luminosity
Apparent Brightness
Luminosity is the total energy output from
an object per second
Measured in Power Units:
Measures how bright an object appears to
be as seen by a distant observer.
• Energy/second emitted by the object (e.g.,
Watts)
Independent of Distance
• What we measure on earth (“observable”)
Measured in Flux Units:
• Energy/second/area from the source.
Depends on the Distance to the object
Luminosity of a star is a measurement of
its total energy production.
Surface area of a sphere = 4  d2
d=1
B=1
d=2
B=1/4
d=3
B=1/9
Appearances can be deceiving...
Does a star look “bright” because
• it is intrinsically very luminous?
• it is intrinsically faint but located nearby?
To know for sure you must know:
• the distance to the star
Luminosity Distance Relation
A star’s luminosity, apparent brightness,
and distance from the earth are related
through the inverse square law. If any
two of these quantities are known, the
third can be calculated.
Flux-Luminosity Relationship:
the inverse square law.
Relates Apparent Brightness (Flux) and
Intrinsic Brightness (Luminosity) through the
Inverse Square Law of Brightness:
Flux =
Luminosity
4 d 2
. Most stars with measured parallax are too faint
to be seen with the naked eye.
. Most bright stars have p too small to measure.
 far away
 more luminous
Bright stars are NOT necessarily closer stars.
Q. What is a parallax?
Summary:
Luminosity of a star:
• total energy output
• independent of distance
Apparent Brightness of a star:
• depends on the distance by the inversesquare law of brightness.
• measured quantity from photometry.
A) The change in the angle subtended by an
object as seen by us.
B) The distance to an object measured in
parsecs.
C) The shift in the position of an object as it
moves.
D) The apparent shift in the position of an object
as we move.
Q. How can we tell that some stars
are relatively close to us?
A) They appear to move back and forth against
the background stars because of the Earth’s
motion around the Sun.
B) They appear to be very bright, so must be
close.
C) They are occasionally eclipsed by our moon,
so they must be close.
D) They show very little Doppler shift.
Q. Suppose that A & B are two identical
stars, having the same luminosity. Star
A is at a distance of 5pc & B at a
distance of 20 pc. How will star B
appear compared to star A?
A)
B)
C)
D)
B will
B will
B will
B will
be 1/20 as bright as A
be 1/4 as bright as A
be 1/16 as bright as A
be 1/5 as bright as A