The ancients thought the stars were motionless and fixed to the firmament, unimaginably far, far away…. Motions of and Distances to Stars: Chapter 17 and 19. How can you guess the distance to stars?. Review: Angles. sin = opposite hypotenuse. cos = adjacent
The ancients thought the stars were
motionless and fixed to the firmament, unimaginably
far, far away…
Motions of and Distances to Stars: Chapter 17 and 19
How can you guess the distance to stars?
sin = opposite
cos = adjacent
tan = opposite
1 radian=2x105 arcsec
Most triangles we will make use of in the Universe are skinny (i.e., <10 deg).
Skinny triangle rule: If is small, sin = (in radians), tan = , cos =1
(e.g., =0.1 radians=5.7 degrees = sin to 0.1 %)and adjacent=hypotenuse
Stars appear fixed to a large,
very distant celestial sphere
(far, far away)
From any point on Earth, you can see half of the celestial sphere at any given time (if you have a clear horizon).
As Earth rotates, stars move across sky-circles centered on NCP, SCP
Two angles fix location of a star on the sphere.
We use right ascension for East-West and declination for North-South
Eight Hour time-lapse exposure looking
at North Celestial Pole
Imaginary point where ecliptic and equator cross
(and the Sun reaches on March 21, vernal
equinox) is 0 RA point
the figure of the constellations changes with location
the figure of the constellations change with time
a constellation star may explode
all of the above
none of the above
Time step=100 years, from 0 AD to 10000 AD
Why? Precession? Nutation?
Also a pattern
No, position changes were along random directions, not periodic…
Some North, some South, etc (even since Tyco’s time)
Why did the brighter stars show larger movements?
Halley reasoned: Brighter=Closer. So?
So, closer means angular (i.e. apparent )motion is greater!
These motions called “proper motions” by Johann
Mayer in 1750’s, measured in ~80 stars.
So, if the Sun is a star, why wouldn’t it move too?
Perhaps it does! How could we tell?
Wouldn’t the Sun’s movement create the appearance of a pattern of star movements, like person walking through forest?
Turn in HW #2
Observing this week, tonight
New HW #3
Johann Mayer, 1760, suggested motion of Sun should appear
as stars perpendicular to motion “move aside”, couldn’t see it.
In 1783 Hershel looked again for this effect, found it, towards Hercules
RA (24 hrs)
Hershel’s paper, 1783, “…we find that Sirius, Castor, Procyon, Pollux, Regulus, Arcturus, and α Aquilae appear to have
respectively the following proper motions in right ascension: -0”.63; - 0”.28; - 0”.80 Nevil Maskelyne, then Great Britains Astronomer Royal. - 0”.93; - 0”.41; - 1”.40; and + 0”.57. And two of them, Sirius and Arcturus, in declination, viz. 1”.20 and 2”.01, both southward. Let figure [17.2] represent an equatorial zone with the above mentioned stars referred to it, according to their respective right ascensions, having the solar system in the center. Assume the direction AB …and suppose the sun to move in that direction from S towards B. Then will that one motion answer that of all the stars together”
Hershel: imagine sun (S) moves to C
Stars physically at positions s will appear
to move from a to b
starspots + spinning
Eclipse by companion star
all of the above
none of the above
Hole in Screen
C. Huygens ~1690-when fraction Sunlight=
Sirius then: hole/whole=bSirius/bSun=dSun2/dSirius2
because brightness 1/d2
Couldn’t make hole small enough! But
got 27,664 AU (700 million times fainter!)
J. Gregory ~1668-when Saturn as bright as
Sirius, same fraction given by light which
reflects from Saturn, reaches Earth. 83,190 AU.
What assumed? Newton: 1,000,000 AU
Unreliable! Parallax would be better…
Recall that the absence of parallax previously argued that the stars were far away. Copernicus, “of near infinite magnitude”
Against backdrop of very distant stars,
Nearby star will move by an angle 2p, in 6 months. Parallax angle=p
“Skinny Triangle” rule, p[radians]=1AU/d so d=1AU/p
If p=1”=1/(2x105) radians then d=2x105 AU. Called “parsec”= 3x1013 km=3.26 light years
Parsec is most common unit for distance in astronomy because its based on how we measure distance
d (pc) =
p (arc sec)
As distance increases, parallax decreases
The distance for which a 1 A.U. baseline has a one arc second (1") parallax is called 1 parsec (pc)
Note: 1" means 1 arc second
60" = 1 arc minute (1')
60' = 1 degree (1°)
360° = full circle
(for example, horizon to zenith = 1/4 circle = 90°)
(1 pc ≈3.26 ly)
Parallax is also a common surveyor’s tool
Meteor ranging in
tens of feet
tens of miles
Optical Range Finder
many feet to few miles
trillions of miles
Galileo wrote about the method of parallax but measurements
were too imprecise and stars to far to get a reliable result.
J. Bradley & Molyneux had tried 1720’s with Draconis,
but had discovered aberration and nutation instead!
(And also had to account for refraction). All these effects
bigger than parallax, and coherent, not individual.
Concluded lack of parallax to ~1”, Draconis > 1 parsec !!
W. Hershel, ~1800, had tried using double stars (so
that refraction, aberration, precession drop out), had
discovered binaries instead!
Many others tried, spurious claims, none successful by ~1830
1838: Friedrich Bessel, 61 Cygni
Bessel’s heliometer--split objective lens
Creates a double image, sections moved
Until a star coincides with another and
Angular separation is read off
Bessel measured a dozen times per
Night for 15 months!
Until stars align
Dial the reference
Star to the bisection pt
Main effects we see: proper motion, 5”/year
looking for a tiny 6 month variation 10 times smaller,
this is hard!!
We correct for (differential) aberration (as Bessel would have),
(Note that the distant stars will also have aberration but
Not parallax) Then zoom in to a 1’ sized field…Hubble like resolution.
See that ripple every 6 months? There it is!! Bessel observed
2.5 of these cycles before he made his claim that….
0.31” +/- 0.02” !! That’s 1/75 of the double separation
(that angle is a dime 5 km away!)
Corresponded to 3 parsecs (modern value = 0.28547”) or
Thomas Henderson, went down to Cape Town,
Alpha Centauri, parallax=1” (had it in 1832-33
but for lack of confidence published in 1839) .
Closest star! Could have been detected in 18th century
If it was in the North.
Friedrich Struve measured parallax of Vega the same year.
to be ~1/8”
Right on Bessel’s Heals…
Measured 120,000 stars to 1 milli-
arcsec precision. That’s
A distance of 1000 pc or 300 ly
(actually 1/10th that distance to get a significant measurement)
rough distance for
2.5 million stars in total
Science of measuring
Positions on the sky: Astrometry
Launch: Aug 2011 by ESA, mission through 2020
will measure parallax of 1 billion stars in the Milky Way
(20 arcsec precision for brightest, 200 arcsec for faintest
a distance of 50 Kpc to 5 Kpc )
Distance and angular position (3D) and 3D motion too.
Will address origin and evolution (life history) of Milky Way.
Scanning, average many rows, error
=0.01 pix /√N rows or 0.001 pix
Imaging: error in position
of star=0.01 pix
Cepheid Star SY AUR @ 2.3 Kpc
Insert Powers of Ten Movie Here.