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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

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motions of and distances to stars chapter 17 and 19

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
Review: Angles

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





axis of




(far, far away)


of B



of A




of B


of A




Positionon Sky

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

ecliptic not equator


Ecliptic (not equator!)
  • Ecliptic=Plane of the Earth’s orbit (~ other planets + Moon too)
  • Tilted at 23 to celestial equator (seasons)

Northern summer

Northern winter

Imaginary point where ecliptic and equator cross

(and the Sun reaches on March 21, vernal

equinox) is 0 RA point

so a star s two angular coordinates should never change unless
So a Star’s two angular coordinates should never change, unless…
  • Edmond Halley (1718) measured stars positions and compared to
  • Ptolemy (Almagest) 1800 years earlier, found changes in
  • some of brightest stars, a degree to a few degrees!!!
  • Compare two bright stars in Bootes to the other stars…


Eta bootes

question when you give directions to an alien why should you leave out the constellations
Question: When You Give Directions to an Alien, why should you leave out the constellations?

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

answer, d)

if we continuously monitored arcturus in bootes
If we continuously monitored Arcturus in Bootes

Time step=100 years, from 0 AD to 10000 AD

what the heck
What the Heck?

Why? Precession? Nutation?

Coherent! Aberration?

Also a pattern


No, position changes were along random directions, not periodic…

Some North, some South, etc (even since Tyco’s time)

the brighter they are the faster they move
The Brighter they are, the Faster they move

Mayer, 1723-1762

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

the stellar wake
The “Stellar Wake”

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

Circle for

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

some stars also vary their brightness in time
Some Stars Also Vary Their Brightness in Time!
  • Star Algol (A-ghoul; “the demon star”) (known since 1660’s) varies by a factor of 4 in brightness every 2 days 20 hours…how could stars vary in brightness?
  • Cepheid and  Aquilae also varied (J. Goodricke 1784)
question what could cause a star s brightness to vary
Question: What could cause a star’s brightness to vary?

starspots + spinning

Eclipse by companion star

changing size

all of the above

none of the above

answer, d)

the holy grail of astronomy 17 th 19th century the distance to a star

Sun with

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!)

What assumed?


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…

“The Holy Grail” of Astronomy, 17th-19th Century:The Distance to a Star

Recall that the absence of parallax previously argued that the stars were far away. Copernicus, “of near infinite magnitude”

parallax and the parsec
Parallax and The Parsec

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



1 A.U.











d (pc) =


p (arc sec)

1 A.U.



1 parsec

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)

more on parallax
More on Parallax

Parallax is also a common surveyor’s tool

broadening the baseline parallax measurements near to far

Human Eyes

Meteor ranging in

Earth’s atmosphere





tens of feet

tens of miles

Optical Range Finder


to Moon







many feet

240,000 miles




to Star









many feet to few miles

trillions of miles

Broadening the Baseline: Parallax Measurements Near to Far
what is the distance of a star with a parallax of 0 05 arcseconds
What is the distance of a star with a parallax of 0.05 arcseconds?
  • 5 parsecs
  • 10 parsecs
  • 20 parsecs
  • 50 parsecs
  • 100 parsecs
if a star were four times as far away from us how many times less light would we receive from it
If a star were four times as far away from us, how many times less light would we receive from it?
  • 1/2
  • 1/4
  • 1/8
  • 1/16
  • 1/64
the astronomical holy grail distance to stars by parallax
The Astronomical “Holy Grail”:Distance to Stars by Parallax

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

space race to measure first parallax 1830 s


“Space Race” to Measure First Parallax, 1830’s

Normal view

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!

Heliometer: adjust

Until stars align

  • Read Bessel’s Letter: He chose 61 Cygni because
  • Big proper motion (6”/yr) means its likely to be close enough for detectable parallax
  • Its near the pole so it will be visible throughout the year
  • Double star (24” sep) so he can better align it , aligning its bisection to calibration stars (stars are 1”)
  • Had to contend with: 1st reference stars too faint, Halley’s comet kicks him off the telescope,
  • Turbulence in the atmosphere means he needs to re-observe a dozen times per night
what bessel saw

Dial the reference

Star to the bisection pt

What Bessel Saw

Easier than

Aligning stars


Main effects we see: proper motion, 5”/year

looking for a tiny 6 month variation 10 times smaller,

this is hard!!

let s cheat a little
Let’s Cheat A little

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….

answer is
Answer is…

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

10 ly!

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…

today the gold standard hipparcos satellite
Today the Gold standard: Hipparcos Satellite


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

tomorrow s gold standard gaia
Tomorrow’s Gold Standard: Gaia

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.

new approach using hubble space telescope precision astrometry with spatial scanning pass
New Approach Using Hubble Space Telescope:Precision Astrometry with Spatial Scanning (PASS)

Scanning, average many rows, error

=0.01 pix /√N rows or 0.001 pix

Imaging: error in position

of star=0.01 pix





First PASS

Cepheid Star SY AUR @ 2.3 Kpc