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Motions of and Distances to Stars: Chapter 17 and 19

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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?

sin = opposite

hypotenuse

cos = adjacent

hypotenuse

hypotenuse

tan = opposite

adjacent

adjacent

1 radian=2x105 arcsec

opposite

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

=width

distance

distance

width

Stars appear fixed to a large,

very distant celestial sphere

North

Celestial

Pole

Earth's

axis of

rotation

celestial

equator

(far, far away)

zenith

of B

B

zenith

of A

A

Earth

horizon

of B

horizon

of A

South

Celestial

Pole

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

Eight Hour time-lapse exposure looking

at North Celestial Pole

q

- 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

- 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…

Arcturus

Eta bootes

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)

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

Why? Precession? Nutation?

Coherent! Aberration?

Also a pattern

Parallax?

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

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

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

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

- 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)

starspots + spinning

Eclipse by companion star

changing size

all of the above

none of the above

answer, d)

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?

Sirius

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

Earth

1 A.U.

B

A

C

p

Sun

p

p

d

d

d

d (pc) =

1

p (arc sec)

1 A.U.

1"

star

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)

Parallax is also a common surveyor’s tool

Human Eyes

Meteor ranging in

Earth’s atmosphere

2.3

inches

several

miles

tens of feet

tens of miles

Optical Range Finder

Distance

to Moon

Moon

several

feet

8000

miles

Earth

many feet

240,000 miles

Surveyor’s

transit

Distance

to Star

Sun

186

million

miles

many

feet

Earth’s

Orbit

many feet to few miles

trillions of miles

- 5 parsecs
- 10 parsecs
- 20 parsecs
- 50 parsecs
- 100 parsecs

- 1/2
- 1/4
- 1/8
- 1/16
- 1/64

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

1784-1846

Normal view

1838: Friedrich Bessel, 61 Cygni

target

reference

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

Dial the reference

Star to the bisection pt

Easier than

Aligning stars

60”

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

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…

1989-1993:

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

scan

parallax

parallax

First PASS

Cepheid Star SY AUR @ 2.3 Kpc

Insert Powers of Ten Movie Here.