Transcript BASIC PROPERTIES of STARS

BASIC PROPERTIES of STARS - 2
Distances to the stars
Stellar motions
Sections 3.1 & 3.2, poorly
covered in the text
DISTANCES to the STARS
 Wide
variety techniques to measure
distances.
 With
increasing distance, each technique
relies on measurements of nearer objects.
 An
error at one step translates through all
subsequent steps.
objects  “Most distant” is a
sequence of decreasing accuracy.
 “Nearby”
Astronomical Distance Pyramid
Distances inside Solar System
Laser distance to Moon, radar distance
to Venus.
Accuracy of a
few cm (10-8 %
for Moon).
Radar timing to
Venus gives
accurate
distance to Sun.
Some Laser Ranging Facts
US Apollo manned missions to Moon left
arrays of mirrors on Moon (late ‘60s - ‘70s)
Like highway signposts
Aiming to hit one of
these like hitting dime
With rifle from
distance ~1 km
Echo signal weak only 1 in 1018 photons sent is detected
Distances inside Solar System: Distance to the Sun
Closest approach of E
and V
Orbit of
Earth
Most distant E and V
Time radar returns
Sun
Orbit of
Venus
(Tdistant + Tnearest) x c / 4 =
E-S distance
1 Astronomical Unit (AU) =
1.49597870 x 108 km
accuracy of about 100 m
Flashcards
Venus is about 105,000,000 km from the Sun.
(1) What is approximate time to get the return signal
from Venus when it is at its closest to Earth? C = 3 x
105 km/s (A 150; B 200; C 300; D 400 seconds)
(2) What is the approximate time to get a return signal
from Venus when Venus is at its most distant
position? (A 850; B 1700; C 2550; D 3400 seconds)
If (1) is 300 seconds and (2) is 1700 seconds, what is 1
AU in km?
Stellar Aberration & AU
Because of Earth’s
motion, light from stars
appears to come from a
direction different from
that if Earth were
stationary.
v<<c  displacement
small
tan = v/c,  is the angle
between direction motion
and star
Measure maximum 
(20.5”) get v = 29.8 km/s
First measured in 1725 by Bradley
Get AU = (29.8x3.2x107)/2
= 1.5 x 108 km
PARALLAX §3.1
PARALLAX
With a Sun-centered Solar System
and a moving Earth, objects outside
the Solar System can potentially
exhibit parallax. Whether we can
measure it will depend on their
distance.
Tycho Brahe looked for parallax of
the stars in the 1570’s as proof of
the Copernican Theory. Did not
see it - concluded that Earth did not
move. Measurement accuracy 1’
whereas the parallax of nearest star
< 1”.
STELLAR PARALLAX
STELLAR PARALLAX §3.1
Only direct way of getting distances to stars
Smaller the parallax, farther is star
Over year star, describes ellipse on sky (special
cases: circle at pole, line if in ecliptic) - semi
major axis is parallax ()
Unit of distance is parsec (pc) defined so that at 1
pc star subtends angle 1” on E-S baseline
From small angle formula:
1” = 1 AU / 1 pc
 1/206265 = 1AU / 1parsec
 1 pc = 206265 AU = 3 x 1013 km
D = 1/,  in “, D in pc;
nearest star:  = 0.762”, 1.31 pc (limit 100 pc)
STELLAR PARALLAX
Distance measurements possible with various baselines
Parallax and position
Position of star
determines the
parallax effect
Bessel Measures Stellar
Parallax 1838!
61 Cygni
Parallax 0.314”
Manhattan taxi
as viewed from
Mexico City
STELLAR PARALLAX §3.1
Only direct way of getting distances to stars
Smaller the parallax, farther is star
Over year star, describes ellipse on sky (special
cases: circle at pole, line if in ecliptic) - semi
major axis is parallax ()
Unit of distance is parsec (pc) defined so that at 1
pc star subtends angle 1” on E-S baseline
From small angle formula:
1” = 1 AU / 1 pc
 1/206265 = 1AU / 1parsec
 1 pc = 206265 AU = 3 x 1013 km
D = 1/,  in “, D in pc;
nearest star:  = 0.762”, 1.31 pc limit 2-300 pc
Aside: Stellar Motions p.16-17

Before continuing with distances we must have
a small diversion and discuss stellar motions.

Beyond apparent motion due to parallax, many
stars exhibit motion in a constant direction proper motion.

Velocity of a star can be divided into 2
components.
Vr is the radial velocity
Vt is tangential velocity
RADIAL VELOCITIES
Data obtained with spectrograph
/o = v/c
Velocities of stars in our Galaxy range up
to +/- 300 km/sec. A few up to 600 km/s
(escape velocity from Galaxy). Typical for
stars in disk is 30 km/sec.
PROPER MOTIONS p.17
Measured over a period of years from direct
images. Unit is “/year.
Largest measured Barnard’s star 10.25”/year.
Few 100 stars with PM > 1”/year. Note that PM
will depend on distance.
Effect of proper motions
Parallax and position
This shows how
parallax and
proper motion
are distingushed.
Parallax repeats
Itself yearly while
proper motion
does not. Solve
for both
simultaneously.
Back to distances
Star Clusters
Clusters are groups stars
formed at same time in same
region space - gravitationally
bound. More later.
Moving Cluster Method Distance Determination
§16.2
Taurus and the Hyades: Pleiades at top, Saturn
to left, Aldebaran is not a member.
Moving Cluster Method Distance Determination
Raphael Santi’s “The School of Athens” 1511
Moving Cluster Method Distance Determination
Moving Cluster Method Distance Determination
True space velocity = v
Radial velocity = vrad
Tangential velocity = vt
vt = 4.74 r
vrad = v cos 
vt = v sin 
vt/vrad = tan 
Thus:
r = vrad tan  / 4.74
Do this for every star in cluster
average r values to get distance
Moving Cluster Method Distance Determination
By measuring PMs, radial velocities, and
the best position of the convergent point
of stars in the Hyades, we derive the
distance to the cluster.
dhyades = 47 +/- 4 pc (8% precision cf Venus)
Limit of technique ~100 pc
Hyades cluster is one of fundamental
calibrators of stellar distances - do with
parallax and moving cluster.
A Problem
The proper motion of Aldebaran is  =
0.20”/year
The parallax of Aldebaran is  = 0.048”
A spectral line of iron at  = 440.5 nm is
displaced 0.079 nm towards the red.
What are radial, tangential and total velocities?