Download Document

!
!Homework Reading Quiz!
!
What is orbital speed of earth around sun, in km/s?!
!!
2 π au/yr = 30 km/s = 10-4 c!
!
!
How many powers of ten between size scale of people
(1m) and that of the observable universe?!
!
Log[10 Gly/m] ~ 26!
!
!
What are 3 observable properties of stars?!
!
! 1. Position 2. Brightness 3. Color (spectrum)"
!
1
Computing earth sun distance
AU = Dev/Cos(48 deg)
Dev=c tev/2
tev=669 sec
2
Angular size, distance, & parallax
•  How do we infer distance?
1.  Decline of angular size for a given fixed size
2.  Stereoscopic eyes -- bending angle Size Illusion
Angular size
s
s
a = 360o ______
a = 360°
2π D 2πD
a
D
s
Class Example
Person of size s = 2 m
At distance D = 6 paces ~= 4 m
a
D
Angle a = 360 2/(2π 4) = 50/π = 15o
Parallax
s/
1
au
D/pc = ______
a/arcsec
*
a
a
s
D
For earth s orbit with size/radius s =1 au, then
a (in arcsec) represents the parallax angle to an star/object at distance D in parsec (pc).
s
9
10
Angle, distance, parallax
a = 360o s/2πD
= s/d (radian)
aarcsec = sau/dpc a = angular size
s = linear size
d = distance
aarcsec = parallax angle in arcsec
sau = separation/size in au
dpc = distance in parsec (pc)
12
⎛α⎞ R
sin ⎜ ⎟ =
⎝ 2⎠ d
for α << 1,
2R
α
d
13
Earth s orbit from a star
•  Suppose you observe the earth s orbit with
radius s=1 AU from a star at distance D.
o
360
D = s _____
•  The angular size would be very small, about 2π a
1 arcsec = (1/3600) of a degree!
Solve for the distance:
•  For s=1 AU, a=1 arcsec, get:
8
D = 1.5 x 10 km 360x3600/(2π) = 1.5 x 1013 km
This is defined to be 1 parsec (PC)
*
a
a
s
D
s
!
!
!More practice calculations!
!
Compute (to one decimal) a light year (ly) in km and m:!
!!
13 km = 1016 m !
c
x
yr
=
3
km/s
3
s
~
10
5
7
!
!
How many au in a parsec (pc)?!
!
! pc/au = rad/arcsec = 180/π 60 60 = 206,265 ~= 25 !
!
Compute (to one decimal) a pc in km and m:!
!
! 25 au = 25 1.58 km = 313 km = 318 m "
!
15
!
!
!More practice calculations!
!
Compute (to one decimal) a light year (ly) in km and m:!
!!
13 km = 1016 m !
c
x
yr
=
3
km/s
3
s
~
10
5
7
!
!
How many au in a parsec (pc)?!
!
! pc/au = rad/arcsec = 180/π 60 60 = 206,265 ~= 25 !
!
Compute (to one decimal) a pc in km and m:!
!
! 25 au = 25 1.58 km = 313 km = 318 m "
!
16
Parallax
Dpc =
1
aarc sec
•  Ex. #1: Alpha Centauri is nearest star
–  parallax angle a=0.7 arcsec
–  distance D = 1/0.7 = 1.3 pc
•  Ex.#2: Star at D=10 pc
–  parallax angle a= 1/10 = 0.1 arcsec
Example: Galactic Center Galactic center is at distance D = 8000 pc.
For an angle size of a=0.1 arcsec, what is the
physical size s? s/au = a/arcsec D/pc = 0.1 8000 = 800 au Angle, distance, parallax, resolution
•  a = 360o s/2πd •  aarcsec = sau/dpc a = angular size
s = linear size
d = distance
aarcsec = parallax angle in arcsec
sau = separation size in au
dpc = distance in parsec (pc)
Solid angle Ω
θ
θ+δθ
δΩ=sinθ δθ δφ
δφ
Assignments for Tues. 17Feb
•  Read secs. 3, 4, 5 of DocOnotes-stars1
•  Start HW1 (due Thurs. 19Feb) •  Compute the following to 2 sig. figs.:
a.  The fraction of the sky covered by full moon, i.e. compute
Ωm/4π, where Ωm is the moon’s solid angle.
b.  Next, if the moon were to reflect all light hitting it
(albedo=1), compute the apparent brightness ratio of full
moon to sun, Fm/Fsun
c.  Compare answers to a and b, and explain.
21