AST443, Lecture 3
Stanimir Metchev

• Keys to ESS 437A
– see Owen Evans (ESS 255, 2-8061)
– $25 refundable deposit
• Homework 1:
– Bradt, problems 3.22, 3.32, 4.22, 4.53
• Reading for next week:
– Bradt: 5, 6.3
– Wall & Jenkins: 1–2
– Howell: 1–3
2

• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
3

• equatorial
↔
ecliptic cos " cos # = cos $ cos % cos " sin # = cos $ sin % cos & ' sin $ sin & sin " = cos $ sin % sin & + sin $ cos & cos $ sin % = cos " sin # cos & + sin " sin & sin $ = sin " cos & ' cos " sin # sin &
!
• equatorial ↔ horizontal cos a sin A = " cos # sin HA cos a cos A = sin # cos $ " cos # cos HA sin $ sin a = sin # sin $ + cos # cos HA cos $ cos # sin HA = " cos a sin A sin # = sin a sin $ + cos a cos A cos $
φ ≡ observer’s latitude
!
4

• FK4
– precise positions and motions of 3522 stars
– adopted in 1976
– B1950.0
• FK5
– more accurate positions
– fainter stars
– J2000.0
• ICRS (International Celestial Reference System)
– extremely accurate (± 0.5 milli-arcsec)
– 250 extragalactic radio sources
• negligible proper motions
– J2000.0
5

• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
6

• sidereal time
– determined w.r.t. stars
– local sidereal time (LST)
• R.A. of meridian
• HA of vernal equinox
– sidereal day: 23h 56m 4.1s
• object’s hour angle
HA = LST – α
7

• sidereal time
– determined w.r.t. stars
– local sidereal time (LST)
• R.A. of meridian
• HA of vernal equinox
– sidereal day: 23h 56m 4.1s
• object’s hour angle
HA = LST – α
• solar time
– solar day is 3 min 56 sec longer than sidereal day
8

• universal time
– UT0: determined from celestial objects
• corrected to duration of mean solar day
• HA of the mean Sun at Greenwich (a.k.a., GMT)
– UT1 : corrected from UT0 for Earth’s polar motion
9

10

• universal time
– UT0: determined from celestial objects
• corrected to duration of mean solar day
• HA of the mean Sun at Greenwich (a.k.a., GMT)
– UT1 : corrected from UT0 for Earth’s polar motion
• 1 day = 86400 s, but duration of 1 s is variable
– UTC : atomic timescale that approximates UT1
• kept within 0.9 sec of UT1 with leap seconds
• international standard for civil time
• set to agree with UT1 in 1958.0
11

• The Earth precesses …
– Sun’s and Moon’s tidal forces
– precession cycle: 25,800 years
– rate is 1º in 72 years (along precession circle) = 50.3
″
/year
• … and nutates
– Sun and Moon change relative locations
– largest component has period of
18.6 years (19
″
amplitude) N
E ecliptic coords
12

• tropical year
– measured between successive passages of the Sun through the vernal equinox
– 1 yr = 365.2422 mean solar days
• mean sidereal year
– Earth: 50.3
″ /yr precession in direction opposite of solar motion
– 365.2564 days
• Julian calendar
– leap days every 4th year; 1 yr = 365.25 days
– Julius Caesar in 46 BCE
– t
0
= noon on Jan 1st, 4713 BC
• Gregorian calendar
– no leap day in century years not divisible by 400 (e.g., 1900)
– 1 yr = 365.2425 days
– Pope Gregory XIII in 1582
• by 1582 tropical and Julian year differed by 12 days
13

• Coordinates are given at B1950.0
or J2000.0
epochs
– Besselian years (on Gregorian calendar; tropical years)
– Julian years (Julian calendar)
• Gregorian calendar is irregular
– complex for precise measurements over long time periods
• Julian epoch:
– Julian date: JD = 0 at noon on Jan 1, 4713 BC
– J = 2000.0 + ( JD – 2451545.0) / 365.25
– J2000.0 defined at
• JD 2451545.0
• January 1, 2000, noon
14

• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
15

• distance to nearby star is 1 parsec (pc) when angle p = 1 arc second (1")
• 1 pc = 3.26 light years (ly) = 2.06x10
5 AU = 3.09x10
18 cm
• Proxima Cen is at 1.3 pc ~ 4.3 ly
16

•
•
≡ annual proper motion
≡ position angle
(PA) of proper motion
Barnard’s star, 1.8 pc, µ =10.3
″ /yr
θ
N
E equatorial coords
17

!
•
•
≡ annual proper motion
≡ position angle
(PA) of proper motion
µ
"
= µ cos #
µ
$ cos " = µ sin #
θ
N
E equatorial coords
18

• Celestial coordinates (cont.)
• Astronomical time
• Distance measurement
• Brightness measurement
19

• Stefan-Boltzmann Law: F = σ T 4 [erg s –1 cm –2 ]
• apparent magnitude : m = – 2.5 lg F / F
0
– m increases for fainter objects!
– m = 0 for Vega; m ~ 6 mag for faintest naked-eye stars
– faintest galaxies seen with Hubble: m ≈ 30 mag
• 10 9.5
times fainter than faintest naked-eye stars
– dependent on observing wavelength
• m
V
, m
B
, m
J
, or simply V (550 nm), B (445 nm), J (1220 nm), etc
• bolometric magnitude (or luminosity): m bol
(or L bol
)
– normalized over all wavelengths
20

• The apparent magnitude of a star at 10 pc
– used to compare absolute brightnesses of different stars
M = m + 2.5 lg F ( r ) / F (10 pc)
• Distance modulus (DM)
– a proxy for distance m – M = 5 lg ( r / 10 pc)
– DM = 0 mag for object at 10 pc
– DM = –4.4 mag for Proxima Cen
– DM = 14.5 mag to Galactic center
21