(e) Masses and radii of stars from binary systems, Kepler's (e) Masses and radii of stars from binary systems, Kepler's Laws, Mass-radius relationship. Pre-reading pages 23 - 33, Laws, Mass-radius relationship. Pre-reading pages 23 - 33, 48 - 49, 180 - 198. 48 - 49, 180 - 198.
(f) Hertzsprung-Russell Diagram, dwarf, giant and (f) Hertzsprung-Russell Diagram, dwarf, giant and supergiant stars, white dwarfs, first clues to stellar supergiant stars, white dwarfs, first clues to stellar evolution. Pre-reading Chapter 8. evolution. Pre-reading Chapter 8.
Basic Properties of Stars Basic Properties of Stars Basic Properties of Stars Basic Properties of Stars
Celestial Sphere (not really a stellar property)
Some stellar statisticsSome stellar statisticsSome stellar statisticsSome stellar statistics
A few 1000 visible to the naked eye A few 1000 visible to the naked eye Polaris (North Star) not brightest (only 50th)Polaris (North Star) not brightest (only 50th)Sirius is brightestSirius is brightest
SOME STELLAR STATISTICSSOME STELLAR STATISTICSSOME STELLAR STATISTICSSOME STELLAR STATISTICS
A few billion stars can be seen with best A few billion stars can be seen with best telescopes (not counting distant galaxies telescopes (not counting distant galaxies where individual stars generally where individual stars generally unresolved but light is still detected).unresolved but light is still detected).
Estimate # of stars in observable Universe Estimate # of stars in observable Universe ~ 10~ 102323
Nearest star (Proxima Centauri) is 300,000 Nearest star (Proxima Centauri) is 300,000 times more distant than Sun. times more distant than Sun. (by comparison, Neptune is 30 times (by comparison, Neptune is 30 times farther than Sun).farther than Sun).
Small and Great Circles Small and Great Circles Small and Great Circles Small and Great Circles Small Circle: Curve on sphere produced by plane NOT containing the centre.
Great Circle: Curve on sphere when plane contains centre.
Only 1 great circle passes through any 2 given points on sphere, Q, Q’. Arc QQ’ is shortest distance between these points.
The line perpendicular to plane that passes through the centre intersects sphere at poles P, P’.
Location of a Point on a SphereLocation of a Point on a Sphere Location of a Point on a SphereLocation of a Point on a Sphere
Either XYZ coordinates or 2 angles, and , can be used to locate a point, P, on the surface of a unit sphere.
Note that for angle, , a reference point along the equator is required.
Latitude, Longitude on Earth Latitude, Longitude on Earth Latitude, Longitude on Earth Latitude, Longitude on Earth
Reference plane is equator.
Small circles parallel to equator are parallels of latitude. + north, - south.
Altitude of celestial pole is your latitude. (Vancouver?)
Semicircles from pole to pole are meridians.
Longitude is angle between meridian and zero meridian (Greenwich). + west, - east.
Earth’s axis inclined 23.5 degrees Earth’s axis inclined 23.5 degrees to plane of its orbitto plane of its orbit
SEASONS on EARTHSEASONS on EARTHSEASONS on EARTHSEASONS on EARTH
The Sun follows a well-defined pathThe Sun follows a well-defined path
Origin of time-keeping.Origin of time-keeping.
Sun's apparent motion across the Sun's apparent motion across the sky just caused by Earth's orbit.sky just caused by Earth's orbit.
Sun 'moves' in front of 12 constellations; the Sun 'moves' in front of 12 constellations; the zodiac.zodiac.
Right Ascension and DeclinationRight Ascension and Declination Right Ascension and DeclinationRight Ascension and Declination
is position of crossing of celestial equator and equatorial plane of Earth - position of vernal equinox. This is a fixed point from which to measure angles. is Right Ascension
Most members of Solar System are near ecliptic, and tend to pullequatorial bulge of Earth towards it. Mostly due to Moon and Sun.
Because Earth rotating, this torque cannot change inclination ofequator to ecliptic, but causes rotation axis to turn in a directionperpendicular to axis and torque, describing a cone (P = 26,000 yr).
PRECESSION p.12 - 14PRECESSION p.12 - 14PRECESSION p.12 - 14PRECESSION p.12 - 14Precession of Precession of pole is slow. pole is slow. Angle of Angle of inclination does inclination does not change. not change.
Precession Precession changes changes position of NCP position of NCP and and , so we , so we must define must define when when and and are measured.are measured.
Some precession detailsSome precession detailsSome precession detailsSome precession details
Polaris is currently within 1 degree of pole. Where will it Polaris is currently within 1 degree of pole. Where will it be in 13,000 years?be in 13,000 years?
Same effect causes 50.3”/year westward motion of vernal Same effect causes 50.3”/year westward motion of vernal equinox - use tropical year for calendar.equinox - use tropical year for calendar.
J2000 is reference (Jan 1, 2000 noon at Greenwich)J2000 is reference (Jan 1, 2000 noon at Greenwich)
= [ m + n sin = [ m + n sin tan tan ] N ] N Eq 1.2 and 1.3 in textEq 1.2 and 1.3 in text
= [n cos = [n cos ] N] N
N = # years between desired time and reference epoch N = # years between desired time and reference epoch (can be negative), and m = 3.07419s/yr, n = 20.0383”/yr (can be negative), and m = 3.07419s/yr, n = 20.0383”/yr for reference epoch = 2000. Eg 13,000 years from now, for reference epoch = 2000. Eg 13,000 years from now, where will Polaris be?where will Polaris be?
