# Physics 312 Introduction to Astrophysics Lecture 3

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1 Physics 312 Introduction to Astrophysics Lecture 3 James Buckley Lecture 3 Celestial Coordinates the Planets and more History Reason for the Seasons Summer Solstice: Northern Hemisphere receives most direct sunlight (actually the distance from the sun is larger than in the winter) 23.5 Fall (Autumnal) Equinox: Sun shines equally in northern and southern hemisphere. Beginning of Fall in the North Winter Solstice: Northern Hemisphere receives least direct sunlight Physics 312, J. Buckley

2 For Fun Circular acceleration a = Figure out what the Game of Thrones Solar system must look like to have many years between seasons. Just how old is a 14 year old anyway? Physics 312, J. Buckley The Sun Never Sets in the Arctic Circular acceleration a = The sun never sets in the summer :) but the sun never rises in the winter :( (and the opposite in Antarctica) Physics 312, J. Buckley

3 When living above the arctic circle in the winter remember that there will be summer (eventually) (see problem 1.5 in the textbook - apparently Hemingway was not that good of a backyard astronomer.) Physics 312, J. Buckley Tropic of Cancer... Physics 312, J. Buckley

4 Tropics of Cancer and Capricorn Sun is directly overhead on the summer solstice along a line of geographic latitude known as the tropic of cancer. Further north, it will never be directly overhead. Path of Sun Throughout Year The Sun rises in the East, Sets in the West, but during the course of the year, it appears to get higher in the sky (during summer) and cross the Horizon at different Points. If the sun spends longer above the Horizon, then it is warmer! Ancient structures marked times of year, by aligning objects with the position that the Sun crossed the Horizon in different seasons.

5 Analemma Circular acceleration The analemma is a diagram that shows the deviation of the sun from its average during the course of a year. motion a = This is most dramatically shown by superimposing photos of the sun at the same mean solar time throughout a solar year (with no daylight savings time). Clearly the sun is at its highest on the summer solstice and lowest at the winter solstice - but the sun doesn t rise at its earliest or fall at its latest at these times. Why the weird asymmetric shape? Think about it for next time (clue Kepler) Local Horizon Coordinates Measuring Angles Circular acceleration Horizon coordinates use the observers alocal = horizon as the fundamental plane. East or CW from north) and Angles are measured as azimuth, AZ (the angle altitude, ALT (angle above the horizon along a great circle through the zenith). Easy to estimate by naked eye and hand - count fists up from the horizon (ALT) and dropping a line down from Polaris to define N, count fists east from N along the horizon. P

6 Horizon Coordinate System NCP Zenith Az=135deg E Alt=+45deg Horizon Circle W S Altitude (ALT) is the angle measured along a great circle through the zenith and the star from the local horizon up to the star, Azimith (AZ) is the angle east of north along the equator to the great circle of the star and zenith. Equatorial Coordinates DEC = 60 NCP DEC = 90 Hour Circle Ecliptic Celestial Equator DEC = 30 RA = 18h DEC = 0 RA = 20h RA = 22h RA = 0h RA DEC RA = 2h RA = 4h Spring (Vernal) Equinox RA = Right Ascension, measured in hours east of the Vernal Equinox where 24h = 360deg DEC = Declination, measured in degrees north of the celestial equator (negative for southern stars)

7 Transits of Stars NCP Zenith DEC=40deg 40deg Celestial Equator Horizon A star with Declination angle (DEC) equal to the geographic latitude will transit at the Zenith Sidereal Time Apparent spin of celestial sphere DEC = 90 DEC = 60 meridean DEC = 30 Zenith DEC = 0 RA = 20h RA = 22h RA = 0h RA = 2h HA of Vernal Equinox = Sidereal Time When the RA of a star = Sidereal Time, the star is at transit!

8 Sidereal Time Circular acceleration To distant star 1 1 noon a = one sidereal day later it takes 4 more minutes for solar noon Sidereal and Solar Time Simulator To distant star SkyGazer Software Circular acceleration a = Can purchase SkyGazer software for \$29 from the Carina Software online store:

9 Non-euclidean geometry B Arc length on unit sphere c r=1 a A a C b Sum of the angles in a triangle > 180 deg Law of sines: sin a sin A = sin b sin B = sin c sin C Physics Lecture 5 p.10/12 Angular Circular acceleration Distance Star A at (α, δ), Star B at (α + α, δ + δ) α N δ φ θ B Celestial Equator V α A δ sin( α) sin( θ) a = = sin φ sin [90 (δ + δ)] sin( α) cos(δ + δ) = sin( θ) sin φ α θ sin φ cos δ sin sin Physics Lecture 5 p.11/12

10 gular Distance Star A at (α, δ), Star B at (α + α, δ + δ) Angular Distance Continuing to use the small angle approximation, one can write an expression for the change in declination and combine the results: α Celestial Equator sin( α) sin( θ) V = α N δ φ A δ θ B δ = θ cos φ θ sin φ = α cos δ ( θ) 2 cos 2 φ + ( θ) 2 sin 2 φ = ( α cos δ) 2 + ( δ) 2 sin φ sin [90 (δ + δ)] sin( α) cos(δ + δ) = sin( θ) sin φ α θ sin φ cos δ Leading to the important result that the angular distance θ between two points differing in RA and DEC by ( α, δ) is: Physics Lecture 5 p.11/12 sin ular Distance ( θ) 2 ( α cos δ) 2 + ( δ) 2 Circular Angular acceleration Distance tar A at (α, δ), Star B at (α + α, δ + δ) Physics Lecture 5 p.12/12 α If = 0, get a simple result: /2 N /2 B Celestial Equator V {z } δ A α φ δ θ sin( ) sin( ) = sin( /2 ) sin( /2) sin( α) sin( θ) = a = sin φ sin [90 (δ + δ)] sin( α) cos(δ + δ) = sin( θ) sin φ α θ sin φ cos δ sin( ) =sin( ) cos Or for small angles, with a small di erence in both RA and DEC: ( ) 2 ( cos ) 2 +( ) 2

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